3
levels of Data in statistics
In addition to being classified as either quantitative or qualitative, data may also be classified based on how much real information they provide. There are four levels of data (or measurement): nominal, ordinal, interval, and ratio. As the level of the data collected increases from the lowest level (nominal) to the highest (ratio), so does the amount of information that is available from the data. We will now look at each level separately, starting with the lowest level.
Nominal-level data consist of names only. The data may be sorted into named groups or categories but no other comparisons are possible with this low level of data. No calculation or other mathematical manipulation may be done with nominal-level data. The “names” do not contain any inherent or implied order. Nominal-level data are qualitative in nature.
Ordinal-level data do contain more information than nominal-level data. Data of this level may be sorted into categories like nominal-level data but, in addi- tion, these categories may be placed into a meaningful order. Generally speaking, ordinal-level data are qualitative in nature.
examPle 1 ClassiFyinG QUalitative Data
If you were to ask someone what color his or her eyes were, you would get data such as blue, brown, green, and hazel. There is no way to place eye color in a meaning- ful order that has to do with eye color. (Alphabetical order has to do with the al- phabet, not eye color. In fact, translating these colors into another language could change their alphabetical order. For example, in Portuguese these colors are azul, maroon, verde, and avela. Placing these color names in alphabetical order would place avela, which is hazel, first in the list.) This means that eye color is nominal- level data. If you were to ask someone what their level of anxiety was in regard to taking a test on this chapter, you would get answers like high, medium, and low. These answers do have a meaningful order and thus are ordinal-level data.
Interval-level data can be placed in a meaningful order like ordinal-level data but also have the distinction of having equal intervals. Interval measurements allow us to make meaningful claims about measurable differences in amount between observations. Most measurement scales, such as for measuring temperature, are clearly interval-level data. Because interval measurements are numerical, this level of data is quantitative in nature. Also, “zeros” here are not “real zeros” in the sense of meaning “nothing” or “none of.”
Ratio level is the highest level of data. Ratio-level data allow us to introduce the idea of one measurement exceeding another, not by just a certain amount as in interval-level data, but by a certain ratio such as “twice as much.” Zeros here are “real,” and this level of data is quantitative in nature.
435
436 Appendix 3
levels of measurement
Level Properties
examPle 2 ClassiFyinG QUantitative Data
Consider measuring a temperature (we will use the Celsius scale) and measuring a height (we will use meters). First, look at the “zeros.” There is a zero in both measurements but only one is a “real” zero. A temperature of 08C is not a real zero in that it does not mean that there is no temperature at all or that there is no temperature below it. A measurement of 0 m is a real zero. It means no height and there is no measurement shorter than 0 m. A temperature of 408C is not twice as hot as a temperature of 208C but a height of 40 m is twice a height of 20 m. Thus, the Celsius temperature scale is interval level and heights in meters are ratio level.
The following table is a brief summary of the four levels of measurement that have been discussed.
Items Show Examples Type of Data
Nominal Classifications Differences in kinds Gender Qualitative Political party
Colors
Ordinal Classification order Differences in degree Letter grades Qualitative Graded attitudes
S, M, L
H, M, L Scale of 1–10
Interval Classification order Measurable differences Celsius and Fahrenheit Quantitative Equal intervals in amount temperature scales
GPAs
Ratio Classification order Equal intervals
True zero
Measurable differences in total amount
Income Quantitative Weights
Lengths
Times
Now decide the proper level of data for each of the following:
(a) years of education that you have had
(b) your favorite TV show
(c) your daily caloric intake
(d) your place of birth
(e) your blood type
A
Answer Key
71 1. 22.6, 2!5, 21, 0, , 3
practice set r-4
ChApter r
A review of AlgebrA fundAmentAls
1. 230,000,000 3. 3000 5. 0.605 7. 0.003 9. 7.5 11. 6.53102 13. 3.23109
15. 531022 17. 7.531027 19. 6.53100
practice set r-1
, 4
5. 2 7. 211 9. undefined 11. 2 13. 211
21. 1.47 3 108 km 25. 1.2495 3 1029 29. 4.6865 3 1021
23. 4.8 3 1024 27. 4.375 3 10210
3. (a),(b).(c).
15.4 17.23 19.12 21.214
24
31. 3.057 3 1021 Chapter r review problems
13 2
32 3
23.–5 25.23 27.210 29.0 31.13
1. 22,3 2. 9,21 3. 22 3 2 9
33. 5 5 1.25 35. 21 37. 0 39. 14.3125 44
4. 272 195249195240 5. 8.25
6. 26.865 (about) 7. 9 8. 21 9. 42,500
41. 1952.375 43. 76 45. 0 47. 4 49. 0 8
practice set r-2
1. x5210 3. x523.5 5. x510 7. x510 9. x54.5 11. x522.5 13. x511
15. x521 17. x55 19. x521.5
21. x51.25 23. x595 25. w521520.125 8
27. x52455211.25 29. x5213 4 3
31. x50 33. k5120.54 35. x524
37. x 5 21.9 39. no solution 41. a 5 22.5 43. x526 45. x524.5 47. x512
49. x522520.4 5
practice set r-3
1. 2 3. 180 5 9 5. 1 7. 0.05 9. 0.0005 25 100 5 3 2
11. 0.015 13. 1.25 15. 0.5% 17. 663% 19. 150% 21. 11.25 23. 0.48 25. 1340
27. 50 29. 68% 31. 11% 33. 75% 2
35. 7.8 ø 8 free throws 37. $58.50 39. 46.8 lb 41. $3.83 43. 3%, 21 people 44. 150 people 45. approximately 430,435 47. $8.06/hr
49. 12% discount 51. 62% increase 3
3 10. 510 11. 0.0000175 12. 0.61
13. 1.508 3 106 14. 8.5 3 100 15. 2.78 3 1021 16. 1.08 3 1024
17. x516 18. x523 19. x524 7 3
20. n52 21. x518 22. x56
23. x526 24. x50 25. 18.75
26. 12.5% 27. 1600 28. $320 29. 48%
30. (1.5%)($1800) 5 $27, $1800 1 $27 5 $1827 new monthly salary 31. 1.6 kg 32. 1.5742 meters
33. 7.8% 34. 8% 35. $11.25 36. $999.98
37. $7.50 40. $25.48
38. 125 lb
39. 6 ft 11 in.; 5 ft 61 in. 2 2
Chapter r test
1. The absolute value of a number is its distance from zero on the number line, and distances are always positive.
2. It is the “same” number with the opposite sign, or it is the number with the same absolute value, but on the opposite side of zero on the number line. 3. 216 4. 7 5. 231 6. 0.000208
7. 6.123109 8. y5226 9. x56 10. x51.8 11. y5225 12. x51
13. 12.75 16. $1.80 19. 113 V
14. approximately 22.3%
17. $6.87 18. 56.67% decrease
15. 650
20. max. 5 0.454 cm, min. 5 0.452 cm
A-1
A-2 Answer Key
ChApter 1
fundAmentAls of mAthemAtiCAl modeling
8. $12/hour 9. 5.5 bushels/tree 10. $3.66/lb 11. x512 12. x56 13. x59 14. x521
practice set 1-2
1. t 5 2.5 hours 7. h 5 9 inches
3. $500 9. 30 in.2
5. 28.26 in.2 11. 20oC
15. 6 in.27 16. 1440 liters 17. 69 dentists
18. $1.24 1 (x 2 4)($0.28) 5 $3.76; the call was 13 minutes long 19. 138 minutes 20. 2.5 hours 21. 15 in., 18 in. 22. 13 cm, 27 cm, 39 cm
23. $34.00 24. Let n be the number of nickels and so 2n 2 2 5 the number of dimes. There are 18 nickels and 34 dimes in the bank. $4.30
25. 3.5 hours 26. N 5 950 units produced
27. First remove the parentheses by use of
the distributive property, then add 2.
2 1 3(2x 1 4) 5 2 1 6x 1 12 5 6x 1 14.
28. 5x 1 3 5 6x; x 5 3 29. 30°, 60°, 90°
30. 312 in. 5 26 ft
Chapter 1 Test
1. w5V 2.v5h116t2 3.1:6 4.3:4 lh t
13. 14oF 15. m521 17. z521 19. c55 3 3
21. $7834.96 23. x 5 26 or 1
25. 2,204,421 bacteria 27. r 5 I 29. b 5 2A
3
1F 2 322
1.3:8 3.1:12 5.2:3 7.7:2 9.1:40
11. 32 mpg 13. $0.35/min 15. $4.80/day
17. 1.6 lb/person 19. x 5 3.75 21. x 5 7
23. x512 25. x56 27. x53 29. $1.49/ft2 31. $0.56/oz 33. Brand Z 35. 160 calories
37. 6 dozen 5 72 muffins 39. approx. 10.16 ft 5 10 ft 2 in. 41. 54 volts 43. approx. 35.3 lb
45. 12.5 lb 47. $300 49. 45 toddlers
pt h P 2 2W 2A 2 bh
31. L5233.B5h 35. y522x12 37. x52A2y
41. BMI 5 22.4; normal
39. C 5 practice set 1-3
5. $103.30 per day 7. 5 eggs per chicken
10. 18 11. 675 12. 64 ft
13. Let x 5 the number of miles driven: $20.00 1 $0.10/mile(x) 5 $10.00 1 $0.30/mile(x); x 5 50 mi
14. 750 passengers 15. Sarah is 9, and Michelle is 35 16. 5 ft, 16 ft 17. $2.52/gal
18. 35,898 people (rounding up to the nearest whole
person) 8 years ago; down about 987 people per
year
19. A grade of 99 is required, which is possible. 20. lot 5 $17,882, house 5 $134,118
ChApter 2
AppliCAtions of AlgebrAiC modeling
practice set 2-1
1. 1040 feet 3. 165 ft2; 18.3 yd2 5. 182.3 in2
7. approx. 158–160 plants 9. 35 bags
11. 35.6 in.2 13. no 15. 16 in. is the better buy. 17. 123.6 m2 19. (a) $0.75 per ft2 (b) $172.50 per front ft (c) $32,670 per acre
21. (a) four times the area, twice the perimeter
(b) one-fourth the area, one-half the perimeter
(c) nine times the area, three times the perimeter (d) four times the area, twice the perimeter
23. 78.5%
5 9
51. 22 ft long, 15.5 ft wide 55. 2.5 days 57. 1.5 mL
practice set 1-4
53. 2359.72 mph 59. 2.7 miles
1. 2x16 3. 7x22 5. 3(41x) 7. 1x25
6. 1.25 lb/person
8. x 5 35 9. x 5 260
18 7
9. Ann 5 x 1 5000, Bill 5 x 3
11. Width 5 x, Length 5 2x 1 5 13. x 5 25
15. Emily, $24; Elena, $48 17. 20 m, 40 m
19. 86 21. about 470 kWh 23. $44
25. 20 points 27. 28, 29, 30 29. 289, 291, 293 31. lot 5 $23,333; house 5 $151,667
33. $12.32 35. approx. 2.94 hr 5 2 hr 56 min
37. 16 male and 16 female 39. 36 bags
41. automotive div. 5 $378 million;
financial div. 5 $105 million
43. Ohio State 5 105,278; Penn State 5 104,234 45. $149.95 47. $76 49. $1000
51. BMI 5 23.4; normal
Chapter 1 Review problems
1.t5I 2.y522x13 3.d5C
Pr 3 p
4. c5P2a2b 5. 3:20 6. 4:3 7. 1:10
25. (a) h < 21.3w 1 10 ft
practice set 2-5
1. to make drawings in 2-dimensions that are true representations of what we see in 3-dimensions with our eyes
3. The term symmetry implies that balance or a regular pattern exists.
5. horizontal symmetry: B, C, D, E, H, I, O, X; vertical symmetry: A, H, I, M, O, T, U, V, W, X, Y; F, G, J, K, L, N, P, Q, R, S, and Z do not have reflec- tion symmetry
7. H, I, O, S, X, Z
(b)
(c)
y
(0, 10)
Answer Key A-3
Width
(7.7, 0)
x
9. 120° 13.
w
0
1
2
3
h
10
8.7
7.4
6.1
(d) theoretically, an infinite number 22
11. 72°
b121in.25336ft
800 cm
a 4 b 18.2cm2 56560cm565.6mwide
21. 23.
25.
Practice Set 2-6
1. Pitch refers to how our ears interpret different frequencies of sound. The higher the frequency of a sound wave, the higher the pitch we would hear.
3. A recording in which the actual wave form is copied as closely as physically possible.
5. Frequencies are measured numerically and recorded as numbers in short strings.
7. (261.626 Hz)(2) 5 523.252 Hz is one octave higher. (261.626 Hz)y2 5 130.813 Hz is one octave lower.
27. 50.3 ft 29. $148.28 31. 20.3 in.
33. increased by a factor of 2 (i.e., twice the original volume)
practice set 2-2 2 2
1. 90°, right triangle 3. 43°, obtuse triangle
5. 61°, right triangle 7. A 5 3.75 cm2
9. A 5 30 in.2 11. A 5 8750 mm2
13. A 5 111.8 in. 15. A 5 2664 cm
17. A 5 15.02 cm2 19. 45°, isosceles triangle
21. 116°, obtuse triangle 23. h 5 11 in.
25. A 5 88.18 ft2 27. A 5 21.3 ft2
29. The area of one face is approximately 181,935 ft2.
practice set 2-3
15. a
17. a b1175cm25131.25cm
16 ft
800 cm
19. a1 in. b 142.2 cm2 5 33,760 cm 5
5000
a b 182 540,000cm 5 400m
3
1 cm 337.6 m long
1. The triangle must be a right triangle, and you must know the length of 2 sides.
3. c 5 15 5. a 5 10.4 7. b 5 24 9. 24 ft
11. 9.4 m 13. 17.1 5 17-in. screen 15. 68.7 miles 17. 20.7in. 19. 17.1ft 21. P560cm,A5120cm2 23. 8.9 units 25. No 27. 7.1 in.
practice set 2-4
1. Two side lengths must be known.
3. It must first have one right angle and, in addi- tion, you must know the length of two sides or else one side length and one acute angle size.
5. 0.6428 7. 0.8391 9. 0 11. 0.7880
13. 0.1724 15. 0.6115 17. 8.6° 19. 45.0°
21. 45.0° 23. 15.4° 25. 18.0°
27. /A 5 21.7°, b 5 1047.9, c 5 1127.8
29. a 5 367.1, /A 5 26.7°, /B 5 63.6°
31. b52.3,/A543.4°,/B546.6°
33. c537.8,/A525.2°,/B564.8°
35. /A546.2°,a54.5,b54.4
37. 27.4 ft 39. 118.6 m 41. 16.1°
43. 33.7° 45. 36.4° each, 107.2°
1 cm
0.5 in.
a 1 b1600mi256in.
573 ft < 216.2 ft/in. 2.65 in.
50 mi
(23 ft)(1.618) 5 37.214 ft 5 37 ft 2.5 in. (45.5 cm)(1.618) 5 73.6 cm;
27.
29.
(45.4 cm)y(1.618) 5 28.1 cm
Unless otherwise noted, all content is © Cengage Learning.
Height
A-4 Answer Key
9. (392 Hz)(1.05946) 5 415.3 Hz
11. 2 13. 3 15. 1 quarter note
17. 1 eighth note 19. None are required. 21. similar to Figure 2.30(c)
23. similar to Figure 2.30(c)
Chapter 2 review problems
1. P 5 70 m; A 5 186 m2
2. $12.02 3. 93°; obtuse triangle
4. A 5 1017.9 cm; C 5 113.1 cm
5. A 5 90 in.2; P 5 63 in.
6. 276.5 ft2 7. 126 in.2 8. (a) 2.4 times the
original S.A. (b) 0.45 times the original S.A. (a little less than half the original S.A.)
9. 21.3 in.2 10. (a) 1492.4 ft2 (b) $3,693.50 11. 17 ft 12. 84.9 ft 13. yes, by the Pythagorean theorem 14. 21.6 in.
ChApter 3
grAphing
practice set 3-1
1.–12.
5
y
25. (group project)
4
8
5
7
10
3
9
6
2
1
11 12
x
15. 16. 17. 20.
21.
23.
24. 25. 26.
