Teks Book Additional Mathematics KSSM (F5)

(b) y 2.
(a) 30x + 25y < 3 000, x > 20, y > x + 10 (b) y
100
90
80
70
60
50
40
30
20
10
0
(c) (i)
40x + 20y = 2 000 y = 3x
(20, 60)
R
30x + 60y = 1 800
10 20 30 40 50 60 70
x
Formative Exercise
7.2
15
(ii) RM21 000
2x + 3y = 60 105 R y = 5
y = 4x (16, 64)
R
80
70
60
50
40
30
20
10
0
30x + 60y > 1 800 or its equivalent, (b) y < 3x or its equivalent
x + y = 80 10 20 30 40 50 60 70 80
x = 20
y = x + 10 R
30x + 25y = 3 000 20 40 60 80 100 x
(c) (i)
2. (a) 40x + 20y < 2 000 or its equivalent,
3.
(a) x + y < 7 000, y < 2x, y > 1 000 (b) y
30 < y < 60 (ii) RM5 440
y
7 000 6 000 5 000 4 000 3 000 2 000 1 000
0
x + y = 7 000 y = 2x R
y = 1 000
1 000 2 000 3 000 4 000 5 000 6 000 7 000
1. (a) 4x + 5y > 1 000 or its equivalent, 0.4x + 0.3y < 300 or its equivalent,
3x + 5y = 60 x 0 5 10 15 20 25 30 35
(i) x = 5, y = 17 (ii) RM1 560 5x + 6y > 60, 3x + 4y < 60, x < 2y
y
(b) y – x < 200 or its equivalent
900
800
700
600
500
400
300
200
100
0.4x + 0.3y = 300 (b) y – x = 200
16 14 12 10
y – x = 10
120
100
80
60
40
20
(c) y 2. (a)
(342, 542)
R
4x + 5y = 1 000
0 100 200 300 400 500 600 700
x
8R
6
4
2 5x + 6y = 60
0 2 4 6 8 10 12 14 16 18 20 x (c) RM324
(c) (i) 500 (ii) RM2 497.80
x
20 15
x
0
(c) RM1 350
(c) (i) 5 000 litres (ii) RM330 000
Summative Exercise
1. (a) (b)
3x + 5y > 60, 2x + 3y < 60, x > 5, y > 5
y
x =5 (5, 17)
3x + 4y = 60
x = 2y
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3. (a) 12x + 5y < 60, y < 3x, y > 2
2. (a) –8 ms–1 3. (a) –8 ms–2
Self-Exercise
1. (a) 68 m
2. (a) (i) 8 m
Formative Exercise
(b) 1 s and 7 s (b) 2 s
(c) 1 , t , 7 (c) t , 2
(b) 7 m
(b)
y
(b)
y
Self-Exercise 8.3
1. 2.
12 10 8 6 4 2
12x + 5y = 60
y = 3x
8.2
(b) 111 m 45 m
12 11 10
(a) v = 4 − 8t + 3t2 (c) v = 6t2 – 8t + 2 (e) v = 6t2 – 18t – 5 (a) a = 2t – 1
x + y = 80
s = (t – 2)2
8.1
(ii)
R
y= 2
1.(a)t(s) 1 2 3 4 5 s(m) –3 –4 –3 0 5
0
1 2 3 4 56 7
x
(b)
(a) 2
0, 320 m (a) 4 ms–2 (a) 21 m
s = t2 – 4t
s (m) 5
(c) 4 s
(c)(i) 1<y<4
(ii) RM800
or y < 3x, 100x + 120y > 5 000
4. (a) x + y < 80,
x1
(b)
y
0 2 45 –4
y
> 3 y = 3x
t (s) (b) (i)
80
70
60
50
40
30
20
10
(c) (i) 33 (ii) RM2 300 5. (a) 2x + 5y < 30, 3x + 2y < 24, x < 2y
2. 3. 5. 6. 7.
14 m
(ii) 35 m 9 ms–1, 23 ms–1
4.
