Prime Mathematics 7

From the above table, the ordered pair numbers are (1,4),
(3,6) and (5,8).
Plotting the ordered pairs (1,4), (3,6) and (5,8) and joining
these points gives a straight line passing through the points.

In the graph, we generally put independent variable (x) along
x-axis and the dependent variable(y) along y-axis.

Equation with two variables having the graph as a straight line
is called linear equation.

Example 1. Draw the graph of the equation 3x - y = 2.
Solution:

The given equation is 3x - y = 2
We can write the given equation as y = 3x - 2
When x = 1, then y = 3 × 1 - 2 = 1
When x = 3, then y = 3 × 3 - 2 = 7
When x = -1, then y = 3 ×(-1) -2 = -5

The values of x and y are shown in the following
table.

x 1 3 -1
y 1 7 -5

From the above table, the ordered pairs are (1,1), (3,7) and (-1,-5). Plotting the
ordered pairs and joining them, we get a straight line.

So, the straight line AB is a graph of the equation 3x - y = 2.

Exercise 14.3.5

1. Plot the following points in the graph paper.
a) A(-2,4) b) E(3,7) c) P(6,-6) d) P(-7,-2)
e) Q(-3,0) f) B(0,5) g) C(8,2) h) R(4,-3)

2. Draw the graph of the following equations.
a) x - y = 3 b) x - y = 0 c) y = 2x d) 2x - y + 3 = 0
e) 2x + y = 6 f) x - 2y + 4 = 0 g) x - 2 = y h) y = - 4x

3. Draw the graph of the equations 3x + 4y = 12 and 2x + 5y = 1 in the same graph
paper and answer the following questions.
a) Do these two lines intersect ?
b) Write the Coordinates of the point of intersection.
c) Does the point of intersection satisfy both the equations ?

294 Algebra

Unit Revision Test I

1. Find the degree of the polynomial 6x4 - 7x5 + 3.

2. Find the degree of the polynomial 2x2 - 5xy4 + 7xy - 2y3.

3. Is x3 - 4x + 2 - 7 a polynomial ? Give your answer with the suitable reason.
x

4. Write the name of the alegbric expression 2x3 - 4xy + 6 according to term.

5. Find the sum of 3x3 + 2y2 - 5z, 4x3 + 2z - 5y2 and 3y2 + 2x3 - 5x.

6. What should be added to 4x - 3 y + 7 so that the result will be 9x + 2y - 3 ?

7. Multiply

a) (5x - 3y) by 4xy b) (x2 - 2xy + 3y2) by 5xy2 c) (m2 - n) by (m + n)

8. Find the product of (4a - 5b) and (3a + 4b - 2c). Also find the value of the product
when a = 2, b = -3 and c = -2.

9. The length and breadth of a rectangle garden are (10a + 5b) units and (4a + 3b - c)
units respectively. Find the area of the garden. Also find the acutal area of the
garden when a = 4, b = 2 and c = -1

10. Divde
a) 18a2b by 6ab b) (4m3 - 6m2n + 8mn2) by 2mn

c) (25a2 - 36b2) by (5a + 6b) d) (2x3 - 5x2 + 24x + 18) by (2x + 3)

11. Find the square of a) m2n - 2n2. b) m + 1
m2
( )12. If x +1 1 1 2
x = 7, prove that: (i) x2 + = 47 (ii) x -
x2 x = 45

( )13. If p +1 p 2+ 1 1 2
p p
= 6, find the value of and p2 and p -

Prime Mathematics Book - 7 295

Unit Revision Test II

1. Express into the exponential form :

4a × 4a × 4a × 4a × 4a

2. Express 800 as the exponent form.

3. Express 360000 as the power of 10.

4. Simplify: b) (7ab)2 × a3b2
a) 3y6 × 8y4 1
12y10 3 a2b2 × (2ab)2

5. Simplify: m( )a+b a-b × m( )b+c b-c × m( )c-a c+a

6. Simplify: a( )z x-y × a( )x y-z × m( )y z-x

7. Solve b) x-1 = 5
a) 2x + 3 = -4x - 7 x-2 2

8. There are 575 students in a school. If the number of girls is 54 more than the boys,

how many boys are there in the school ? Find it.