(a) 0.9205 (b) 0.9245 (c) 1.6191
(a) 12.0° (b) 55.4° (c) 71.9°
36.9° and 53.1° 18. 10.9 m 19. 123.6 m
(a) vertical; (b) horizontal; (c) vertical; (d) neither
50cm 5 2 22. (32)(4.125in.)5132in.511ft 75 cm 3
32.4 cm 5 20 cm 1.62
(35 mi)(1 in./20 mi) 5 1.75 in. 1 eighth note and 1 half note 27.5 Hz 27. 6
–5
–5 5
13. (0, 0) origin
15. (23,4) II
17. (23, 23) III
19. (0,23) y-axis
21.C 23.F,C 25.B,F 27.no 29.yes 31. (0, 8) (3, 5) (10, 22) (8, 0)
33. (0, 24) (3, 23) (6, 22) (12, 0)
35. (0, 0) (3, 20.75) (8, 22) (0, 0)
37. (0, 0) (3, 3) (22, 22) (0, 0)
39. (0, 23) (3, 24.5) (22, 22) (26, 0)
practice set 3-2
Chapter 2 Test
1. P 5 60 cm; 120 cm2 2. 15.5 in.2
3. S.A. 5 277 in.2 4. S.A. 5 41.2 ft2 5 5938 in.2
1. Let the y value 5 0 in the equation and solve for x. 3. Calculate the coordinates of another point on the line by assigning either x or y a nonzero value, and solving for the matching coordinate.
5. 56.5 ft
7. A 5 3 ft
9. 4.4 ft2
(b) $1,026.07 (or $1047.90 if cannot buy fractional part of a square yard)
11. 25.6 ft 12. 2.9 cm
13. (a) 65.97 in. 5 5.498 ft (b) approx. 961 times 14. (a) 65.3° (b) 84.0° (c) 67.1°
15. (a) 0.1994 (b) undefined (c) 0.1840
16. 6.3 ft 17. 79.0 ft 18. 17.0°
19.O 20.O,X
5. (6, 0) (0, 26)(4, 22)
7. (3, 0) (0, 6) (4, 22)
9. (3, 22) (0, 22) (any real #, 22)
11. (5, 0) (0, 2) (10, 22)
13. x-intercept (24, 0) y-intercept (0, 22) 15. x-intercept (25, 0) y-intercept (0, 22.5) 17. x-intercept (3, 0) y-intercept (0, 2)
19. x-intercept (5, 0) y-intercept (0, 23)
6. 90°; right triangle 8. 48 cm2
10. (a) P 5 80 ft; A 5 370.125 ft2
3
21. x-intercept a , 0b y-intercept (0, 23)
1 cm
21. 16250m2a b52.5cm
87 ft
23. No 24. the legal pad-size paper
25. 3520 Hz 26. 1 eighth note
27. The number of quarter notes per measure is different: 3 in 3y4 time and 4 in 4y4 time.
Unless otherwise noted, all content is © Cengage Learning.
4
23. x-intercept (0, 0) y-intercept (0, 0)
1 ft
22. 175 ft2a b 5 0.862 ft 5 10.3 in.
25. x-intercept (0, 0) y-intercept (0, 0)
27. x-intercept (24, 0) y-intercept (0, 22) 29. x-intercept (2, 0) y-intercept (0, 21) 31. x-intercept (20, 0) y-intercept (0, 24) 33. x-intercept (3, 0) y-intercept (0, 6)
35. x-intercept (23, 0) y-intercept none
2500 cm
2 37. x-intercept none y-intercept a0, b
39. x-intercept (4, 0) y-intercept a0,
3 4 3
b
practice set 3-3 19. 4y 2 x 5 10 1. slope525 3. slope5 2 5. slope5 5 m51,
Answer Key A-5
2 11 2 4
7. slope58 9. x55 11. y522 13. y524x11
y-intercept5(0,2.5) y
m 5 24, y-intercept 5 (0, 1)
y
(0, 2.5)
x
x
m=–4 15. 3x12y56
m 5 23, 2
m = 14 21. 3x21y55
y-intercept 5 (0, 3) y
m53 2
y-intercept 5 (0, 21.25) y
428
(0
,–1.25)
x
x
m = – 32 17. 2x23y54
m 5 2, 3
m = 32 23. y52x
m 5 21 y-intercept 5 (0, 0)
y-intercept 5 (0, 21.33) y
y
(0, 0)
,–
4
0
3
m = 23
(0,
1)
(0, 3)
x
x
m = –1
Unless otherwise noted, all content is © Cengage Learning.
A-6 Answer Key 25. 4y5121x
m51 4
y-intercept 5 (0, 3) y
x
27. m58 29. m56 31. m51 33. m50 35. undefined 37. perpendicular 39. neither practice set 3-4
1. 3. 5. 7.
9.
11. 13.
17.
19. 21. 25. 27. 29.
31. 33. 37.
13. (a) 780 760 740 720 700 680 660 640
(0
,3)
m = 14 31
No, it will not exceed 800 by 2015.
(b) rate of change 5 12 students per year
(c) y 5 12x 1 650 where x 5 number of years
after 2009
(d) y 5 12(8) 1 650 5 746 students
15. (a) Income $37,0 0 0.0 0
$35,000.00 $33,000.00 $31,000.00 $29,000.00
Year
Yes, it will be more than $35,000 before 2019.
(b) The rate of change is not constant between consecutive years.
(c) Since there is no steady rate of change, you cannot write a linear prediction equation. (d) Using the graph to predict, the salary will
be approximately $36,800. (Table represents a 2.5% increase in salary each year, so cal- culated amount is $36,841.45.)
Year
y 5 22x 1 8, 2x 1 y 5 8 y51x25,x22y510
2
y 5 22x 2 25, 2x 1 y 5 225
y 5 5x 1 13, 5x 2 2y 5 213 22
y521x15,x13y55 33
y 5 2x 2 5, 2x 2 y 5 5
y522,y522 15. y52x13,x1y53
y 5 1 x 2 13, 3x 2 6y 5 13 26
y 5 22.5x 2 7, 5x 1 2y 5 214 x53,x53 23. x51,x51 y 5 22x 2 5, 2x 1 y 5 25
y 5 23x 1 19, 3x 1 y 5 19
y52x17,x1y57
y 5 25 x 2 21, 5x 1 2y 5 221
17.
125,000 120,000 115,000 110,000 105,000 100,000
95,000
22
x53,x53 35. y53,y53
Total Refuse
Year
y51x21,x23y53 39. y52x,x1y50 3
practice set 3-5
1. y521x 3. y522x12 5. y51x23 22
7. y51x12 9. y5x 11. y53 3
Unless otherwise noted, all content is © Cengage Learning.
Tons of Refuse
Income Enrollment
2008 2009
2010 2011
2012 2013
2014 2015
2016 2017
2009 2011
20 13 2015
20 17 2019
2021 2023
2008 2010
2012 2014
2016 2018
2020
A reduction of 7253 tons per year is the rate of 13. y change. A constant rate for the next 7 years would
be improbable since there is only so much refuse that
can be recycled, thus reducing the total amount.
Answer Key A-7
Chapter 3 review
1.–4. y
x
II
2
3
4
1
I
x
7. (6, 240) 10. a0, 2
x
m = –2 14. y
(0, 5)
(2.5, 0)
III
IV
5. yes 6. (22, 212) 9. (any real number, 7)
11. y
b
11
3
8. (0, 4)
x
(–2,0)
(0, 3)
(3, 0)
m = 32 15. y
(0,
1)
(–3, 0)
(0, –1)
m=1 x 3
12. y
(–
4, 0)
m = 13 x 16.y
(0, 3)
no y-intercept m = undefined
x
no x-intercept m=0
Unless otherwise noted, all content is © Cengage Learning.
A-8 Answer Key
17. m53 18. m522 19. m5undefined
20. m57 21. y52x23 22. y510x126 2
23. y522x110 24. y521x14 2
25. y53x14 26. y51x21 42
27. y521x14 2
28. rate of change 5 19,000 y 5 19,000x 1 139,000
29. (a) rate of change 5 20 miles per gallon
(b) y 5 20x (c) 360 miles
6. y
(–2,
0)
(0,–4)
x
m = –2 7. y
(5,
0)
30. (a)rateof change5$4billion (c) $72 billion
Chapter 3 test
1.–3. y
II I
(b)y54x18
x
1
2
3
x
IV
no y-intercept m = undefined
8. y
(0,
3)
(3,
0)
III
4. no
5. y
x
(1, 0)
(0, –
4)
m = –1 9. y
x
(0, –2)
m =4
x
Unless otherwise noted, all content is © Cengage Learning.
no x-intercept m=0
10. m 5 1 11. m 5 1 12. slope is undefined 21. 53
23.
17. y521x14orx12y58 18. x52 2
19.y523x 20.y53x 44
21. (a) 0.072 (b) 7.113 billion people (2015); 8.193 billion people (2030) (c) 2028
22. (a) 1698 (b) $45,828 in 2006; $37,338 in
Answer Key A-9
$0.20
$0.10
0$1 $5 $10 Purchase
1985 1995 2005 Year
13. m51 14. y523x13or3x1y53 15. y51x14orx22y528
2
16. y56x24or6x2y54
2011 (c) 2014
23. y 5 .614286x 2 1220.6714 approx. $17.7 billion 24. (a) y 5 24357.14x 1 35,000 (b) 24357.14
The office equipment depreciates in value by
$4357.14 per year. (d) approx. 8 years
ChApter 4
funCtions
practice set 4-1
(c) $13,214.30
1. A function is a relation or rule in which for each input value there is exactly one output value. The independent variable is the input and is the variable that we control. The dependent variable is the out- put, and its value is a result of the original choice of the value of the independent variable.
3. (a) 68° (b) The high temperature is a function of the date. (c) temperature (d) dates
5. (a) The independent variable is the year, and the dependent variable is the world population.
(b) Domain includes the years 1980–2010, and the range is 4.2 billion–6.4 billion.
7. Grades are a function of student ID.
9. As the weight of a bag increases, the price of the bag increases, so price is dependent on weight.
11. As the slope of a hill increases, the speed of
the scooter going uphill decreases, so the speed is dependent on the steepness of the hill.
13. As a person’s age increases, his target heart rate when exercising decreases, so the target heart rate when exercising is dependent on a person’s age.
15. 9:45 p.m. 17. January 2 and December 30 19. 10:15 p.m. is the latest; 2:50 p.m. is the earliest
27. d 5 315 ft; graph is not linear. The faster the speed, the longer the stopping distance.
29.
25.
Age (time)
1. g102525 3. g1102525 5. f1x252x11;f1222523
rate 5.5
payment 709.74 729.47 749.44 769.65 790.09 810.75 831.63
5.75 6.0
6.25 6.5 6.75 7
2
7. f1x253x 21;f1222511
9. f1x25 x24;f1222529 2
practice set 4-2
11. f 122 5 576; 2 sec after the ball is thrown, it is 576 ft above the ground. 13. 173.41 cm
15. 50.63 cm 17. (a) 230 5 1,073,741,824
(b) $10,737,418.24 19. (a)$960 (b)M1n2 5 $7.50n (c) domain 5 0–200 people; range 5 $0–$1500
5
Unless otherwise noted, all content is © Cengage Learning.
Height Percent of homes Sales tax with computers
21. f 1202 5 170 and f 1602 5 136; as a person gets older, his target heart rate decreases.
23. f 1 3 2 5 $29,080; a person with 3 years of teach- ing experience will make an annual salary of $29,080; the independent variable is the number of years of experience and the dependent variable is the salary. 25. f 1 4 2 5 0721, which means that the sun rises at 7:21 a.m. on Jan 4th; g1102 5 1654, which means that the sun sets on Jan 10th at 1654 hours or
A-10 Answer Key
$4500 $4000 $3500
2008 2009 2010 Year
29. f 1 100 2 5 30 which means that it costs $30 to rent this car and drive 100 miles; the domain is numbers $ 0, and the range is numbers $ $25.
(c)
(d) $7010
19. (a) f1x2 510015xwherex5inches. 60in. (b) f 1672 5 135 lb
practice set 4-4
4:54 p.m.; the independent variable is the date; the dependent variables are the sunrise and sunset times. 27. (a) 75 mi (b) approx. 130 mi from the graph (127.5 using the formula)
k"n 13. m5 p3
1. direct 3. inverse 5. direct 7. y 5 kz
practice set 4-3
1. (a)
9. a5kbc 11. d5kef3
k 5 1 3
k 5 54 k 5 6
k52
x f (x)
19. y 5 k"x 2
15. y5kx 17. y 5 k
y 5 12 y 5 1.5
y 5 36 y51536
1
$1.75
3
$5.25
5
$8.75
7
$12.25
9
$15.75
(b) Initial value is 0; rate of change is $1.75 per mile. (c) f 1x2 5 $1.75x where x 5 miles
(d) f 182 5 14, which means that an 8-mile taxi ride will cost $14.00 3. (a) 5.5 million
x
21. y5kxz 23. p 5 kq
k 5 32 27. 4.5 in.
p 5 12 29. 294 ft
(b) 2% per year (c) 5.6 million
5. (a) C1x2 5 $525 1 $17.50x where x 5 number of guests (b) $4025 (c) 150 people
7. (a) 2$340/year
(b) V1x2 5 1800 2 340x where x 5 years
(c) V142 5 440; after 4 years, the value is $440
4
43. (a) direct variation (b) a bp (c) 972p in.
13. (a) rate of change 5 120/year
(b) f1x2 5450120xwherex5years
(c) f 1 15 2 5 750; that in the year 2011, the predicted population is 750 people. 15. (a) $80,000/year
(b) f 1 x 2 5 $600,000 1 $80,000x where
x 5 number of years after 2003
(c) in 11.25 years or during the year 2015
17. (a) $579/year (b) f 1 x 2 5 $3536 1 $579x where x 5 number of years after 2008
roots 5 21 and 25
1
2 25. 153.86 cm
r
2
31. 2.5 sec 33. 4 in. 37. 2.8 hr 39. 480 W
35. 90 lb/in. 41. 0.72 in.
y
2
9. f1x252 x 11. f1x255 5
practice set 4-5
1. minimum 5 24
3
45. 10.0 A 47. 450 kg m/s 49. 250 lb
3
Unless otherwise noted, all content is © Cengage Learning.
x
Tuition
3. minimum 5 22.3 y
roots 5 21 and 24
x
roots 5 1.7 and 21
Answer Key A-11 11. 9 sec, 5 sec 13. 6 sec, 8 sec 15. 3 sec
5. maximum 5 5.3 y
2 7. f1x253x
y
x
1. f1x255 f122525
35. 120 machines (b) Neither is linear.
17. 0.2 sec, 4.6 ft
19. (a) 426 ft, 21. $2070
p(w)
(b) 431.64 ft,
w
(c) 6.6 sec
23. 5.00, 23.00
27. 3.00, 21.50
31. 33 sec 33. 72 units 37. (a) Neither is linear.
25. 2.18, 0.15 29. 2 sec, 5 sec
x
y
x
3. f1x253 22
y
practice set 4-6
x
9. f1x251x3 3
y
f12257 x
x
x
Unless otherwise noted, all content is © Cengage Learning.
1x1 5. f1x25a b f1225
x
7. f1x25e f12257.39
A-12 Answer Key
y
24
Chapter 4 review
1. You will pay $0.72 tax on a $12 purchase.
2. Answers will vary.
3. Both the domain and the range values must be greater than or equal to 0.
4. As the age of a person increases, his height increases up to a certain age. Then it remains steady with some shrinkage in later years.
5. As time passes, the number of bacteria in a culture increases.
6. The faster the speed of a car, the less time it takes to drive from home to school.
7. independent variable: number of minutes; depend- ent variable: cost
8. domain: $0 minutes; range: $ $5.00
9. f1202 540ft; f1402 5120ft; f1602 5240ft;
x
f 1 80 2 5 400 ft; the graph is nonlinear.
y
5.0
4.0
3.0
2.0
1.0
–3.0
–2.0
–1.0
1.0
2.0
–1.0
x
240 120
20.5x 9. f1x25e
f12250.37
(a)210 (b)26 (c) 2 (d)25 f1x2523x12 12. f1x252 x22
10. 11.
3 f1x25x28 14. f1x252 x13
20 40 60 80 Miles per hour
f 1x2 5 24x 1 1
(a) 23 (b) 3 (c) 0
2
11. f 1102 5 15,767 people
13. 28,733 people 15. 11,819 deer
17. 11,668,044 in 10 years; 8,643,900 in 50 years 19. 140,839,731 people 21. 46.7 g, 1.28 g
23. 218 g 25. $31,308.07 27. $2.38; 11.58 years Unless otherwise noted, all content is © Cengage Learning.