(b) t . 2 (b) 55 m
(a) 0123456
Time, t (s)
Displacement, s (m)
R
0 10 20 30 40 50 60 70 80 x
(b)
s (m) 21
9 6 5 6 9 14 21 + 5 (c) 20 m
(b) v = 16 – 2t
(d) v = 27t2 + 24t3 + 5t4 (f) v = t2 – 6t + 5
(b) a = 6t – 10
(d) a = 18t – 30
9
8
7 68
3x + 2y = 24 (5, 4)
t2
(a) v = 2 – 2t, a = –2
(f) a = 18t2 + 8
3.
(b) s/v/a 9
t3
95
0 2 6
t (s)
(c) a = –12t (e) a = 6t + 1
x = 2y
54
2
0 1 2 4
t
3 R 2
1
–2 a=–2
2x + 5y = 30 0 2 4 6 8 10 12 14
–6 v = 2 – 2t
(c) (i) 4 (ii) RM2 000
CHAPTER 8 KINEMATICS OF LINEAR MOTION
(b) (i) 12 second (ii) 2 seconds (iii) 3 seconds 2. (a) 8 ms–1 (b) 23 second, 1 second
Self-Exercise 8.1 1. (a) (i) –3 m
(ii) 4 s
(ii) –5 m (c) t . 3
(c)0<t, 23 ort.1 Self-Exercise 8.5
1. (a) 8 ms–2 (b) –8 ms–2 (c) 4 seconds 2. (a) 1 second (b) t , 1
x
Self-Exercise 8.4 1. (a) (i) –2 ms–1
(ii) 5 ms–1 (iii) 21 ms–1
292
(b) (i) 3 s
100x + 120y = 5 000
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Formative Exercise 8.2 1. (a) –2 ms–1
(c) 4 m
–1 (iii) –1.5 ms
(b) –12 ms–1 (c) 6 ms–2 (ii) 12 mmin–1
v=6t2 –18t+12
t (s)
The particle is at point X after 0.5 second with a velocity
2. (a) h = 1, k = 1
2 –1 –1
(b)
4. (a) (b)
(c) 6 seconds
8. (a) –10 ms–1 9. (a) t = 4
(b) (i) 1 ms (ii) 0 ms 3. (a) v = 3t2 – 10t – 8, a = 6t – 10
0 1 3
3. (a) m = 12.5, n = –12.5
t (s)
14. (a) (i) (b)
6 cms–1 (ii) 1 , t , 6 v (ms–1)
6
01 1 6 t(s)
(iii) t . 2
12
0 46t(s) (a)47m
(c) 2 ,t,2 3
Summative Exercise
(a) 208 m (b) 48 ms–1
(c)t.3
v (ms–1)
(c) 4 s (e) 84 m
(b) 2 ms–1 (b) –2 ms–1 (b) –12 ms–1 (c) 1.5 s
(b) 14 m
(b) –16 m (b) 8 m
– 18t, v = 4t2
(b) 35 m on the right O
12
(b) No
(c) 20 m
15.
–6 4 (a) –1 ms–1
(b) 43 m v=t2–6t+8
18 m
2. (a) –7 m
3. (a) (i) 12 mmin–1
(b) 3 seconds (d)10m (e)t.1
(iii) 6 mmin–2
v (ms–1) 36
(iv) 149 m
(b) –11 ms–1, 8 ms–2 (d) 1 s, 6 s
Self-Exercise 8.6
1. (a) 10 ms–1
2. (a) –13 ms–1 3. (a)2,t,6 4. (a) 32 cms–1
Self-Exercise 8.7 1. (a)2712m
(b) 36 cms–1
(d) 9 s
of 5 ms–1. 8 ms–1
t = 1 s, 3 s
7. (a) m = 5, n = –20
5. (a) 6. (a)
(b) –10 m (b) 69 13 m
0
1.5
–1.5 1
v = 10t, s = 5t2
4
2
2. (a) –10 m
3. (a) 48 m
(b) s = 56 t3 – 10t2 + 30t 35
4. (a) s = 43t3 (c) 9 km
+ 3t2 8.3
– 6t – 18
(d) 6 m (b) 14 ms–2 (b) 113 m
Formative Exercise
6
(c) The car reverses for 4 seconds and then moves forward.