9. Three consecutive even numbers add upto 48. Find the numbers.

10. A man is 26 years older then his son. After 10 years, he will be three times as old
as his son. Find their present ages.

11. Solve 2x - 5 m 3 and show the solution in a number line.

12. Write down an inequality to express the given statement and solve them. Also
show the solution in a number line. If 4 is added to the thrice of a number, the result
will be greater than or equal to 16.

13. A function machine is given in the adjoining figure, The function of the machine

is to send the number outside after processing to each number (-1,1,2,3)
put into it.

(a) Write down the set of numbers in output in the form of a 1
table.

(b) Write down an equation for the relation of output (y) and
input (x).

(c) Draw an arrow diagram to show the relation between x and y.

14. Draw the graph of the equation 5x - y = 1.

296 Algebra

Answers

Unit:14 Algebra

Exercise: 14.1.1

1. Show to your teacher. 2. Show to your teacher. 3. Show to your teacher.

4. a) 2 b)5 c)4 d)3 e)3 f)7 g)6

5. a) 11 b) 10 c) 4 d) 0 e) -7 f) 1 g) - 1
7. 17cm, 29cm, 28cm 3 6
29 , 17 5
6. 4 4 , 4

1. a) 5a + 5b - c Exercise: 14.1.2 c) 5x + 3y - 5
b) 5a + 3b - 6 f) 5x2y + 3xy2 + 4
d) 6a+ 2b + 2c + 3 e) 4x3 + 2y3 + 3z2 + 5 c) 3a2 - 6ab + 3b2
2. a) 2a - 4b + 7 b) 2x + 2y2 + 2 f) 2x2y + 2xy2 - 3
d) 2a + 2b + c e) -m3 + m2 - m + 12 c) 2x2 + 2xy - 3y2
3. a) 7a2 - a + 3 b) 13a2 - 7ab + 9b2 f) 4p2 + 14p + 14
d) -3m2 - 6mn + 8n2 e) 2a + 11b - c
4. a) -x + 8z - 6y b) -2x2 - 25xy + 9y2 c) 3m - 4n + 1 d) 3a2 - 3ab + y2

Exercise: 14.1.3

1. a) 6x3y b)-6ab3c c) -10m3n3y3 d) -12ab3c

e) 40a2bcx2 f) 60x4y2z2 g) 84a2b3c4 h) 42p3q3r4y

i) 2x3y2 j) 3 a3b3 k) 24x4y3
2 b) 60ab2cm2
b) 105abc cm3
2. a) 12xycm2 b) 15x2y2 - 10xy3 c) 8.4np2cm2
e) 2x3y2- 2x2y4 + 6xy5
3. a) 60xyz cm3 b) 6mp + 5np c) 9.1xy cm3

4. a) 12a2b + 6ab2 c) 8x3y2 + 6x2y3

d) -10m3n+2mn3 f) 8p4q - 4p3q-3

5. a) 12x2 + 8xy c) 5xy + 5x2
2

Prime Mathematics Book - 7 297

1. a) x2 -xy -2y2 Exercise: 14.1.4 c) m2 - 2mn + n2
b) 2a2 + 5ab + 2b2
d) 4x2 - z2 e) x2 - 3ax - 10a2 f) 30p2 - 61pq + 30q2
g) 2x3 - 3x2y + 2xy2 - 3y3 h) 9x2 - 25y2 i) a4 - b2