15.
17.
18. C11202 5 $36.20, the cost of renting a car and driving 120 miles
19. (a) C1x2 5 75 1 30x (b) $435
20. (a) f 1x2 5 1000 1 5.50x where
x 5 number of books printed
(b) Domain is natural numbers $ 250.
(c) f13752 5 $3062.50
21. (a) f 1x2 5 1400 1 0.151x 2 14,0002, where x is taxable income (b) f 1 32355 2 5 $4153.25
22. (a) f 1s2 5 $1000 1 0.25s (b) $1625
23. f1x2 52x23 24. f1x2 50.5x14
25. independent variable: time; dependent variable: length of fingernails; direct variation
26. independent variable: temperature; dependent variable: time; inverse variation
y
5.0
4.0
3.0
2.0
1.0
–3.0
–2.0
–1.0
1.0
2.0
3.0
–1.0
x
13.
3
2
16. 7, 1, 21, 1, 7
Feet
27.s5kt 28.z5pk"3z 29. m5krs 30. x5 y2
k 5 8 k518 k51.33 k52.25 k516.1 k57200
(b) g 23 5 54
k12
Answer Key A-13
31. u 5 kv3 32. x5 k
u 5 64 x50.72 s556 N54.5 d5144.9ft
y2 33. s5ktg
kL2 34. N5 M3
39. 10.4, 20.385 42. (a) f1222 5
(b) g1222 5 4
35. d5kt2 36. f5 k
40. 2 sec
41. 8
f518units 37. (a) minimum 5 28; roots 5 21, 3
d2
1
9
y
y
y
y
x
(b) maximum 5 9; roots 5 24, 2
38. (a) f 1 23 2 5 40.5
43. 122.9 million 45. 45,359 bacteria
Chapter 4 test
44. 51,242 bacteria 46. 769,112 people
x
y
x
y
x
x
x
1. $25,000 initial value; 2$1500 in value per year
2. The cost of a house is a function of its square footage. The larger the amount of square footage, the more a house usually costs. independent variable: the square footage; dependent variable: cost
3. (a) independentvariableistime;dependentvariable is the number of widgets produced
(b) initial value is 0; the function is not perfectly linear.
Unless otherwise noted, all content is © Cengage Learning.
A-14 Answer Key
4. f1x252x24 f12425212
5. f1x255 f124255 2
6. f1x2523x 22 f12425250
7. V1t2 5 $22,500 2 $2200t
8. C1122 5 $10.50; a cab ride of 12 mi. is $10.50
9. (a) f 1x2 5 $21 1 $28x where x is number of credit hours taken
(b) domain: set of whole numbers 12–15; range: 5$357, $385, $413, $4416
(c) f 1 14 2 5 $413; cost of 14 credit hours
10. f1x2523x12
11. independent variable: speed; dependent variable: time to complete the race; inverse variation
12. independent variable: time; dependent variable: diameter of tree; direct variation
ChApter 5 Key
mAthemAtiCAl models in Consumer mAth
practice set 5-1
1. (a) $1.92 (b) $11.68 (c) $19.21 3. state 5 $1600.94; county 5 $512.30 in merchandise; $2009.60 in taxes
7. $199.95 9. $330 per year
5. $25,120
13. t5kB P2
k55 t535 15. 158.4 grams
14. $1139.69
16. maximum 5 9; roots 5 3, 23
1. I5$45;M5$545 3. I5$216;M5 $1416 5. 12% 7. $11.25 9. $212
11. $162.50 13. (a) $420 (b) $2020 (c) 14% 15. interest 5 $85; rate 5 10.2% 17. $2148.85 19. $33,671.38 21. (a) M 5 $955.51;
I 5 $55.51 (b) M 5 $955.61; I 5 $55.61
23. no; the account will contain $6104.98.
25. $2.17 more if compounded monthly
27. $29,045.86 29. $170,996.39
practice set 5-3
1. $5.26 3. $10.82
5. June: $5.25 finance charge; $342.10 unpaid balance July: $342.10 beginning of month; $5.13 finance charge; $297.63 unpaid balance
August: $297.63 beginning of month; $4.46 finance charge; $416.24 unpaid balance
7. October: $0.90 finance charge, $371.51 unpaid balance
November: $371.51 beginning of month; $5.57 finance charge, $581.74 unpaid balance
December: $581.74 beginning of month; $8.73 finance charge; $926.89 unpaid balance
9. June:$19.43financecharge;$1259.43unpaid balance; July: $1259.43 beginning of month; $18.89 finance charge; $2,407.17 unpaid balance; August: $2407.17 beginning of month; $36.11 finance charge; $2349.35 unpaid balance
11. averagedailybalance:$177.28;financecharge:$2.66
11. $1207.14 13. 12% 15. loss of $53,500 17. profit of $6500
19. loss of $8000
21. profit of $602,000
23. profit of $340
25. (a) C1x2 5 0.01x 1 3500 of $1245
(b) $375 (c) profit of $1875 27. $54.25 29. 80% markup
practice set 5-2
(b) $3705
(c) loss
17. f1425216
4 2
y
24
y
Unless otherwise noted, all content is © Cengage Learning.
68
x
x
19. 428.7 million people 21. Answers vary.
18. $11,484.09
20. 4.22, 20.55
22. 156 ft 23. 6.3 sec 24. 136,772 persons
13. average daily balance: $356.74; finance charge: $5.35
15. average daily balance: $694.49, finance charge: $10.42
practice set 5-6
1. Insurance is an economical way of helping an individual deal with a severe financial loss by pooling the risk over a large number of people.
3. The amount of insurance specified by the policy is called the face value of the policy.
5. The payment that the insurance company makes to reimburse the policyholder is called an indemnity.
7. 20/40/15
9. Collision insurance pays for repairs to the vehicle of the insured when the policyholder is responsible for an accident.
11. $300.00 13. $204.60 15. $631.80
17. $211.40 19. $175.00 21. $264.60
23. $581.40 25. (a) $8,000 (b) $0
practice set 5-7
1. (a) $114,915.00 (b) $2298.30 3. (a) $1195.00 (b) $22.93
5. (a) $41,580 (b) $873.18
7. (a) $900.60 (b) $27.52
9. (a) $100 (b) 29,120,000 shares
(d) $11.29 (e) 21.6% 5 down 1.6%
11. (a) $24.00 (b) 7,575,000 shares
(d) $25.64 (e) up 1.3% 13. 250 shares
15. 350 shares 17. Bonds are issued by companies or governments who are trying to raise money for projects. Bonds are generally safer investments than stocks. If a company goes bankrupt, the bondhold- ers are paid before the stockholders receive any money. (answers may vary)
19. Invest more of your money in stocks and mutual funds since, over long periods of time, these invest- ments usually grow at a better rate than bonds or savings accounts.
practice set 5-8
1. $1488.65 3. $3,520 5. $2297 7. $3125 9. $9.75 11. $5400 13. 8.5%
15. (a) $3199.65 (b) $3284.65
17. He will owe $49 less using the 4.5% rate. 19. $27,000 gross salary; $1045 tax
21. (a) Pay 5 800 1 0.095(sales) (b) 0.095
(c) makes $9.50 for every $100 of sales
(d) yes (e) commission because it is dependent on sales (f) $18,157.89
23. total expenses 5 $1450; $1855 2 $1450 5 $405; 7%(1855) 5 $129.85 so he can save 7%
25. $296.70 27. (a) $1400.40 (b) fed/state tax $637.50; utilities $180.63; food $573.75; savings $233.75; entertainment $170; gas/car maint. $212.50; health ins. $85; misc. $396.47
29. Answers will vary.
17. 12.5% APR
21. 9.0% APR
APR
25. total interest $207.55
practice set 5-4
19. 11.0% APR
23. finance charge: $113.68; 8.5%
1. Answers will vary.
3. Lower monthly payments, repairs are under warranty (Answers will vary.)
5. Customize the car, sell the car at any time (Answers will vary.)
7. $48,394.50 9. $31,227.60
11. $60,887.28 13. interest 5 $5493.18; monthly payment 5 $722.96
15. interest 5 $2362.05; monthly payment 5 $503.03 17. interest 5 $5721.32; monthly payment 5 $776.51 19. Total paid: $11,430.00; finance charge: $2430
21. Total paid: $19,608.56; finance charge: $3158.56 23. 9% 25. 6% 27. finance charge 5
$579.20; APR 5 9.0%
29. $240.30 31. $21,803.79 33. amount to fi- nance 5 $22,500, payments 5 $523.13, total
cost 5 $27,610
35. $936
practice set 5-5
1. Interest rate, type of loan, fees, points (Answers may vary.)
3. Subtract your monthly bills from your gross income and multiply by 36%.
5. Use the maximum amount of loan formula and the amortization table.
7. down payment 5 $15,325.00;
amount financed 5 $137,925.00
9. down payment 5 $44,975.00;
amount financed 5 $134,925.00
11. down payment 5 $94,650.00;
amount financed 5 $220,850.00
13. $306.05 15. $594.00 17. $1,098.00 19. $926.16 21. $559.89 23. $804.42 25. $425.85 27. $856.80 29. $1423.05 31. $167,037.86
33. $369,261.48
35. $125,246.55
37. monthly payment 5 $1,094.20 39. (a) down payment 5 $17,775.00;
(c) $11.11 (c) $25.97
monthly payment 5 $495.51 41. Answers will vary.
(b) $196,158.60
27. $236.68
29. $121.31
Answer Key A-15
A-16 Answer Key
Chapter 5 review problems
41
41. a , 2 b 43. no solution 45. (3, 4)
1. state tax: $564.66; county tax: $313.70 2. $3950 3. $2.23 4. 20%
5. $2350 6. $10,000 7. $1,425
8. Both plans would yield the same amount.
10. $16,650.00 maturity value; $693.75 payment
11. $180 12. $8976.47 13. $477.36
14. $22,255.41 15. $39.38
16. $1355.09 avg daily bal.; $20.33 interest
17. $57.98 18. $28,347.90
19. $1254.83 interest; $485.67 payment
20. $7084.80 total paid; $584.80 interest; 3% interest rate
21. $20,232.91 22. $322.20 23. $491.67
24. $1615.57 25. $714.24 26. $843.48
27. $235.20 28. $331.80 29. $20,000
30. $79,863.49 31. (a) $12,276 (b) $306.90 32. 2500 shares 33. 6.5% 34. $712
35. tax 5 $1275 1 0.07(x 2 $21,250)
36. $1362.50 37. $357.90
Chapter 5 test
31. (22, 26) 37. (26, 28)
33. (3.5, 21) 35. (4, 21)
39. no solution—parallel lines
1. $857.50
4. $16,435
7. $4,891.61
9. $10,432.26 10. $35.00
11. average daily balance $189.50; interest $2.84 12. $56.38
13. monthly payment: $847.38; interest owed: $3125.79
14. $32,200 15. $550.82 16. $1597.50
17. $306 18. $0 19. $16,152.48
20. (a) $257.50 (b) $11.36 (c) $268.86
ChApter 6
2. $27.90 5. $353 8. 5%
3. $1550 6. $9,945
1
1. (3,22) 3. (23,21) 5. a ,1b 7. (1,2)
15. infinite solutions—same line
17. no solution—parallel lines 19. (22, 24)
modeling with systems of equAtions
practice set 6-1
9. 6.5%
55
47. (2, 3) 49. (4, 3) 51. (13, 5)
53. infinite solutions—same line 55. (25, 9) 57. no 59. 11 and 9 61. 12 and 18
63. 16 and 48 65. 21 and 28
practice set 6-3
1. 12 units @ $650 and 8 units @ $825
3. 53 double, 27 single 5. $8000 @ 4.5%; $4000 @ 5% 7. tights 5 $12.50, leotards 5 $45.00
9. pizza 5 $15; soda 5 $4
11. Coca-Cola $41.40 and Pepsi $43.50
13. 14 mL of 10%: 16 mL of 25%
15. 12 g of 60% and 8 g of 40%
17. 20 mL of 10%, 30 mL of 60%
19. 18 pounds of peanuts; 8 pounds of cashews
21. 5 lb of each 23. $66.67; where price equals demand 25. $15 27. equilibrium price is $5
29. 1500 backpacks 31. 160 miles; John’s Rent A Car 33. $18,750; straight 12% commission
35. length 5 5 ft, width 5 2 ft
37. 12 inches by 18 inches 39. 4 yards by 10 yards
1 2
9. e11,02,a ,2 bf
13. The numbers are 3 and 4.
15. 3 and 27 or 7 and 23 17. 12 and 5 19. 15,000 pairs of sunglasses at $37.50 21. 13 ft by 11 ft
Chapter 6 review problems
practice set 6-4
1. {(2, 4), (25, 25)} 5. {(6, 12), (1, 2)}
3. {(21, 21), (0.5, 0.5)} 7. {(3, 5), (21, 23)}
33
11. {(3, 2) (3, 22) (23, 2) (23, 22)}
2 9. (2,0) 11. (4, 1) 13. (0, 1)
1. yes 2. yes 3. no 4. yes 5. (7, 1)
21. (23, 21)
25. no solution
31. infinite solutions—same line
23. infinite solutions—same line 27. (2, 0) 29. (2, 21)
32 18. (24, 1)
11 15. a , 2
b 16. no solution 17. (6, 4)
6. no solution 7. (3, 2)
10. (2, 21) 11. (3, 21.6)
14. infinite number of solutions
8. (1, 3) 9. (0, 2)
12. (1, 23) 13. (3, 12)
practice set 6-2
1. (12, 6) 3. (2.5, 20.5)
9. (5, 1) 11. (5.5, 2.5)
13. infinite solutions—same line 15. 1 17. 0 19. 22 21. (5, 1) 23. (7, 3) 25. (0, 24)
27. (22, 6) 29. infinite number of solutions
19. (5, 6) 20. (21, 3)
21. no solution 22. (1, 26) 23. (1, 5) 24. (0, 8)
25. {(23, 29), (1, 21)} 26. {(2.5, 13.5), (21, 3)}
27. 34 boxes of donuts; 28 stadium cushions
28. 80 mL of 40% acid; 40 mL of 70% acid
29. 200 clocks 30. $79 31. 5 nickels, 55 dimes
32. potatoes $0.34/lb; bananas $0.69/lb
5. (5, 11)
7. (2, 21)
33. 1200 packages 34. length is 24 ft, and width is 18 ft 35. Answers will vary.
Chapter 6 Test
1. yes 2. 7 3. (4, 1) 4. (2, 21) 5. no solution
Answer Key A-17 31. {1, 2, 3, 4, 5, 7} 33. {1, 2, 3, 5, 7, 9}
35. {3, 5} 37. [ or { } 39. {5}
practice set 7-2
1. An experiment is something that you do in order to gain information (data); outcomes are all the possible results of a given experiment; and events are the individual possible outcomes that occur when the experiment is done.
3. The law of large numbers states that the more times an experiment is performed, the more accurately we can predict the probability.