1. (a) 42 ms–1
10. (b) –43 m
11. (a) v = (3t2 – 3) ms–1, a = 6t ms–2
2. (a) 24 ms–2
(b) 2 s
(c) 6 s
(c) 189 m (c) 63 m
3. (a) m = –10, n = 4 27
(b) –24.5 ms–1 5
(b) The particle moves to the left with initial velocity of –3 ms–1 and zero acceleration. For t = 2, the particle moves to the right with velocity of 9 ms–1 and experiences acceleration of 12 ms–2.
4. (a)–2m
5. (a) 18 ms–1
6. (a)25s 2
(b) t , 4
(b) t = 0 s, 6 s
(c) 40 m 3
Self-Exercise 8.8 1. (a) 2 seconds
(b) 75 ms–1
16 8
(c)t.1
12. (a) h = 3, k = –9
(b) 4.5 s
(c) 625 m (b) s = 20t – 5t2
(ii)
(c) 18 ms–2
(d) 14.5 m
(c) (i) 20 m 2. (a) 8 ms–1
4 seconds
(c)
(d) 16 m 3
(b) (i) v (ms–1) 8
(ii)
(c) 17 m
v (ms–1)v=8t–2t2 –6 2
0 t (s) 1 2 3
–6 7
13. (a) 2 ms–1
(b) 3 seconds
6 v = 6 + 4t – 2t2
(c) 125 km 12
(b) –3.125 kmh–1
(b) 9 m
v=t2 –7t+6 3 3 — —2 2
4. (a) 20 ms–2 Formative Exercise
8.4
1. 2. 3.
4.
1.
(a) 56 ms–1
–1–1 1
(a) 8 ms (a) t , 2 (d) s (m)
(b) 104 m
(b) 40 ms —
(b)–43ms–1 (d) 86 m
15 8
27
(c) –12 ms–2
(d) t = 3 s, 5 s
0 2 3 4 7 t(s) –1
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Glossary
Acceleration (Pecutan) Rate of change of velocity. Arc of a circle (Lengkok bulatan) Arc is part of the
Indefinite integral (Kamiran tak tentu) Integration without limits.
Instantaneous acceleration (Pecutan seketika) Rate of change in velocity at a particular time.
Integration (Kamiran) A concept in calculus which is the inverse of differentiation.
Kinematic of linear motion (Kinematik gerakan linear) Kinematic means the movement of an object represented by a straight line in words, diagrams, numbers, graphs and equations.
Limit (Had) The value of a function when a variable approaches a certain value.
Maximum displacement (Sesaran maksimum) Distance between the end point and the starting point in a straight line when the velocity is zero.
Negative angle (Sudut negatif) The angle formed by rotating a straight line at an origin clockwise from the positive x-axis.
Normal (Normal) A perpendicular straight line to its tangent line.
Normal distribution (Taburan normal) A continuous random variable and is one of the most important distributions in statistics because it represents many natural phenomena. The distribution graph is bell-shaped.
Objective function (Fungsi objektif) A function used to determine the optimal value.
Positive angle (Sudut positif) An angle formed by rotating a straight line at an origin anticlockwise from the positive x-axis.
Radian (Radian) The unit used to measure the size of an angle in circular measure.
Radius (Jejari) A straight line from the centre of the circle to any point on the circumference of the circle.
Random variables (Pemboleh ubah rawak) A random variable is a variable whose value is numeric and from a random phenomenon.
Segment (Tembereng) Region that is bounded by a curve and a chord.
Standard normal distribution (Taburan normal piawai) A normal distribution with a mean of 0 and a standard deviation of 1.
circumference of the circle.