5. independent events
7. dependent events
155
6. no solution 7. (2, 21) 8. (3, 1)
18. length 5 27 in. 19. $6.00 ChApter 7
probAbility models
practice set 7-1
20. 4250 leotards
9. (0.5, 1.5) 12. {(20.5, 0.5), (2, 8)}
10. (2, 21) 11. (3, 1)
13. (0, 2), (23.5, 3.75)
15. 60 double rooms
16. 50 mL of 12% solution and 150 mL of 8% solution 17. $4000 at 10.5%: $8000 at 12%
14. 500 calculators
1. True 3. False 5. False 7. False 9. False 11. True 13. A 5 {x|x is a natural number less than 6} 15. {2, 4, 6, 8, 10, 12, 14, . . . , 40, 42, 44, 46, 48}
9. 60,000 5 0.3%
11. cardinal: 1 5 16.7%, robin: 2 5 66.7%
17. finite 19. infinite
21. {1, 2, 3, 4, 5, 6, 8}
13. 70 5 7.1% 15. 672 5 6.1% 8
63 5 41
23. [ or { }
25. {1, 4}
17. 72 5 11.1% 19. 12.5% 21. 5%; 1250 people 23. 37 5 67.3% 25. 9 5 16.4% 27. 27%
U
M2N 3147
5
55 55 29. 1 donor
27. {1, 2, 3, 4, 5, 6, 8}
31. (a) 95 519565.5% (b)50510576.9% 145 29 65 13
(c) 355 7 543.8% (d) 155 3 523.1% 80 16 65 13
33. (a) 120512552.2% (b)50510552.6% 230 23 95 19
(c) 60 54544.4% (d) 75515578.9% 135 9 95 19
practice set 7-3
4 11
U
29. {2, 3, 5}
5. P1s2 5
9. 10 5 1 11. 1 13. 4 5 1
MP
126 3 458
1. Outcomes that have the same chance of occurring in an experiment.
3. No. A theoretical probability of 1 means that the event is certain to occur.
7. P1a2 5 0
20 2 20 52 13
U
MP
126 3 458
15.1351 17.0 19.1253 21. 1 23. 1 52 4 52 13 13 26
25. 351 27. 7 29.1 31.1 33.1 12 4 12 6 2 3
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A-18
Answer Key
35. 1 3
47.1 6
37.2 39.13% 41.0 43. 1 45.4 3 10 5
49.1 51.3557 53.55511 4 90 18 90 18
27. 3 29. 1,757,600 31. 1
4 1,757,600
33. 6
1. 8 5 2 Yes; it is impossible to pick one card
practice set 7-6
55. 24 5 6 57. 84 5 21 59. Answers will vary. 100 25 100 25
practice set 7-4
1.1:1 3.2:3 5.1:12 7.1 9. 3 11. 1
52 13
and get a king and a queen at the same time.
21. 1:2 23. (a) 4
29. 5:3 31. 999,999:1 33. 1 35. 2 37. 9
(b) 1:3 25. 1:12
3. 26 5 1 No; it is possible to pick one card and 52 2
2
17. (a) 1 6
39. 7 41. 1 43. 2 12 7 7
practice set 7-5
14 (b) 1:5
13 19. 1:1
get a black spade because all spades are black!
13. 17:3 15. 3:17 1
5. 32 5 8 No; it is possible to pick one card 52 13
27. 10:3 6 11 14
and get a black face card (jack of spades and clubs, queen of spades and clubs, king of spades and clubs).
3
1.4000 3.125 5.20 7.8 9.8 11.12
13. 1 15. (a) 36 (b) 1 (c) 0 (d) 1 12 6 36
17. S 5 {HH1, HH2, HH3, HH4, HH5, HH6, HT1, HT2, HT3, HT4, HT5, HT6, TH1, TH2, TH3, TH4, TH5, TH6, TT1, TT2, TT3, TT4, TT5, TT6}
7.7 9.5 11.1 8 6
13. 1 15. 110522 3 205 41
17. 85 517 19. 135527 205 41 205 41
21. 143 5 62.7% 228
19. 1 12
21.
A Q J
23.
25.
27.
29.
183 5 48.2% 380
37 5 48.7% 76
33 5 66% 50
37 5 61.7% 60
Ace
A Queen Q
practice set 7-7
1. independent 3. dependent
5. independent 7. 1 9. 5 11. 1
J
A QJ
169 18 12
Jack
13.5510.9%15.85533.6% 46 253
17. 108 53.5% 19. 32 51.0%
S 5 {AA, AQ, AJ, QA, QQ, QJ, JA, JQ, JJ} 23. 1
3125
3125
9
25.
21. (a) 21 5 21.2% 99
(b) 14 5 8.5% 165
boy
boy
girl
23.125.127.4429. 1
8 8 585 133,225
practice set 7-8
1. 21 3. 42 5. 362,880
7. Only positive whole numbers have a factorial value; thus, no value here.
boy girl
girl
S 5 {bb, bg, gb, gg}
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9. In a combination, order is unimportant, so that 1, 2 and 2, 1 are the same combination of the numbers 1 and 2. In a permutation, order is important, so that 1, 2 and 2, 1 are different permutations (orderings) of the numbers 1 and 2.
11. If Jane must be on the committee, then the other three members will be chosen from the nine remain- ing students, and order doesn’t matter here. 9C3 5 84 13. 9! 5 362,880 or 9P9 5 362,880
15. A person may choose no toppings, or 1 or 2
or . . .
no toppings 1 1 topping 1 2 toppings 1 3 toppings 1 4 toppings 1 5 toppings
115C1 15C2 15C3 15C4 15C5
1 1 5 1 10 1 10 1 5 1 1 5 32
17. 24 19. (a) 362,880 (b) 3,024
11. In problems where several outcomes are possible, use the addition rule if the word “or” is used to con- nect the events and use the multiplication rule if the word “and” is used.
12. A probability is the proportion of outcomes considered favorable compared to the total number of possible results. The odds of an event compares outcomes considered favorable to the number of outcomes considered unfavorable.
13. 5 14. 0 15. 5 16. 7 17. 13
18.
36
1 19. 63 114 200
12
20. 6 25
20
21. 63
113
20
22. 24
49
Answer Key A-19
21. (a) 40,320 (b) 336 (c) 1680
23. 72 25. 1,000,000,000 27. 210 29. 84
31.5 33.1 35.1 37.3 42 5 14 14
39. (a) 720 (b) 360 41. 1 14
23. There are three face cards (K, Q, J) per suit
(4 suits); thus, there are 12 face cards. This means that there are 40 nonface cards in the deck. Odds in favor of drawing a face card 5 12:40 5 3:10.
24. 109 5 1 billion 25. Yes, because by 2050 the population will be well over 1 billion.
26. 73 or about a 97% chance 75
27. 92 or about a 25% chance 28. 22 5 51.2% 365 43
29. 26 5 60.5% 30. 5 5 21.7% 31. 210 43 23
32. 294,000 33. 455 34. 2 :373 35. 24 36. undefined 37. undefined 38. 35
39. 2520 40. 1771
Chapter 7 test
1.
43. (a) .940606 5 94.1% (b) Answers will vary. 45. 1 47. 2 5 0.05128 49. 1
539 12 51. 1000 53. various answers
Chapter 7 review problems
1.
U
AB
da eb fc
2. {a, b, c, e, g} 3. {f} 4. { } or [
5. {a, c, e, f, g, h}
6. No. All elements in A are NOT in B.
7. No. All elements in C are NOT in A.
8. Yes. There are six elements in set A.
9. No. There are two elements in set D – so it is finite.
10. A probability is a mathematical calculation of
the likelihood of a given event occurring in prefer- ence to all other possible events that could occur in a given situation (or experiment). In other words, it is the proportion (or fraction) of times that a particular outcome will occur.
2. {5, 7, 9} 3. { } or [
5. S 5 {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
U
AB
6851 7
1011 9 3
4. {10, 11, 12, 13, 15} 1 1 17 29 17
6.12 7.4 8.30 9.60 10.45 1
11. 8,985,600 12. 1:1 13. 2 14. 0.41 15. 6
16. 1 17. 1 6
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A-20 Answer Key
18. Only nine plates out of all possible plates will have all four numbers the same.
9 3 9 3 9 3 9 5 6561 different possible plates
951 6561 729
19. 1 20. 1 21. 1 22. 11 2 13 2704 26
23. P(Ringo wins) 5 1 P(Bonnie wins) 5 1 4 16
P(Clyde wins) 5 5 P(Zero wins) 5 2 13 5
24. There are only two choices for children, boy or girl, each time, so for four births, 2 3 2 3 2 3 2 5 16 possible combination of boys and girls. But because order is not specified, many of the groupings are the same. If you list all possible combinations, 6 of the 16 will contain two boys and two girls. P(two girls and
two boys) 5 6 5 3 16 8
25.720 26.0 27. 1 28.2 29.3 30. 3 1024 5 4 20
ChApter 8
modeling with stAtistiCs
practice set 8-1
1. statistical survey 3. statistical survey
5. experimental study 7. inferential
9. descriptive 11. descriptive 13. descriptive 15. descriptive 17. quantitative 19. quantitative 21. qualitative 23. qualitative 25. quantitative 27. cluster sample 29. simple random sample
31. convenience sample 33. cluster sample
35. random sample
37. The numbering scale on graph exaggerates the differences.
39. Ask how many dentists were polled.
41. The number seems too precise for a general statement.
43. A misuse of a percent with a number greater than 100%.
45. The survey is not representative of the general population.
47. Answers will vary.
practice set 8-2
1. (a) four 3.
5.(a) 0 1 2 3 4
(b) six
(c) 25
8
2 22255667788899 01233 6
05
4
(b) Most students took between 12 and 19 minutes to complete the survey.
7. (a) 4.5
4 3.5 3 2.5 2 1.5 1 0.5
0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months
(b) October—March
(c) February—less rainfall
9. The range between the high and low temperatures is very consistent.
100
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95
90
85
80
75
70
65
60
1 2 3 4 5 6 7 8 9 10 October
Kitchen Bathroom Bedroom Other
11. (a) 1 8899
2 002223357
3
4 23 57
(b) The majority of students are in their twenties.
Rainfall amounts in inches
13. (a) 7.6%
(b) Yes, 35.8% is . 1/3
(c) approximately 176,497
(d) Oceania
(e) various answers depending on the years used
(b) 15 10
5
0 25 75 125175225275325375425475525
Answer Key A-21
for comparison
practice set 8-3
1. (a) Classes
Frequency
5. (a) Classes
50–54 1
Frequency
45–49
40–44
35–39
30–34
25–29
20–24
15–19
2 3 4 6
20 12 2
60–66 3
53–59 7
46–52 3
39–45 4
32–38 3
25–31 9
18–24 7
(c) 10 5
0 21 28 35 42 49 56 63
(b)
(c) skewed right, relatively few higher speeds
20
10
17 22 27 32 37 42 47 52
3. (a) Classes
Frequency
7. (a) Classes
Frequency
500–549 1 450–499 0 400–449 3 350–399 3 300–349 4 250–299 2 200–249 8 150–199 7 100–149 10
50–99 10 0–49 6
52–57 1 46–51 1 40–45 4 34–39 5 28–33 14 22–27 21 16–21 4
(b)
20 10
0 18 24 30 36 42 48 54
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A-22
Answer Key
9. (a)
Number of people
Frequency
practice set 8-5
1. All data items are identical. 3. mean54.5,R59,s53.0 5. mean58.4,R518,s56.9 7. mean57,R59,s53.3
9. mean55,R512,s53.6
11. forsec.1:R580,s524;forsec.2:R580,
s 5 27; Equal R’s might lead you to conclude that the sets were identical, but the standard deviation num- bers tell you that the sets are really different.
13. Forever batteries, because they have the smaller standard deviation
15. Small standard deviation indicates a consistent packing process.
17. (a) The mean increases by the amount added
to all numbers but the standard deviation does not change. (b) Since 3% of each amount is different, different amounts are being added to each number; thus, both the mean and standard deviation will change. 19. The mean will increase by the amount added. The range and standard deviation will not change.
21. The standard deviation would not change.
practice set 8-6
1.
3. Five-number summary: Minimum 5 0, Q1 5 20, Median 5 45, Q3 5 60, Maximum 5 120
(a) Range 5 120 minutes; IQR 5 40 minutes
(b) Yes, it has a positive skew.
5. (a) The median of both tests is 70.
(b) Range Test 1: 50 points; Range Test 2: 60 points (c) Test1:Q1 565,Q3 580;Test2:Q1 560,Q3 585 (d) 25%
7. 34.1% 9. 15.9% 11. 84.1%
13. 71,550 15. 0.067 (or about 7%)
17. about 920 hours 19. 1397 hours
21. 0.159 (or about a 16% chance)
23. 0.988 (or about a 99% chance)
25. mean 5 36.3 in. s 5 15.1 in.
27. 91.9% 29. 60% 31. 85%
33. Ray, because his z-score (1.4) is larger than Susan’s (1.3)
35. z 5 0.8 37. It would mean that your test score was below the class average of 78; 70
6–11
12–18 3
19–25
26–32 16 33–39 3 40–46 6 47–53 2
54–60
7
1
2
(b) 16
14 12 10
8 6
42 0
(c) normal
practice set 8-4
1. Answers will vary.
3. mean 5 4.6, median 5 3.5, mode 5 2, best avg. is the mean
5. mean 5 12.6, median 5 6, mode 5 9, best is the median
7. mean 5 3.65, median 5 2.865, mode 5 none, best is the median
9. A relatively few individuals with huge incomes (like Michael Jordan and Bill Gates) “drag” the mean average off center. The median income is the best for most comparisons for persons and families of “nor- mal” incomes.
11. (a) mode (b) mean (c) median (d) mean
13. mean 5 0.125°C, median 5 0.5°C, mode 5 0°C 15. GPA 5 3.4
17. Answers will vary.
19. 110
21. (a) mean 5 4.57; median 5 4; mode 5 4
(b) The mean becomes 5 and the others remain unchanged.
Luann: mean 5 82.5, median 5 80, mode 5 80
23. The mean would increase by $2000.
25. No, because one extremely large salary will
skew the mean to a higher number than that of the typical resident.
27. 12
29. Answers will vary based on survey results.
1 2 3 4 5 6 7 8 9 10 Q1 Median Q3
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39. 75% 41. 75 43. 71 and 129 45. about 3110 customers (62.2%)
practice set 8-7
47. about 1.2%
17. (a)
200 190 180 170 160 150 140 130 120 110 100
Answer Key A-23
1. negative; as age increases, price decreases
3. negative; as weight increases, mileage decreases 5. (a) independent variable, education; depend-
ent variable, personal income (b) strong positive correlation (c) As the years of education increase, personal income increases.
7. 3.4 9. 2.787
11. (a)
90 80 70 60 50
14 12 10
8 6 4 2 0
Area in sq. feet
13. (a)
15. (a) 10 8 6 4 2 0
2 4 6 8 10
20 25 30 35 40
Age
(b) r 5 0.82; strong correlation
(c) y 5 0.197x 2 185
(d) 125.275 or $125, 275; fairly reliable since the
correlation is strong 19. (project)
Chapter 8 review problems
1. Descriptive statistics makes no predictions or guesses. It summarizes a population of data. Infer- ential statistics takes descriptive data and uses them to help make “educated guesses” about the data or about the group from which the data were gathered. 2. Quantitative data are data that can be “quantified,” i.e., they have amounts or numbers associated with them. Qualitative data are generally nonnumerical in nature.
3. experimental study 4. convenience sample
5. stratified sample
6. Sample results cannot be applied to the general population since it was not representative.
7. Sample size is not given and the number is too precise for weight loss.
8. 760 people; 137 people; Polls indicate he has a poor chance of reelection.
9. mean 5 14, median 5 14, mode 5 none,
R 5 8, s 5 2.7
10. mean 5 17.3, median 5 8.5, mode 5 8,
R 5 55, s 5 17.2
(b) no, r 5 0.16
(c) y 5 0.065x 1 7.35
(d) 9.43 or 9 days; not reliable because of weak
correlation
150 140 130 120 110
0
15 20 25 30
(b) a moderate correlation (c)y51.6x192.5 (d)r50.64
(e) 124.5 lb
(b) moderate correlation; somewhat linear
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Days
Price in thousands
1300 1350
1400 1450
1500 1550
1600 1650
1700 1750
1800 1850
A-24 Answer Key
11. The data in #10 have more variability. The larger value of the standard deviation tells us this.
12. For the data in #9, the mean average is best. The numbers are all relatively in the same size category. For data in #10, the median is the best average be- cause the relatively large value of 57 drags the mean average off center for the group.
13. (a) Yes, the median weight went down from 188 lb to 183.5 lb.
(b) The range of weights in February is less than it was in January. (28 lb versus 22 lb)
(c) The minimum weight in February was 173 lb, down from the January weight of 176 lb. The maximum weight of 195 lb in February was also less than the January maximum of 204 lb.
16. 15.9% 17. 50% 18. 81.8%
19. z88 on math 5 1.6 and z88 on history 5 1.0. The z-scores indicate that you would be farther above average for the math group than for the history group.
20. 0.034 (or about 3%) 22. 23
22 21 20 19 18
0 10 11 12 13 14 15 16 17
Age at first contact
21. 0.271 (or about 27%)
Moderate correlation
(d) yes
January Febuary
170
14. Classes
13–14
11–12
9–10
7–8 5–6 3–4
175 180
185
190
195
200
205
23. y 5 25.3 2 0.40x 24. 19.7 = 20 years old 25. r 5 20.61
26. The r-value indicates a moderate negative correlation of these two variables.
Chapter 8 test
1. statistical survey 2. qualitative 3. qualitative 4. The number of students who took the test is not given.