Binomial distribution (Taburan binomial) The probability distribution involving n Bernoulli trials which are similar or identical where the possibility of ‘success’ is constant in every trial and every trial is independent of each other.
Binomial experiment (Eksperimen binomial) Composed of n Bernoulli trials which are independent but similar. Each trial has only two outcomes, which are ‘success’ and ‘failure’.
Chord (Perentas) A straight line connecting any two points on the circumference of the circle.
Circumference of a circle (Lilitan bulatan) Perimeter for a circle.
Combination (Gabungan) A selection of all or part of a set of objects, regardless of their orders of the selected objects.
Complementary angle (Sudut pelengkap) Angle A is the complementary angle of angle B if A + B = 90°.
Composite function (Fungsi gubahan) A function that combines two or more functions.
Constant velocity (Halaju malar) The velocity of linear motion of an object that is not changing.
Constraint (Kekangan) Limitations within a situation like a lack of raw materials, capital, operating time and so on.
Definite integral (Kamiran tentu) An integration whose value is fixed by a certain range of values.
Event (Peristiwa) Set of possible outcomes for an experiment. An event is a subset of sample space.
Factorial (Faktorial) n objects can be arranged in n(n – 1)(n – 2)...(3)(2)(1) ways. This product can be represented by the symbol n! which is called a
n factorial.
Feasible region (Rantau tersaur) A region that satisfies all the mathematical model requirements for a situation.
Generated volume (Isi padu janaan) The volume of an object formed when a shaded region rotates on an axis, which can be the x-axis or the y-axis.
Gradient of tangent (Kecerunan tangen) Gradient of a straight line that touches a curve at only one point.
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References
Barret, R. (2008). NCEA Level 2 Mathematics Year 12. New Zealand: ESA Publications (NZ) Ltd.
Chow, W. K. (2013). Discovering Mathematics (2nd ed.). Singapore: Star Publishing Pte Ltd.
Deborah, B. (2012). Complete Mathematics for Cambridge Secondary 1. UK: Oxford University Press.
Greenwood, D., Robertson, D., Woolley, S., Goodman, J. & Vaughan, J. (2017). Essential Mathematics for the Australian Curriculum Year 10. Australia: Cambridge University Press.
Ho, S. T., Khor, N. H. & Yan, K. C. (2013). Additional Mathematics 360. Marshall Cavendish Education.
Ho, S. T. & Khor, N. H. (2007). Additional Mathematics. Singapore: Panpac Education.
Dewan Bahasa dan Pustaka. Istilah Matematik untuk Sekolah-sekolah Malaysia (2003). Kuala Lumpur. Malaysia: Dewan Bahasa dan Pustaka.
Lim, L. N. (2007). GCE O Level Additional Mathematics Key Points Exam Guide. Singapore: Redpost Publications Pte Ltd.
Patrick, T. (2004). Mathematics Standard Level (3rd ed.). Australia: IBID Press.
Pemberton, S. (2016). Cambridge IGCSE and O Level Additional Mathematics Coursebook.
UK: Cambridge University Press.
Robert, H., Sandra, H., Michael, H., Matjut, M. & Mark, H. (2012). Mathematics for the International
Student: Mathematics SL (3rd ed.). Australia: Haese Mathematics.
Rondie, P. L., Kemp, E., Buchanan, L., Fensom, J. & Steve, J. (2012). Oxford IB Diploma Programme:
Mathematics Standard Level Course Companion. UK: Oxford University Press.
Teh, K. S & Looi, C. K. (2006). New Syllabus- Additional Mathematics (7th ed.). Singapore: Shinglee
Publishers Pte. Ltd.
Thomas, E. J. & Brunsting, J. R. (2010). Styles and Strategies for Teaching Middle School Mathematics. USA: Corwin Press.
Val, H. & Jeanette, P. (2018). Cambridge IGSCE ® and O Level Additional Mathematics. UK: Hodder Education.
Wong, M. K., Chen, C. W., Tan, P. L. & Nor A’idah Johari (2012). Matematik Tambahan Tingkatan 5. Malaysia: Percetakan Rina Sdn. Bhd.