5. data set B
6. for data set A, the mean average and for data set B, the median
7. mean 5 36.5, median 5 36, mode 5 36,
R 5 12, s 5 3.9
8. median 5 M
Frequency
4 5 5
13 12 11
9.
0 3
1 2708892 8
2 7 7291618916
3 0 5865823212312 4 2715 3
51
14 12 10
8 6 4 2
0 5 1525354555
15.
Positive skew
**
*****
*****
******
****** ** *
********** *
************
3 4 5 6 7 8 9 10 11 12 13 14
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Age at incarceration
10. normal distribution
11. Five-number summary: Minimum 5 60, Q1 5 63, Median 5 64, Q3 5 66, Maximum 5 69
12. Range 5 9 inches; IQR 5 3 inches
13. No, it does not appear to be skewed.
14. approximately 16%
15. z 5 23.00 16. grade 5 88.75
17. 0.977 (or about 98%)
18. 0.464 (or about 46%) 19. z 5 2.00
20. 0.092 (or about 9%) 21. 146 lb.
22. r 5 0.80 (interpretations will vary)
23. 12,000
6,000 05060708091011121314
24. y 5 544.4x 2 1,085,438 25. 14,250 restaurants
Answer Key A-25
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I
Index
Domain of functions, 156–157, 198 Dot plots, 373
E
Elements, 288, 312
Elements, The (Euclid), 54 Empirical probability, 316–318, 356 Empirical rule, 400
Empty sets, 314
Equally likely outcomes, 324 Equals
indicator words, 41
sets, 312 Equations
linear, 112, 118, 130–135
rewriting, 32
Equilateral triangle, 63
Equilibrium point, 296
Equivalent equations, 9
Euclid, 54
Evaluating functions, 161–162 Events, 316
Experimental studies, 364 Experiments, 29, 316
Exponential functions, 193–197, 198
calculator mini-lesson on, 194
deriving from data set, 425 Exponential growth functions,
194–196, 198
Exponents, calculator mini-lesson
on, 223
Extremes of a proportion, 36
F
Factorial, 348–349, 356 calculator mini-lesson on, 348
Factoring to solve problems, 186–187, 188
Financial instruments models, 252–258
Financial planning, 252 Finite sets, 312
First harmonic, 96 First overtone, 96
First quartile (Q1), 396
Five number summaries, 396–397 Fixed-rate mortgages, 242–243, 267 Flat keys, 97
Formulas, 30–34
Fractions
and percents, 14
solving linear equations with,
10–11
Frequency and music, 96, 97, 98,
99–100
Frequency distributions, 380–381 Frequency tables, 380
Functional relationships, 155–157 Function notation, 160–167, 161 Functions, 152–160, 198
defined, 153 distance, 161
A
Binomial models, 362
BMI (body mass index), 31–32, 47 Body mass index (BMI), 31–32, 47 Bonds, 254
Box-and-whisker plots, 396, 397
comparing, 398 Break-even analysis, 297 Break-even points, 297–298 Budgets, 261–263
Business models, 212–217
C
Calculators, use for combinations and
permutations, 350 exponential functions, 194 exponents, 223
factorial, 348
functions min/max and roots, 183 histograms, 383
linear equations on, 146–149 nonlinear systems of equations,
301–302
order of operations, 6–8 parabolas, 183
prediction equations, 412 real numbers, 2–6
scientific notation, 21 standard deviation, 394, 395 system of equations, 282–283
Cards, probabilities with, 319–320, 328
Car insurance rates, 246–251 Causal models, 28
Centers for Disease Control and
Prevention (CDC), 31 Circle graphs, 374–375
Circles
area of, 56, 101 circumference of, 55, 101
Circumference, 55, 101 Closed-end credit, 226
Closing costs, 239
Cluster sampling, 365, 366, 367 Combinations, 349–350, 351,
352–353, 356
calculator mini-lesson on, 350
Combined variation, 176, 198 Commission payments, 258–260 Common sense, 40
Composite figures, 72–73 Compound interest, 31, 220–225, 267
continuous, 224–225 monthly, 223–224 quarterly, 224
Compound interest formula, 31 Comprehensive/collision insurance,
246, 248–250
Conditional probability, 319–321 Cones, 58
Consecutive integers, 43–44 Consistent systems, 280, 287
Constant of proportionality, 174 Constant of variation, 174 Consumer Credit Counseling
Service, 262
Consumer credit models, 226–232 Consumer Protection Act, 228 Continuously compounded
interest, 224–225
Convenience sampling, 365, 366–367 Coordinates of a point, 110
identifying, 111–112 Correlation, negative, 410 Correlation coefficient (r), 412–413 Cosine function, 77, 78–79
Cost, problems of, 292–294
Cost of production, 214–215 Counting numbers, 2
Counting principle, 334–335, 336,
348–349
Cramer’s rule, 278, 288–291, 295, 305 Credit cards, 226–228 Cross-multiplication property,
36–37, 47 Cubes, 58
Cylinders, 58
D
Data, 364
Decibels (dB), 98 Decimal notation, 20–21 Decimals and percents, 14 Demand, 296
equations for, 296–297, 303 Dependent equations, 288 Dependent events, 319
and the multiplication rule, 345 Dependent systems, 280, 287
solutions for, 281–282 Dependent variables, 152, 155 Depreciation, 170–171, 213–214,
271–272 Descriptive models, 28
Descriptive statistics, 364, 385–391 Determinants, 288–289
Digital recordings, 98
Digital signal processing, 98 Digitizing music, 98
Direct proportion, 174
Direct variation, 174–175, 176,
198, 411 Disjoint sets, 314
Dispersion, 392 Distance
formula, 30
functions, 161 Distributive property, 11 Dividends, 253
Division
indicator words, 41
of rational numbers, 6 of real numbers, 4–5 of signed numbers, 23
Absolute values, 3, 403 Accumulated amount, 256 Acute angles, 62
Acute triangles, 62 Addition
indicator words, 41
of real numbers, 4
of signed numbers, 23
Addition property of equality, 9 Addition rule, 340
events that are not mutually exclusive, 341–343
Additive inverses, 3 Add-on interest, 233, 234 Adjacent side, 76–77 Adjustable-rate mortgages
(ARMs), 243 Algebraic solutions
nonlinear systems, 302–303
system of equations, 284–292, 305 Amortization table, 240–241 Amplitude of sound, 99
Analog recordings, 98
And problems, 345–347 Angles, 62–63
and trigonometric functions 79–81
Annual percentage rate (APR), 228–230
automobile purchases, 235–236 Annuities, 256
Arcsine of an angle, 79
Areas, 56–58, 101
of composite figures, 72–73 of irregular figures, 66–67 surface, 58, 63
of triangles, 63–65, 101
Area under the normal curve, 400, 404–405
Automobile insurance rates, 246–251 Automobile purchases, 233–239
leasing, compared with, 237 Average daily balance method,
227–229 Averages, 385, 388–389
calculating, 43 Avogadro, Amedeo, 21 Avogadro’s number, 21–22
B
Banker’s Rule, 221
Banking models, 218–226
Bar graphs, 372–373, 374
Base, 15
Beats, 95
Bell curve graph shape, 373, 384 Bell curves, 398. See also Normal
curves Best-fit lines, 411
Bias, 366
Bimodal data, 386
I-1
domain of, 156–157
evaluating, 161–162
graphs of, 164
range of, 156–157
relationships of, 155–157
tables of variables, 163–164, 171 velocity, 161
word problems, 163 Fundamental frequency, 96, 97 Future value, 256
G
General form of a linear equation, 112, 125, 130, 134, 142
Geometry applications for linear systems, 298
Geometry models, 54–62 Golden mean, 90
Golden Ratio, 90–91, 101
and music, 98
Golden rectangles, 91–92 Graphs
bar graphs, 372–373, 374 box-and-whisker plots, 396,
397, 398
circle graphs, 374–375
dot plots, 373
of functions, 164 histograms, 382–384 interpreting, 154–155
of linear equations, 115–119,
136–139
line graphs, 373, 375–376 misleading, 368
origin of, 110, 117 reading and interpreting,
372–3880
scatter diagrams, 409–413 system of equations, solutions
for, 278–284, 305
uses of, 135–142
using slope-intercept form,
125–126
using the slope of a line, 123–125
Gross income, 214–215 “Guesstimation,” 364
H
Hambridge’s Whirling Squares, 92 Harmonics, 98
Hero’s formula, 65, 101 Histograms, 382–384
calculator mini-lesson on, 383 Home purchasing models, 239–245
loan maximum, 241
monthly payment, 240–241 Horizontal lines, 118–119
equation of, 132–133, 134
slope of, 123, 142
Hypotenuse of a triangle, 70, 76–77
I
Income tax, state, 260–261 Inconsistent systems, 280, 287 Indemnity, 246
Independent events, 319, 339
and the multiplication rule, 345 Independent outcomes, 339 Independent variables, 152, 155 Indicator words, 41
Individual retirement accounts (IRAs), 256
Inferential statistics, 364
Infinitely many solutions, 288, 291 Infinite sets, 312
Infinite solutions, 288, 291
Initial value of a function, 168 Input of a function, 155 Installment buying, 226 Installment loans, 233 Insurance models, 246–251 Integers, 2
consecutive, 43–44 Intercepts, 115, 116 Interest
compound, 31, 220–225 financial planning, 252 on a loan, 218
simple, 219–220
Interquartile range (IQR), 397 Intersection of sets, 313–315 Inversely proportional, 175
Inverse trigonometric functions, 79 Inverse variation, 175–176, 198 Irrational numbers, 2
Irregular figures, area of, 66–67 Isosceles triangles, 63
J
Joint variations, 176, 198
L
Lateral surface area (L.S.A.), 58 Law of large numbers, 318, 327 Laws of probability, 326, 356–357 Laws of probability theory, 326–328 LCD (least common denominator), 10 Leasing an automobile, 235–237 Least common denominator
(LCD), 10 Least-squares line, 411
Leibniz, Gottfried Wilhelm von, 94 Liability insurance, 246–249 Linear combinations, 284,
286–287, 305
Linear equations, 112, 118, 130–135
calculators and, 146–149 general form of, 112, 125, 130,
134, 142
graphing, 115–119, 136–139 slope intercept form of, 125, 134 solving, 9–13, 112–114
Linear functions
depreciation, 170–171 formula for, 168, 198
as models, 167–174
tables, derivation from, 171
Linear regression analysis, 411 Linear systems
applications of, 292–301 geometry applications, 298 infinite solutions, 288, 291 no solutions, 287–288, 291
Line graphs, 373, 375–376 points, plotting, 115–116
Loads fees, 254 Loans
interest on, 218
maximum, 241
Location of an operation, 40 Logarithmic spirals, 92 Lotteries, 332
L.S.A. (lateral surface area), 58
M
Markups, 215
Mathematical models, 28–34. See
also Systems of equations
in automobile purchases, 233–239 in banking, 218–226
in business, 212–217
in consumer credit, 226–232
in financial instruments, 252–258 formulas as, 29
in home purchase, 239–245
in insurance, 246–251
in personal income, 258–266 Maturity value of a loan,
218–219, 267
Maximum height, 185–186 Maximum values, 396
Mean averages, 385, 387–388, 417
standard deviation of, 393 Means of a proportion, 36 Measures of central tendency,
385, 388
Medians, 385, 386–387, 388
five-number summaries, 396, 397 Midpoint of the class, 382 Mini-lessons, calculators
combinations and permutations, 350
exponential functions, 194 exponents, 223
factorial, 348
functions min/max and roots, 183 histograms, 383
order of operations, 6–8 real numbers, 2–6 scientific notation, 21 standard deviation, 394
Minimum values, 396
Misuses of statistics, 367–369 Mixture problems, 294–296 Modal class, 381
Models. See also Mathematical
models causal, 28
descriptive, 28
exponential functions as, 193–197 in geometry, plane and solid,
54–62
linear functions as, 167–174 price-demand, 29
Models of real events, 157 Moderate correlation, 413 Modes, 385–386
Mole, 21
Monthly compounded interest, 223–224
Mortgages, 239, 240–244 adjustable-rate, 243 fixed-rate, 242
Multiplication
indicator words, 41
of real numbers, 4–5 of signed numbers, 23
Multiplication property of equality, 9–10
Multiplication rule, 345–346 Multiplicative inverses, 5–6 Music and mathematics, 94–100
sine waves, 98–99, 101 Mutual funds, 253–254 Mutually exclusive events, 339,
340–341
N
National Association of Securities Dealers Automated
Quotations (NASDAQ), 252 Natural exponential functions,
194, 198 Natural numbers, 2
Negative correlation, 410, 411 Negative relationship, 411 Net profit, 214–215
Index I-2 Newton, Sir Isaac, 94
Newton’s Second Law of Motion, 179
New York Stock Exchange (NYSE), 252
Nonlinear functions
power functions, 189–190 quadratic functions, 181–189 transformations of, 206–207
Nonlinear systems of equations, 301–304, 305
calculators and, 301–302 Normal curves, 398–400
area under, 400
and probabilities, 400, 403,
404–405
Normal distribution, 383–384 Normally distributed, 399 Notes
adding, 95–96
symbols for, 95 Null sets, 314 Number line, 2
O
Observational studies, 364 Obtuse angles, 62
Obtuse triangles, 62 Octave, 97
Odds, 330–334, 356 against, 331
in favor, 330–332
and probabilities, 332–333 Ohm’s Law, 178
Open-end credit, 226 Opposites, 3
Opposite side, 76–77
Order of operations, 6–8, 23
slope calculation, 122 Ordinary annuities, 256 Ordinary interest, 221 Origin on a graph, 110, 117 Or problems, 339–345 Outcomes, 316, 334–335 Outliers, 397
Output of a function, 155
P
Parabolas, 182–183
calculator mini-lesson on, 183
Parallel lines, 126–127, 142 equations for, 133–134 slope of, 127, 128, 133
Pearson, Karl, 412
Pearson correlation coefficient,
412–413 Percentage, 15
Percentile ranks, 405–406 Percents, 13–19
increase/decrease, 17–18, 44 Perimeters, 54–57
formula for, 30 Permutations, 349–350, 351,
352–353, 356
calculator mini-lesson on, 350
Perpendicular lines, 127–128, 142 equations for, 133–134
slope of, 128–129, 133
Personal income, mathematical models for, 258–266
Perspective, 85–87
Pie graph, 374
Pitch in music, 97
Playing cards, probabilities with,
319–320, 328
I-3 Index Points, plotting, 110–111
line, graphing a, 115–116 Point-slope equation of a line, 130–131, 134, 143
Policyholders, 246
Polling results, 368 Populations, 365–366
Positive relationships, 411 Power functions, 189–190, 198 Prediction equations, 411–412
calculators, using, 412 Premiums, insurance, 246–247
comprehensive/collision insurance, 248–249
liability insurance, 247–248 Price-demand models, 29 Principal of a loan, 218
Principal vanishing point, 85 Probabilities. See also Theoretical
probabilities
and the normal curve, 400, 403,
404–405
and odds, 332–333
with playing cards, 319–320, 328
Probability theory, 316–324 laws of, 326–328
Problems, 345–355 Profit, 214–215
from stock transactions, 253 Proportional
directly, 174
inversely, 175 Proportions, 36–38, 88
and percents, 15
solving word problems, 37–38 using cross-multiplication to
solve, 36–37 Pyramids, 58
Pythagoras, 90
Pythagorean theorem, 70–73, 101
Q
Quadrants, 110
Quadratic equation, 188–189 Quadratic formula, 187,
188–189, 198
Quadratic functions, 181–183, 198
maximum height of, 185–186
roots of, 184 Quadrivium, 94 Qualitative data, 365
bar graphs of, 372–373, 374 circle graphs, 374–375
dot plots, 373
mean averages, 387
median of, 386
mode of, 386
Quality control and standard
deviation, 393 Quantitative data, 365
line graphs of, 375–376
mean averages, 388
median of, 386
mode of, 386
stem-and-leaf displays of, 376–377
Quantity, problems of, 292–294 Quarterly compounded interest, 224 Quartiles, 396–397
R
Random process, 316
Random sampling, 365, 366, 367 Range, 392, 417
Range of functions, 156–157, 198 Rates, 35
of change, 167–168 of interest, 218 unit, 35–36
Rational numbers, 2 division of, 6
Ratios, 34–36 Real numbers, 2–8
calculator mini-lesson on, 5, 7 Reciprocals, 5–6
Rectangles
area of, 56, 101
golden, 91–92
perimeter of, 54–55
reflection symmetry of, 87–88
Rectangular coordinate system, 110–114
Rectangular prisms, 58 Reflection symmetry, 87 for a rectangle, 87–88
Relations, 152
functional relationships,
155–157
Replacement, with or without,
336–337, 345–346 Residual value, 213
Rests, in music, 95
Retirement planning, 252, 256 Right angles, 62
trigonometric functions of, 79, 80–81
Right triangles, 62, 70–84 trigonometry of, 76–84
Roots of a function, 183 quadratic functions, 184
Rotational symmetry, 87, 88
S
Sales prediction graph, 138–139 Sales tax, 212–213
Samples, 365–366
Sample size, 368
Sample space, 324–325
Sample standard deviation, 393 Scale drawings, 88–89
Scale factor, 88
Scalene triangle, 63
Scaling triangles, 89–91
Scatter diagrams, 409–413 Scientific notation, 19–22
calculator mini-lesson on, 21 Second harmonic, 96
Second overtone, 96
Second quartile, 397
Semitones, 97
Set-builder notation, 312
Set notation, 312
Sets, 312
Set theory, 312–315
Shareholders, 252
Shares of stock, 252–253
Sharp keys, 97
Sigma (s), 393
Signed numbers, 23
Similar triangles, 89
Simple interest, 218, 219–220, 266
bond payments of, 254
vs. compound interest, 222–223 Sine functions, 77, 78–79
inverse of, 79
Sine waves and music, 98–99, 101 Size of samples, 368
Slope-intercept form, 124–126, 130, 131–132, 134, 143
Slope of a line, 119–129, 167 calculation of, 120–123
equation of, 121, 142
graphing using, 123–127 horizontal lines, 123, 142
parallel lines, 127, 128, 133 perpendicular lines, 128–129, 133 vertical lines, 123, 142
Solids, 58
Solutions. See also System of
equations
for dependent systems, 281–282 factoring for, 186–187, 188
of linear equations, 9-13,
112–114
no solutions, 280–281,
287–288, 291 of systems, 278
Spheres, 58–60
Spirals, 92
Square root, 2
Squares, 56, 101
Standard deviation, 392, 393, 417
calculator mini-lesson on, 394 computing with a calculator, 395 of a data set, 394
Standard scores, 400, 402 Statistics, 364–371
misuses of, 367–369 Stem-and-leaf displays, 376–377 Stocks, 252–253
reading a stock table, 254–256 Straight commission payments,
258–260 Straight-line method of
depreciation, 213 Strata, 366, 367
Stratified sampling, 365, 366 Strong correlation, 413
Subsets, 314
Substitution method of solutions,
284–285, 305 Subtraction
indicator words, 41
of real numbers, 4
of signed numbers, 23
Supply, 296
equations for, 296–297, 303
Surface areas, 63 three-dimensional objects, 58
Surveys, 364, 365
Symbols, musical, 95
Symmetrical curves, 400 Symmetry, 87, 182
Synthesizers, 98
Systematic sampling, 365, 366, 367 System of equations
algebraic solutions for, 284–292, 305
calculator solutions for, 282–283 dependent systems, 281–282 graphing solutions for,
278–284, 305
no solutions for, 280–281,
287–288, 291
System of inequalities, 308
Systems of linear equations, 287–288
T
Tables, as functions, 163–164, 171 Tables of areas, 400–401, 403
Tangent functions, 77, 78–79 Tempo, 95
Terms of a proportion, 36 Theoretical probabilities, 316–317,
324–330, 356 calculating, 325–326 formula for, 325
Third quartile (Q3), 396–397 Tip payments, 259
Total surface area (T.S.A.), 58 Tree diagrams, 334–338 Triangles, 62–70
acute, 62
area of, 63–65, 101 equilateral, 63
isosceles, 63
lettering conventions, 73 obtuse, 62
right, 62, 70–84
scalene, 63
similar, 89
Trigonometric functions, 77, 101 angle calculations with, 79–81 inverse of, 79
side length calculations with, 81–83
Trigonometry of right triangles, 76–84 Truth-in-lending Act, 228
T.S.A. (total surface area), 58 Twain, Mark, 367, 369
U
Underwriters, 246
Union of sets, 312–314, 340 United States Census Bureau, 365 Unit rates, 35–36
Universal set, 312
Unpaid balance method, 227
V
Variation, 391–395
Variation equations, 176–177 Variation problems, solving, 177–178 Velocity function, 161
Venn diagrams, 312, 313–315
Vertex of a triangle, 63
Vertical lines, 118–119
equation of, 132–133, 134
slope of, 123, 142
Volumes of three-dimensional
objects, 58
Weak correlation, 413 Weighted means, 389–390 Weight loss graph, 137–138 Whiskers, 397
Whole numbers, 2 Word problems, 163
of proportions, 37–38 strategies for, 40–47
X
x-axis, 110