Yeo, J., Keng, S. T., Cheng, Y. L. & Chow, I. (2013). New Syllabus Additional Mathematics. (9th ed.). Singapore: Shinglee Pte Ltd.
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Index
Acceleration 256, 257, 260, 262, 264, 265, 267, 269
Acceleration functions 267, 269
Approximation 30, 70, 71, 73, 76
Area of a sector 12, 13, 15, 17, 18, 20, 23
Area under the curve 95, 96 Bernoulli trial 152, 153, 154, 161,
184
Binomial experiment 152, 153, 155
Binomial random variables 153, 155
Chain rule 42, 46, 65, 66, 67, 76, 77
Chord 7
Circular measure 2, 20, 23
Circumference 5, 6, 12
Combination 132, 133, 135, 137, 138, 139
Complementary angles 194, 228
Constraints 234, 235, 237, 240, 246
Continuous random variables 143, 144, 166, 173, 184
Cosecant 193, 196
Cotangent 193, 196
Definite integral 92, 93, 94, 97, 114
Differentiation 260, 272
Discrete random variables 143, 144, 145, 148, 161, 184
Displacement 252, 253, 254, 255, 260, 262, 269, 275
Events 120, 121, 137
Factorial 122
Feasible region 240
First derivative 35, 36, 38, 39, 40, 43, 44, 49
First order differentiation 49, 63
Generated volume 106, 107, 111, 114
Gradient of tangent 34, 35, 36, 51, 52, 70
Indefinite integral 85, 86, 92, 114
Instant acceleration 256, 257
Integral 83, 85, 86, 87, 92, 93, 94, 97, 98, 99, 114, 117
Integration 82, 83, 85, 86, 87, 90, 92, 111, 114
Kinematics of linear motion 275
Limits 30, 31, 34, 35, 42, 76
Linear programming 234, 240, 246
Maximum point 57, 58, 59, 60, 62
Minimum point 57, 58, 59, 61, 62
Multiplication rule 120, 121, 122, 124, 128, 135, 137
Negative angles 190, 191, 198, 228
Normal 53, 76
Normal distribution 166, 167, 168, 170, 171, 172, 173, 174, 184, 185
Objective functions 234, 240, 242, 246
Optimal value 237, 246
Outcomes 142, 144, 145, 152, 153,
155, 156, 166, 169, 170
Permutation 121, 122, 123, 124, 125, 126, 127, 132, 134, 137, 138, 139
Point of inflection 57, 58, 62, 76
Positive angles 190, 191, 228
Probability 145, 148, 152, 153, 155, 156, 157, 158, 161, 166, 167, 168, 169, 173, 174, 175, 184
Radian 2, 3, 4, 6, 9, 13, 20, 23
Radius of a circle 2, 3
Random variables 142, 143, 144, 145, 148, 152, 153, 155, 156, 158, 161, 166, 170, 171, 172, 173, 184, 185
Random variations 169, 170
Rate of change 60, 65, 66, 67, 68, 76
Reference angle 197, 222, 228
Secant 193, 196
Sector of a circle 2, 18
Second derivative 49
Second order differentiation 60
Segment 23
Small changes 70, 71, 76
Standard deviation 162, 167, 169, 170, 171, 172, 184
Standard normal distribution 170, 172, 173, 174
Stationary point 57, 58, 76 Tangent 34, 35, 36, 38, 51, 52, 53,
55, 57, 58, 59, 60, 62, 70, 76
Trigonometric ratio 193, 196, 197, 198, 199, 212, 213, 215, 216, 222, 228
Turning point 57, 58, 59, 60, 61, 76, 77
Variance 162, 184
Velocity 254, 255, 256, 257, 260,
262, 264, 265, 267, 269, 275 Velocity at an instant 254, 256 Velocity function 267, 269
z score 171
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RM 10.50
ISBN 978-983-2914-68-6
9 789832 914686
FT435002
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