x-coordinates, 110 x-intercepts, 115, 116, 118, 142
Y
y-axis, 110
y-coordinates, 110 y-intercepts, 115, 116, 118, 142
Z
Zero factorial, 356 Zeros of a function, 183 z-scores, 400–404, 417
W
Correlations to the Texas Essential Knowledge and Skills (TEKS): Student Material
Subject
Chapter 111. Mathematics
Subchapter
Subchapter C. High School
Course
§111.43. Mathematical Models with Applications, Adopted 2012 (One-Half to One Credit).
Publisher
Cengage Learning, Inc./Brooks Cole
Program Title
Mathematical Models with Applications, TX Adoption Package
Program ISBN
9781305215429
(a) General requirements. Students can be awarded one-half to one credit for successful completion of this course. Prerequisite: Algebra I. This course must be taken before receiving credit for Algebra II.
(b) Introduction.
(1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while focusing on fluency and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century.
(2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and number sense to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
(3) Mathematical Models with Applications is designed to build on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I. This mathematics course provides a path for students to succeed in Algebra II and prepares them for various post-secondary choices. Students learn to apply mathematics through experiences in personal finance, science, engineering, fine arts, and social sciences. Students use algebraic, graphical, and geometric reasoning to recognize patterns and structure, model information, solve problems, and communicate solutions. Students will select from tools such as physical objects; manipulatives; technology, including graphing calculators, data collection devices, and computers; and paper and pencil and from methods such as algebraic techniques, geometric reasoning, patterns, and mental math to solve problems.
(4) In Mathematical Models with Applications, students will use a mathematical modeling cycle to analyze problems, understand problems better, and improve decisions. A basic mathematical modeling cycle is summarized in this paragraph. The student will:
(A) represent:
(i) identify the variables in the problem and select those that represent essential features; and
(ii) formulate a model by creating and selecting from representations such as geometric, graphical, tabular, algebraic, or statistical that describe the relationships between the variables;
(B) compute: analyze and perform operations on the relationships between the variables to draw conclusions;
(C) interpret: interpret the results of the mathematics in terms of the original problem;
(D) revise: confirm the conclusions by comparing the conclusions with the problem and revising as necessary; and (E) report: report on the conclusions and the reasoning behind the conclusions.
(5) Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples.
(c) Knowledge and Skills.
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace
(i) apply mathematics to problems arising in everyday life
Instruction
9781305096691
15
Section R-3, Example 2, 4-5
Activity
9781305096691
18 34 141
Section R-3 #37-38 #41-42
#14-15, 18
Instruction
9781305096691
20 137
Example 2 Example 2
Review
9781305096691
24 48
#28, 38, 40 #18-19, 21-25
Assessment
9781305096691
38 244
#10, 12, 15-17 #22
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace
(ii) apply mathematics to problems arising in society
Instruction
Activity
9781305096691
38 46
#46 #50
Activity
9781305096691
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#13 #14, 17 #19-20
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
Review
9781305096691
24 144
#39 #30
Assessment
9781305096691
48 145
#18 #21
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace
(iii) apply mathematics to problems arising in the workplace
Instruction
9781305096691
17
Example 7
Activity
9781305096691
17 38
#41-42 #29-30
Instruction
9781305096691
29 137 138
Example 1 Example 2 Example 3
Review
9781305096691
24 48
#30, 34-37 #16-17, 20, 26
Assessment
9781305096691
49 145
#11 #23-24
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution
(i) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process
Instruction
9781305096691
40 41 42
Word Problem Strategies Example 1
Example 2
Activity
9781305096691
45 47
#13-15 #3
Instruction
9781305096691
43 44
Example 3-4 Example 5
Review
9781305096691
48
#15-30
Assessment
9781305096691
49
#10-20
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution
(ii) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the reasonableness of the solution
Instruction
9781305096691
40 41 42
Word Problem Strategies Example 1
Example 2
Activity
9781305096691
45 46 47
#13-29 #30-49 #50-52
Instruction
9781305096691
43 44
Example 3-4 Example 5
Review
9781305096691
48
#15-30
Assessment
9781305096691
49
#10-20
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
(i) select tools, including real objects as appropriate, to solve problems
Instruction
Activity
9781305096691
49
Lab Exercise 1-2
Activity
9781305096691
105
Lab Exercise 2
Activity
9781305096691
360
Lab Exercise 1
Activity
9781305096691
421
Lab Exercise 1
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
(ii) select tools, including manipulatives as appropriate, to solve problems
Instruction
Activity
9781305096691
49 50
Lab Exercise 2 Lab Exercise 4
Activity
9781305096691
105
Lab Exercise 2
Activity
9781305096691
360
Lab Exercise 1
Activity
9781305096691
421
Lab Exercise 1
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
(iii) select tools, including paper and pencil as appropriate, to solve problems
Instruction
9781305096691
30
Formulas, Example 1-2
Activity
9781305096691
106
Lab Exercise 4
Activity
9781305096691
361
Lab Exercise 2, 4
Activity
9781305096691
41
Example 1
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
(iv) select tools, including technology as appropriate, to solve problems
Instruction
9781305096691
16
Example 3
Activity
9781305096691
146
Lab Exercise 3
Activity
9781305096691
204
Lab Exercise 3
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
(v) select techniques, including mental math as appropriate, to solve problems
Instruction
9781305096691
120 340 341
Example 1 Example 1 Example 2
Activity
9781305096691
106 146
Lab Exercise 3-5 Lab Exercise 2
Instruction
9781305096691
348 349
The Counting Principle, Permutations, and Combinations, Example 1 Example 2-3
Activity
9781305096691
354
#16-37
Review
9781305096691
357 358
#1-22 #23-38
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
(vi) select techniques including estimation as appropriate, to solve problems
Instruction
9781305096691
375
Example 3
Activity
9781305096691
414
#9
Activity
9781305096691
415
#17
Activity
9781305096691
421
Lab Exercise 4
Activity
9781305096691
423
Lab Exercise 7
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems
(vii) select techniques, including number sense as appropriate, to solve problems
Instruction
9781305096691
81
Example 4
Activity
9781305096691
45
#9-12
Instruction
9781305096691
163
Example 6
Activity
9781305096691
50
Lab Exercise 3
Activity
9781305096691
100
#25-26
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(i) communicate mathematical ideas using multiple representations, including symbols as appropriate
Instruction
9781305096691
30 31
Formulas, Example 1-2 Example 3-4
Activity
9781305096691
33 34
#1-32 #33-40
Instruction
9781305096691
32
Example 5-6
Review
9781305096691
47
#1-4, 11-14
Knowledge and Skills Statement
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
Student Expectation
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
Breakout
(iii) communicate mathematical ideas using multiple representations, including graphs as appropriate
(iv) communicate mathematical ideas using multiple representations, including language as appropriate
(v) communicate mathematical reasoning using multiple representations, including symbols as appropriate
(vi) communicate mathematical reasoning using multiple representations, including diagrams as appropriate
Citation Type
Activity
Instruction
Review
Assessment
Instruction
Activity
Instruction
Review
Assessment
Instruction
Activity
Instruction
Review
Assessment
Instruction
Activity
Instruction
Review
Assessment
Instruction
Activity
Instruction
Review
Assessment
Component ISBN
9781305096691
9781305096691
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9781305096691
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9781305096691
9781305096691
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Page (s)
339 340 341
357
358
372 373
377 378
374 375
417
420
40 41
45 93 106
412
48 198
25 201
278
279 280
301
281 282 283
305 306
306 307
110 111
114
112 113 114
143
144
Specific Location
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(ii) communicate mathematical ideas using multiple representations, including diagrams as appropriate
Assessment
Instruction
9781305096691
9781305096691
48 49
334 335 336
337 338
Test #1-2 Test #8-9
Tree Diagrams Example 1-3 Example 4-6
#7-8 #9-10
Or Problems Example 1 Example 2
#1
Chapter 7 Test #1
Practice Set, #1-2 #3-8
Example 2 Example 3
#4-5
#11-14, 22-26
Word Problem Strategies Example 1
#28
#12
Lab Exercise 3, 6
Example 3
#27 #4-5
#1 #2
Solving Systems by Graphing, Example 1
Example 2
Example 3
#1-12
Example 4 Example 5 Example 5
Review Problems #1-15 #16-25
Test, #1-5 #6-11
Rectangular Coordinate System, Example 1
Example 2
#13-26, 30-39
Example 3-4 Example 5 Example 5
Review, #26-27
Test, #19-20
Reading and Interpreting Graphical Information, Example 1 Example 1 continued
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(vii) communicate mathematical reasoning using multiple representations, including graphs as appropriate
Instruction
9781305096691
130 131
Writing Equations of Lines, Example 1-2
Example 3
Activity
9781305096691
134 135
Practice Set, #1-5 #6-40
Instruction
9781305096691
132 133 134
Horizontal and Vertical Lines Example 4-5
Example 5
Review
9781305096691
143 144
Review Problems, #1-28 #29-30
Assessment
9781305096691
144
Test, #1-20
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(viii) communicate mathematical reasoning using multiple representations, including language as appropriate
Instruction
9781305096691
16
Example 3-6
Activity
9781305096691
22
#22-32
Instruction
9781305096691
19
Scientific Notation
Review
9781305096691
24
#13-16
Assessment
9781305096691
25
Test, #1, 6-7
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(ix) communicate [mathematical ideas'] implications using multiple representations, including symbols as appropriate
Instruction
9781305096691
19
Scientific Notation
Activity
9781305096691
22
#1-32
Instruction
9781305096691
20
Example 1-2
Review
9781305096691
23 24
Review Problems, #1-6 #7-40
Assessment
9781305096691
25
Test, #1-20
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(x) communicate [mathematical ideas'] implications using multiple representations, including diagrams as appropriate
Instruction
9781305096691
312 313
Sets and Set Theory Example 1
Activity
9781305096691
314
Practice Set, #25-30
Instruction
9781305096691
314
Example 2
Review
9781305096691
199
#6, 17
Assessment
9781305096691
201
Test, #3
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(xi) communicate [mathematical ideas'] implications using multiple representations, including graphs as appropriate
Instruction
9781305096691
164 167
Example 8
Linear Functions as Models
Activity
9781305096691
166
#27-30
Instruction
9781305096691
168 169 170
Example 1 Example 2 Example 3
Review
9781305096691
357
Review, #1
Assessment
9781305096691
201
Test, #3
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(xii) communicate [mathematical ideas'] implications using multiple representations, including language as appropriate
Instruction
9781305096691
40 41
Word Problem Strategies Example 1
Activity
9781305096691
45 48
#28 #27
Instruction
9781305096691
42 43 44
Example 2 Example 3-4 Example 5
Review
9781305096691
198
Review, #1-2
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
Assessment
9781305096691
201
Test, #8-9
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(xiii) communicate [mathematical reasoning's] implications using multiple representations, including symbols as appropriate
Instruction
9781305096691
76 77
Right Triangle Trigonometry Right Triangle Trigonometry
Activity
9781305096691
83
#27-30
Instruction
9781305096691
78 79 80
Example 1 Example 2 Example 3
Review
9781305096691
102 103
Review, #1-14 #15-27
Assessment
9781305096691
103 104
Test, #1-3 #4-22
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(xiv) communicate [mathematical reasoning's] implications using multiple representations, including diagrams as appropriate
Instruction
9781305096691
312 313
Sets and Set Theory Example 1
Activity
9781305096691
315 337
#25-30 #7-8
Instruction
9781305096691
334 335 339 340
Tree Diagrams Example 1-4 Or Problems Example 1
Review
9781305096691
315
Practice, #1
Assessment
9781305096691
358
Test, #1
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(xv) communicate [mathematical reasoning's] implications using multiple representations, including graphs as appropriate
Instruction
9781305096691
364 365
Introduction to Statistics Example 1
Activity
9781305096691
372 377
#37-38, 47-48 #1-2
Instruction
9781305096691
372 373
Reading and Interpreting Graphical Information, Example 1
Example 1 continued
Review
9781305096691
417 418
Review, #1-5 #6-18
Assessment
9781305096691
419 420
Test, #1-8 #9-25
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
(xvi) communicate [mathematical reasoning's] implications using multiple representations, including language as appropriate
Instruction
Activity
9781305096691
300 306
#23-24 #35
Activity
9781305096691
321
Practice, #2-3
Activity
9781305096691
361
Lab Exercise 3
Review
9781305096691
357
Review, #11
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(E) create and use representations to organize, record, and communicate mathematical ideas
(i) create representations to organize mathematical ideas
Instruction
9781305096691
152
Functions
Activity
9781305096691
160 172 174
#25 #4 #17-18
Instruction
9781305096691
153
Example 1
Review
9781305096691
418
#13
Assessment
9781305096691
419 420
Test, #7-8 #23
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(E) create and use representations to organize, record, and communicate mathematical ideas
(ii) create representations to record mathematical ideas
Instruction
9781305096691
153
Example 1
Activity
9781305096691
48
#17-18
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
Activity
9781305096691
172
Practice, #2, 4
Review
9781305096691
48 418
#14-15 #22
Assessment
9781305096691
419
#78
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(E) create and use representations to organize, record, and communicate mathematical ideas
(iii) create representations to communicate mathematical ideas
Instruction
9781305096691
153
Example 1
Activity
9781305096691
165
#20
Instruction
9781305096691
157
Example 4
Review
9781305096691
418
#13
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(E) create and use representations to organize, record, and communicate mathematical ideas
(iv) use representations to organize mathematical ideas
Instruction
9781305096691
153
Example 1
Activity
9781305096691
172
Practice, #2
Activity
9781305096691
173
#17
Review
9781305096691
418
#13
Assessment
9781305096691
419 420
Test, #7-8 #23
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(E) create and use representations to organize, record, and communicate mathematical ideas
(v) use representations to record mathematical ideas
Instruction
9781305096691
160 162
Example 1 Example 4
Activity
9781305096691
173
#17
Instruction
9781305096691
163
Example 6
Review
9781305096691
418
#13
Assessment
9781305096691
420
Test, #9-10, 22, 25
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(E) create and use representations to organize, record, and communicate mathematical ideas
(vi) use representations to communicate mathematical ideas
Instruction
9781305096691
157
Example 4
Activity
9781305096691
165
#21, 23
Review
9781305096691
418
#8
Review
9781305096691
419
#23-26
Assessment
9781305096691
201 420
Test, #8
Test, #10-14, 24
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(F) analyze mathematical relationships to connect and communicate mathematical ideas
(i) analyze mathematical relationships to connect mathematical ideas
Instruction
9781305096691
28 29
Mathematical Models Example 1-2
Activity
9781305096691
8 204
#5-50
Lab Exercise 3
Instruction
9781305096691
76 78 160
Right Triangle Trigonometry Example 1
Using Function Notation, Example 1
Review
9781305096691
23
#3-5
Assessment
9781305096691
419
Test, #5
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(F) analyze mathematical relationships to connect and communicate mathematical ideas
(ii) analyze mathematical relationships to communicate mathematical ideas
Instruction
9781305096691
391 392
Variation Example 1
Activity
9781305096691
172
Practice, #1-2
Instruction
9781305096691
365
Example 1
Activity
9781305096691
251 361
#23
Lab Exercise 5
Assessment
9781305096691
201 419
Test, #1 Test, #6
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication
(i) display mathematical ideas using precise mathematical language in written or oral communication
Instruction
9781305096691
54
Example1
Activity
9781305096691
281
Example 4
Instruction
9781305096691
167 168
Linear Functions as Models, Example 1 Example 1
Instruction
9781305096691
184 185
Example 2 Example 3
Instruction
9781305096691
281
Example 4
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication
(ii) display mathematical arguments using precise mathematical language in written or oral communication
Instruction
9781305096691
54
Example1
Activity
9781305096691
281
Example 4
Instruction
9781305096691
167 168
Linear Functions as Models, Example 1 Example 1
Instruction
9781305096691
184 185
Example 2 Example 3
Instruction
9781305096691
281
Example 4
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication
(iii) explain mathematical ideas using precise mathematical language in written or oral communication
Instruction
9781305096691
160
Example 1
Activity
9781305096691
45
#28
Activity
9781305096691
48
#27
Activity
9781305096691
60 119
#13 #1-2
Review
9781305096691
199 357
#1 #11
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication
(iv) explain mathematical arguments using precise mathematical language in written or oral communication
Instruction
Activity
9781305096691
45
#28
Activity
9781305096691
48
#27
Activity
9781305096691
60 119
#13 #1-2
Review
9781305096691
199 357
#1 #11
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication
(v) justify mathematical ideas using precise mathematical language in written or oral communication
Instruction
9781305096691
160
Example 1
Activity
9781305096691
385
#10
Activity
9781305096691
390
#10
Review
9781305096691
199
#18
Assessment
9781305096691
201
#8-9
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication
(vi) justify mathematical arguments using precise mathematical language in written or oral communication
Instruction
9781305096691
160
Example 1
Activity
9781305096691
385
#10
Activity
9781305096691
390
#10
Review
9781305096691
199
#18
Assessment
9781305096691
201
#8-9
(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
(A) use rates and linear functions to solve problems involving personal finance and budgeting, including compensations and deductions
(i) use rates to solve problems involving personal finance
Instruction
9781305096691
258 259
Mathematical Models in Personal Income
Example 1
Activity
9781305096691
264 270
#17
Lab Exercise 1
Instruction
9781305096691
260 262
Example 2 Example 3
Review
9781305096691
268 269
#9-29 #30-32, 37
Assessment
9781305096691
269 270
Test, #7-11 #12-20
(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
(A) use rates and linear functions to solve problems involving personal finance and budgeting, including compensations and deductions
(ii) use rates to solve problems involving budgeting, including compensations
Instruction
Activity
9781305096691
265
#19-20
Review
9781305096691
267
#4,8
Review
9781305096691
268
#33-34
Knowledge and Skills Statement
(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
Student Expectation
(A) use rates and linear functions to solve problems involving personal finance and budgeting, including compensations and deductions
(A) use rates and linear functions to solve problems involving personal finance and budgeting, including compensations and deductions
(A) use rates and linear functions to solve problems involving personal finance and budgeting, including compensations and deductions
(A) use rates and linear functions to solve problems involving personal finance and budgeting, including compensations and deductions
(B) solve problems involving personal taxes
(C) analyze data to make decisions about banking, including options for online banking, checking accounts, overdraft protection, processing fees, and debit card/ATM fees
Breakout
(iii) use rates to solve problems involving budgeting, including deductions
(iv) use linear functions to solve problems involving personal finance
(v) use linear functions to solve problems involving budgeting, including compensations
(vi) use linear functions to solve problems involving budgeting, including deductions
(i) solve problems involving personal taxes
(i) analyze data to make decisions about banking, including options for online banking
Citation Type
Instruction
Activity
Instruction
Activity
Review
Instruction
Activity
Activity
Review
Assessment
Instruction
Activity
Activity
Instruction
Activity
Instruction
Review
Assessment
Instruction
Activity
Instruction
Review
Assessment
Instruction
(Drop-down menu)
Component ISBN
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
Page (s)
259
264 265
260
271 272
36
169
172
173 174
198 199
201
172
173
167
172 173
170
198 199
201
252
174 202
258 259 260 262
267 269
269
Specific Location
Assessment
269
Test, #5
Example 1
#17 #19-20
Example 2
Lab Exercise 1 Lab Exercise 2
Example 5
Example 2
#1
#14 #20
Summary #20
Test, #7-8
#4
#15
Example 1
#2, 5-6 #8
Example 3
Summary #19
Test, #9
Mathematical Models in Stocks, Mutual Funds,
and Bonds
#20
Lab Exercise 1
#1-3 #35-36
Test, #1, 6
Mathematical Models in Personal Income Example 1
Example 2
Example 3
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
(C) analyze data to make decisions about banking, including options for online banking, checking accounts, overdraft protection, processing fees, and debit card/ATM fees
(ii) analyze data to make decisions about banking, including checking accounts
Instruction
(Drop-down menu)
(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
(C) analyze data to make decisions about banking, including options for online banking, checking accounts, overdraft protection, processing fees, and debit card/ATM fees
(iii) analyze data to make decisions about banking, including overdraft protection
Instruction
(Drop-down menu)
(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
(C) analyze data to make decisions about banking, including options for online banking, checking accounts, overdraft protection, processing fees, and debit card/ATM fees
(iv) analyze data to make decisions about banking, including processing fees
Instruction
(Drop-down menu)
(2) Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
(C) analyze data to make decisions about banking, including options for online banking, checking accounts, overdraft protection, processing fees, and debit card/ATM fees
(v) analyze data to make decisions about banking, including debit card/ATM fees
Instruction
(Drop-down menu)
(3) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, graphs, and amortization modeling to solve problems involving credit. The student is expected to:
(A) use formulas to generate tables to display series of payments for loan amortizations resulting from financed purchases
(i) use formulas to generate tables to display series of payments for loan amortizations resulting from financed purchases
Instruction
(Drop-down menu)
(3) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, graphs, and amortization modeling to solve problems involving credit. The student is expected to:
(B) analyze personal credit options in retail purchasing and compare relative advantages and disadvantages of each option
(i) analyze personal credit options in retail purchasing
Instruction
9781305096691
226 227
Mathematical Models in Consumer Credit Example 1, 2
Activity
9781305096691
232 238
#5-30 #1-30
Instruction
9781305096691
233
234 235
Mathematical Models in Purchasing an Automobile, Example 1
Example 2
Example 3
Review
9781305096691
269
#16-26
Assessment
9781305096691
269 270
Test, #10-11 #12-16
(3) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, graphs, and amortization modeling to solve problems involving credit. The student is expected to:
(B) analyze personal credit options in retail purchasing and compare relative advantages and disadvantages of each option
(ii) compare relative advantages of each option
Instruction
9781305096691
226 227
Mathematical Models in Consumer Credit Example 1, 2
Activity
9781305096691
232 238
#5-30 #1-30
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
Instruction
9781305096691
233
234 235
Mathematical Models in Purchasing an Automobile, Example 1
Example 2
Example 3
Review
9781305096691
269
#16-26
Assessment
9781305096691
269 270
Test, #10-11 #12-16
(3) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, graphs, and amortization modeling to solve problems involving credit. The student is expected to:
(B) analyze personal credit options in retail purchasing and compare relative advantages and disadvantages of each option
(iii) compare relative disadvantages of each option
Instruction
9781305096691
226 227
Mathematical Models in Consumer Credit Example 1, 2
Activity
9781305096691
232 238
#5-30 #1-30
Instruction
9781305096691
233
234 235
Mathematical Models in Purchasing an Automobile, Example 1
Example 2
Example 3
Review
9781305096691
269
#16-26
Assessment
9781305096691
269 270
Test, #10-11 #12-16
(3) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, graphs, and amortization modeling to solve problems involving credit. The student is expected to:
(C) use technology to create amortization models to investigate home financing and compare buying a home to renting a home
(i) use technology to create amortization models to investigate home financing
Instruction
(Drop-down menu)
(3) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, graphs, and amortization modeling to solve problems involving credit. The student is expected to:
(C) use technology to create amortization models to investigate home financing and compare buying a home to renting a home
(ii) use technology to create amortization models to compare buying a home to renting a home
Instruction
(Drop-down menu)
(3) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, graphs, and amortization modeling to solve problems involving credit. The student is expected to:
(D) use technology to create amortization models to investigate automobile financing and compare buying a vehicle to leasing a vehicle
(i) use technology to create amortization models to investigate automobile financing
Instruction
(Drop-down menu)
(3) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, graphs, and amortization modeling to solve problems involving credit. The student is expected to:
(D) use technology to create amortization models to investigate automobile financing and compare buying a vehicle to leasing a vehicle
(ii) use technology to create amortization models to compare buying a vehicle to leasing a vehicle
Instruction
(Drop-down menu)
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(A) analyze and compare coverage options and rates in insurance
(i) analyze coverage options in insurance
Instruction
9781305096691
246 248
Mathematical Models in Insurance Options and Rates Example 1, 2
Activity
9781305096691
251
#10-25
Instruction
9781305096691
249 250
Example 3 Example 4
Review
9781305096691
268
#28
Assessment
9781305096691
270
#17
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(A) analyze and compare coverage options and rates in insurance
(ii) analyze coverage rates in insurance
Instruction
9781305096691
246 248
Mathematical Models in Insurance Options and Rates Example 1, 2
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
Activity
9781305096691
251
#10-25
Instruction
9781305096691
249 250
Example 3 Example 4
Review
9781305096691
268
#28
Assessment
9781305096691
270
#17
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(A) analyze and compare coverage options and rates in insurance
(iii) compare coverage options in insurance
Instruction
9781305096691
246
Mathematical Models in Insurance Options and Rates
Activity
9781305096691
251
#10-25
Instruction
9781305096691
248
Example 1, 2
Instruction
9781305096691
249
Example 3
Instruction
9781305096691
250
Example 4
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(A) analyze and compare coverage options and rates in insurance
(iv) compare coverage rates in insurance
Instruction
9781305096691
246
Mathematical Models in Insurance Options and Rates
Activity
9781305096691
251
#10-25
Instruction
9781305096691
248
Example 1, 2
Instruction
9781305096691
249
Example 3
Instruction
9781305096691
250
Example 4
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(B) investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans
(i) investigate investment options, including stocks
Instruction
9781305096691
252 253
Mathematical Models in Stocks, Mutual Funds, and Bonds; Example 1
Example 2
Activity
9781305096691
256
Practice, #1-4
Instruction
9781305096691
255
Example 3
Activity
9781305096691
257
#5-12
Activity
9781305096691
274
Lab Exercise 5
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(B) investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans
(ii) investigate investment options, including bonds
Instruction
9781305096691
252 253
Mathematical Models in Stocks, Mutual Funds, and Bonds; Example 1
Example 2
Review
9781305096691
266
Summary
Instruction
9781305096691
255
Example 3
Review
9781305096691
269
#30-31
Assessment
9781305096691
270
#19-20
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(B) investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans
(iii) investigate investment options, including annuities
Instruction
9781305096691
250
Example 4
(Drop-down menu)
Instruction
9781305096691
256
Paragraph 1-6
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(B) investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans
(iv) investigate investment options, including certificates of deposit
Instruction
9781305096691
225
Example 7
Activity
9781305096691
270
Lab Exercise 1
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(B) investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans
(v) investigate investment options, including retirement plans
Instruction
9781305096691
252
Mathematical Models in Banking; Example 1
(Drop-down menu)
Instruction
9781305096691
253
Example 2
Instruction
9781305096691
255
Example 3
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(B) investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans
(vi) compare investment options, including stocks
Instruction
9781305096691
246
Mathematical Models in Insurance Options and Rates
Activity
9781305096691
258
#17, 19
Instruction
9781305096691
248
Example 1, 2
Instruction
9781305096691
249
Example 3
Instruction
9781305096691
250
Example 4
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(B) investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans
(vii) compare investment options, including bonds
Instruction
9781305096691
252
Mathematical Models in Banking; Example 1
Activity
9781305096691
258
#17, 19
Instruction
9781305096691
253
Example 2
Instruction
9781305096691
255
Example 3
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(B) investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans
(viii) compare investment options, including annuities
Instruction
9781305096691
250
Example 4
(Drop-down menu)
Instruction
9781305096691
256
Paragraph 1-6
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(B) investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans
(ix) compare investment options, including certificates of deposit
Instruction
Activity
9781305096691
226
#26
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(B) investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans
(x) compare investment options, including retirement plans
Instruction
9781305096691
250
Example 4
Activity
9781305096691
258
#19
Instruction
9781305096691
252
Mathematical Models in Banking; Example 1
Instruction
9781305096691
253
Example 2
Instruction
9781305096691
255
Example 3
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(C) analyze types of savings options involving simple and compound interest and compare relative advantages of these options
(i) analyze types of savings options involving simple interest
Instruction
9781305096691
218 219
Mathematical Models in Banking; Example 1
Example 2-3
Activity
9781305096691
225 238 268
Practice, #1-8, 15-16 Practice, #23-26 #9-11, 20
Instruction
9781305096691
227 233
254
Example 1
Mathematical Models in Purchasing an Automobile
Example 2
Review
9781305096691
266
Summary
Assessment
9781305096691
269
Test, # 8
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(C) analyze types of savings options involving simple and compound interest and compare relative advantages of these options
(ii) analyze types of savings options involving compound interest
Instruction
9781305096691
220
Example 3
Activity
9781305096691
226
#21-35
Instruction
9781305096691
221
Example 4
Activity
9781305096691
270
Lab Exercise 1
Review
9781305096691
266
Summary
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
(4) Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
(C) analyze types of savings options involving simple and compound interest and compare relative advantages of these options
(iii) compare relative advantages of these options
Instruction
9781305096691
221
Example 4
Activity
9781305096691
226
#26
Review
9781305096691
226
Summary
(5) Mathematical modeling in science and engineering. The student applies mathematical processes with algebraic techniques to study patterns and analyze data as it applies to science. The student is expected to:
(A) use proportionality and inverse variation to describe physical laws such as Hook's Law, Newton's Second Law of Motion, and Boyle's Law
(i) use proportionality to describe physical laws
Instruction
9781305096691
174
Direct and Inverse Variation
Activity
9781305096691
179 181
Practice, #15-19 #43-44
Instruction
9781305096691
175
Example 2
Review
9781305096691
198 200
Summary #31-33
Assessment
9781305096691
201
Test, #13
(5) Mathematical modeling in science and engineering. The student applies mathematical processes with algebraic techniques to study patterns and analyze data as it applies to science. The student is expected to:
(A) use proportionality and inverse variation to describe physical laws such as Hook's Law, Newton's Second Law of Motion, and Boyle's Law
(ii) use inverse variation to describe physical laws
Instruction
9781305096691
174 175
Direct and Inverse Variation Example 1, 2
Activity
9781305096691
179 180
Practice, #1-6, 8, 12-14, 17-18 20, 23-24, 33-34, 36-39, 42-44
Instruction
9781305096691
176 177
Example 3, 4 Example 5
Review
9781305096691
198 200
Summary
#25-26, 28, 30, 32, 34, 36
Assessment
9781305096691
201
Test, #11-13
(5) Mathematical modeling in science and engineering. The student applies mathematical processes with algebraic techniques to study patterns and analyze data as it applies to science. The student is expected to:
(B) use exponential models available through technology to model growth and decay in areas, including radioactive decay
(i) use exponential models available through technology to model growth in areas
Instruction
9781305096691
193 195
Example 1 Example 2
Activity
9781305096691
196 197
Practice, #12-13 #4, 16, 25-28
Activity
9781305096691
208
Lab Exercise 8
Review
9781305096691
198 200 201
Summary #41
#44
Assessment
9781305096691
202
#18
(5) Mathematical modeling in science and engineering. The student applies mathematical processes with algebraic techniques to study patterns and analyze data as it applies to science. The student is expected to:
(B) use exponential models available through technology to model growth and decay in areas, including radioactive decay
(ii) use exponential models available through technology to model decay in areas, including radioactive decay
Instruction
9781305096691
193
Example 1
Activity
9781305096691
197 208
#15, 17-24 Lab Exercise 9
Instruction
9781305096691
195
Example 3, 4
Review
9781305096691
198 200 201
Summary #42-43 #45-46
Assessment
9781305096691
202
#19
(5) Mathematical modeling in science and engineering. The student applies mathematical processes with algebraic techniques to study patterns and analyze data as it applies to science. The student is expected to:
(C) use quadratic functions to model motion
(i) use quadratic functions to model motion
Instruction
9781305096691
185
Example 3
Activity
9781305096691
192
#33, 37
Instruction
9781305096691
186
Example 6
Activity
9781305096691
?
Review
9781305096691
202
#21-24
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(A) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in architecture
(i) use similarity to describe mathematical patterns in architecture
Instruction
9781305096691
91
Example 6
Activity
9781305096691
94
#27-30
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
Activity
9781305096691
106
Lab Exercise 4
Review
9781305096691
101 103
Summary #23
Assessment
9781305096691
105
#23-24
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(A) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in architecture
(ii) use similarity to describe mathematical structure in architecture
Instruction
9781305096691
91
Example 6
Activity
9781305096691
94
#27-30
Activity
9781305096691
106
Lab Exercise 4
Review
9781305096691
101 103
Summary #23
Assessment
9781305096691
105
#23-24
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(A) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in architecture
(iii) use geometric transformations to describe mathematical patterns in architecture
Instruction
9781305096691
84 86
Models and Patterns in Art, Architecture, and Nature Example 1
Activity
9781305096691
92
Practice,#4
Instruction
9781305096691
87 88
Example 2 Example 3
Activity
9781305096691
93
#5-11
Review
9781305096691
103
#20
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(A) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in architecture
(iv) use geometric transformations to describe mathematical structure in architecture
Instruction
9781305096691
84 86
Models and Patterns in Art, Architecture, and Nature Example 1
Activity
9781305096691
92
Practice,#4
Instruction
9781305096691
87 88
Example 2 Example 3
Activity
9781305096691
93
#5-11
Review
9781305096691
103
#20
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(A) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in architecture
(v) use symmetry to describe mathematical patterns in architecture
Instruction
9781305096691
84 86
Models and Patterns in Art, Architecture, and Nature Example 1
Activity
9781305096691
92
Practice,#3-4
Instruction
9781305096691
87 88
Example 2 Example 3
Activity
9781305096691
93
#5-8
Review
9781305096691
103
#20
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(A) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in architecture
(vi) use symmetry to describe mathematical structure in architecture
Instruction
9781305096691
84 86
Models and Patterns in Art, Architecture, and Nature Example 1
Activity
9781305096691
92 93
Practice,#3-4 #5-8
Instruction
9781305096691
87 88
Example 2 Example 3
Review
9781305096691
103
#20
Assessment
9781305096691
104
#19-20
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(A) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in architecture
(vii) use perspective drawings to describe mathematical patterns in architecture
Instruction
9781305096691
84
Models and Patterns in Art, Architecture, and Nature
Activity
9781305096691
92
Practice,#1-2
Instruction
9781305096691
86
Example 1
Instruction
9781305096691
87
Example 2
Activity
9781305096691
93
#13
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(A) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in architecture
(viii) use perspective drawings to describe mathematical structure in architecture
Instruction
9781305096691
84
Models and Patterns in Art, Architecture, and Nature
Activity
9781305096691
92
Practice,#1-2
Instruction
9781305096691
86
Example 1
Instruction
9781305096691
87
Example 2
Activity
9781305096691
93
#13
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(B) use scale factors with two-dimensional and three- dimensional objects to demonstrate proportional and non-proportional changes in surface area and volume as applied to fields
(i) use scale factors with two- dimensional objects
Instruction
9781305096691
88 89 91
Example 3 Example 4, 5 Example 6
Activity
9781305096691
39
#51-52
Activity
9781305096691
93 94 105
#15-20 #21-26
Lab Exercise 1
Review
9781305096691
103
#21-24
Assessment
9781305096691
104
#21-22
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(B) use scale factors with two-dimensional and three- dimensional objects to demonstrate proportional and non-proportional changes in surface area and volume as applied to fields
(ii) use scale factors with three-dimensional objects to demonstrate proportional changes in surface area as applied to fields
Instruction
9781305096691
59
Example 7
Activity
9781305096691
62
#34
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(B) use scale factors with two-dimensional and three- dimensional objects to demonstrate proportional and non-proportional changes in surface area and volume as applied to fields
(iii) use scale factors with three-dimensional objects to demonstrate proportional changes in volume as applied to fields
Instruction
9781305096691
59
Example 7
Activity
9781305096691
62
#34
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(B) use scale factors with two-dimensional and three- dimensional objects to demonstrate proportional and non-proportional changes in surface area and volume as applied to fields
(iv) use scale factors with three-dimensional objects to demonstrate non- proportional changes in surface area as applied to fields
Instruction
(Drop-down menu)
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(B) use scale factors with two-dimensional and three- dimensional objects to demonstrate proportional and non-proportional changes in surface area and volume as applied to fields
(v) use scale factors with three-dimensional objects to demonstrate non- proportional changes in volume as applied to fields
Instruction
(Drop-down menu)
Knowledge and Skills Statement
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(6) Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
Student Expectation
(C) use the Pythagorean Theorem and special right- triangle relationships to calculate distances
(C) use the Pythagorean Theorem and special right- triangle relationships to calculate distances
(D) use trigonometric ratios to calculate distances and angle measures as applied to fields
(D) use trigonometric ratios to calculate distances and angle measures as applied to fields
(A) use trigonometric ratios and functions available through technology to model periodic behavior in art and music
(A) use trigonometric ratios and functions available through technology to model periodic behavior in art and music
Breakout
(i) use the Pythagorean Theorem to calculate distances
(ii) use special right-triangle relationships to calculate distances
(i) use trigonometric ratios to calculate distances as applied to fields
(ii) use trigonometric ratios to calculate angle measures as applied to fields
(i) use trigonometric ratios available through technology to model periodic behavior in art
(ii) use trigonometric ratios available through technology to model periodic behavior in music
Citation Type
Instruction
Activity
Instruction
Review
Assessment
Instruction
Activity
Instruction
Review
Assessment
Instruction
Activity
Instruction
Instruction
Activity
Instruction
Activity
Instruction
Instruction
Activity
Instruction
(Drop-down menu)
Instruction
Activity
Instruction
Review
Assessment
Component ISBN
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
9781305096691
Page (s)
70 71
74 75 76
72
101 102
103 104
70 71
74 75 76
72
101 102
103 104
62
67 68
64
65 66
69 70
62
67 68
64
65 66
69 70
86
94 95 96
100 106
97 98 99
103
104
Specific Location
Models and Patterns in Right Triangles
Example 1, 2
#1-11 # 12-23 #24-28
Example 3, 4
Summary #13-14
Test, #1 #7
Models and Patterns in Right Triangles
Example 1, 2
#1-11 # 12-23 #24-28
Example 3, 4
Summary #13-14
Test, #1 #7
Models and Patterns in Triangles, Example 1
Models and Patterns in Triangles, Example 1
Practice, #1-10 #11-19
Example 2
Example 3 Example 4, 5
#20-27 #28-30
Practice, #1-10 #11-19
Example 2
Example 3 Example 4, 5
#20-27 #28-30
Example 1
Models and Patterns in Music Example 1
Example 1
Practice, #1-26 Lab Exercise 6
Example 1 Continued Example 1 Continued Example 1 Continued
#25-27
#25-27
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(A) use trigonometric ratios and functions available through technology to model periodic behavior in art and music
(iii) use trigonometric functions available through technology to model periodic behavior in art
Instruction
9781305096691
86
Example 1
(Drop-down menu)
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(A) use trigonometric ratios and functions available through technology to model periodic behavior in art and music
(iv) use trigonometric functions available through technology to model periodic behavior in music
Instruction
9781305096691
94 95 96
Models and Patterns in Music Example 1
Example 1
Activity
9781305096691
100
Practice, #1-26
Instruction
9781305096691
97 98 99
Example 1 Continued Example 1 Continued Example 1 Continued
Review
9781305096691
103
#25-27
Assessment
9781305096691
104
#25-27
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(i) use similarity to describe mathematical patterns in art
Instruction
Activity
9781305096691
107
Lab Exercise 8
Activity
9781305096691
108
Lab Exercise 9
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(ii) use similarity to describe mathematical patterns in photography
Instruction
Activity
9781305096691
107
Lab Exercise 8
Activity
9781305096691
108
Lab Exercise 9
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(iii) use similarity to describe mathematical structure in art
Instruction
Activity
9781305096691
107
Lab Exercise 8
Activity
9781305096691
108
Lab Exercise 9
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(iv) use similarity to describe mathematical structure in photography
Instruction
Activity
9781305096691
107
Lab Exercise 8
Activity
9781305096691
108
Lab Exercise 9
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(v) use geometric transformations to describe mathematical patterns in art
Instruction
Activity
9781305096691
107
Lab Exercise 8
Activity
9781305096691
108
Lab Exercise 9
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(vi) use geometric transformations to describe mathematical patterns in photography
Instruction
Activity
9781305096691
107
Lab Exercise 8
Activity
9781305096691
108
Lab Exercise 9
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(vii) use geometric transformations to describe mathematical structure in art
Instruction
Activity
9781305096691
107
Lab Exercise 8
Activity
9781305096691
108
Lab Exercise 9
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(viii) use geometric transformations to describe mathematical structure in photography
Instruction
Activity
9781305096691
107
Lab Exercise 8
Activity
9781305096691
108
Lab Exercise 9
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(ix) use symmetry to describe mathematical patterns in art
Instruction
9781305096691
84
86 87
Models and Patterns in Art, Architecture, and Nature Example 1
Example 2
Activity
9781305096691
92 93
Practice, #1-4 #5-30
Instruction
9781305096691
88 89 91
Example 3 Example 4, 5 Example 6
Review
9781305096691
103
#20
Assessment
9781305096691
104
#19-20
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(x) use symmetry to describe mathematical patterns in photography
Instruction
(Drop-down menu)
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(xi) use symmetry to describe mathematical structure in art
Instruction
9781305096691
84
86 87
Models and Patterns in Art, Architecture, and Nature Example 1
Example 2
Activity
9781305096691
92 93
Practice, #1-4 #5-30
Instruction
9781305096691
88 89 91
Example 3 Example 4, 5 Example 6
Review
9781305096691
103
#20
Assessment
9781305096691
104
#19-20
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(xii) use symmetry to describe mathematical structure in photography
Instruction
Knowledge and Skills Statement
Student Expectation
Breakout
Citation Type
Component ISBN
Page (s)
Specific Location
(Drop-down menu)
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(xiii) use perspective drawings to describe mathematical patterns in art
Instruction
9781305096691
84
86 87
Models and Patterns in Art, Architecture, and Nature Example 1
Example 2
Activity
9781305096691
92 93
Practice, #1-4 #5-30
Instruction
9781305096691
88 89 91
Example 3 Example 4, 5 Example 6
Review
9781305096691
103
#20
Assessment
9781305096691
104
#19-20
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(xiv) use perspective drawings to describe mathematical patterns in photography
Instruction
(Drop-down menu)
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(xv) use perspective drawings to describe mathematical structure in art
Instruction
9781305096691
84
86 87
Models and Patterns in Art, Architecture, and Nature Example 1
Example 2
Activity
9781305096691
92 93
Practice, #1-4 #5-30
Instruction
9781305096691
88 89 91
Example 3 Example 4, 5 Example 6
Review
9781305096691
103
#20
Assessment
9781305096691
104
#19-20
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(B) use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography
(xvi) use perspective drawings to describe mathematical structure in photography
Instruction
(Drop-down menu)
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(C) use geometric transformations, proportions, and periodic motion to describe mathematical patterns and structure in music
(i) use geometric transformations to describe mathematical patterns in music
Instruction
9781305096691
94 95 96
Models and Patterns in Music Example 1
Example 1
Activity
9781305096691
100 106
Practice, #1-26 Lab Exercise 3
Instruction
9781305096691
97 98 99
Example 1 Continued Example 1 Continued Example 1 Continued
Review
9781305096691
101
Summary
Assessment
9781305096691
105
#25-27
(7) Mathematical modeling in fine arts. The student uses mathematical processes with algebra and geometry to study patterns and analyze data as it applies to fine arts. The student is expected to:
(C) use geometric transformations, proportions, and periodic motion to describe mathematical patterns and structure in music
(ii) use geometric transformations to describe mathematical structure in music
Instruction
9781305096691
94 95 96
Models and Patterns in Music Example 1
Example 1
Activity
9781305096691
100 106
Practice, #1-26 Lab Exercise 3
Instruction
9781305096691
97 98 99
Example 1 Continued Example 1 Continued Example 1 Continued
Review
9781305096691
101
Summary
Assessment
9781305096691
105
#25-27
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