j) 25x2 - 1 + 3 - 3y k) x2 - 1 l) 4x2 + 2 + 1
y2 y 25x2 4y2 4x2

2. 6m2 - mn - 2n2, 40 3. 20a2 + 3ab - 2b2, 190m2
4. 15m2 - m - 6, 52
5. a) x3 - x2 - 3x + 6 b) 2m3 + 7m2 + 12m + 9 c) x3 + 4x2 + x - 6
d) x3 - y3 e) 2a3 + 3a2b - 4a2c - 2ab2 - 3b3 + 4b2 c f) m3 + n3
6. p3 - 5p2 + 10p - 8 , 0 7. 2x2 + 5xy + 2y2 + 3x + 6y, 0
8. a) 6a2 + 5ab + b2 b) 10x2 + 11xy + 3y2
c) 21p2 + 22pq + 3.75q2 d) 5mx + 5nx + 5px + 2my + 2ny + 2py
e) 1.5x2 + 5.5xy + 5y2 + 2xz + 4yz

Exercise: 14.1.5

1. a) 3ab b) -3mn c) -40x3yz d) 2a + 3b
f) -x2 + 4x
e) 5m2 + 3 - 4n b) 2m - 3n g) x- y2 + x2 y h) 2a2 + 3a + 4b
m b
2 6
2. a) 4 c) x4 + x5 d) a+3

e) x - 3 f) 4b - 19, Remainder = 173 g) 4x + 3y h) x - 3

3. 4x + 19, 131, -31 cm

4. a) (x - 3) units b) 14x - 20 units c) 7m, 53m, 371m2

5. x + 8, Rs. 299, 13, Rs. 23.

Exercise: 14.1.6

1. a) x2 + 4x + 4 b) m2 - 6m + 9 c) a2 - 10a + 25

d) 4a2 + 12ab + 9b2 e) x4 + 4x2y + 4y2 f) 16m2 - 24mn2 + 9n4

g) x4y2 - 4x2y3 + 4y4 h) 9a4 - 12a2y3 + 4y6

2. a) a2 + 6a + 9 b) x2 - 2x + 1 c) x2 + 2x + 4 d) 4p2 + 12pq + 9q2

3. a)m4 - 6m2n + 9n2 b) x2y2 + 2abxy + a2b2 c) x4y2 + 2x2y3z + y4z2

d) a2 + 4b2 c2 + 4ab + 4bc + 2ac e) x2 + a2 + b2 - 2ax + 2bx - 2ab

298

f) 9x2 + 4y2 + 25p2 - 12xy + 30px - 20 py

4. a) x4 + 2x + 1 b) a2 + 2 + 1 c)a6 + 2a2 + 1 d) 9p6 + 1 + 1
x2 a4 a2 36p6

5. a) 23, 25 b) 14, 12

6. a) 104, 102 b) 167, 165 7) c) 34,
8. a) 2x2 + 2y2
b) c2 - 2bc - a2 -2ab c) 34c2 - 48cd + 40d2 d) -14x + 78

1. a) 23 b) (-4)4 Exercise: 14.2 d) 26
c) (2a)5

e) (3x)15 f) (- 1 )18
2. a) 2 × 102 2
3. a) 300
4. a) 25 × 52 b) 5 × 103 c) 24 × 104 d) 23 × 7 × 104 e) 17 × 106
b) 6000 c) 80000 d) -1200000 e) 7
b) 25 c) 24 × 33 d) 23 × 33 × 53

e) 26 × 33 f) 22 × 32 × 53 g) 26
53

5. a) 36 b) x4 c) 54 d) (11)5

e) ( 4a )14 f) 57 b2 g)xb+c-d h) (3b)10
5b 35
2
6. a)1 b)1 c)1 d) 3 e)1

f)1 g)1 h)6 i) 7
9
b) 15552x9 6
7. a) 42a4 f) 3y2 c) 5 a8 d) 1
b) 5
e) 24m4 b) 1 g) 147x
8. a) 125 g) 1 4
9. a) 1 c) 9 d) 27
c) p2y d) 1 e) 1
f) 1 h) 1

1. Show to your teacher. Exercise: 14.3.1
2 Show to your teacher.

3. a) 11 b) 12 c) -4 d) 5 e) 1 f)- 15 g) 1 h) 3
4. a) 6 b) 3 d) 1 16 g) 5 h) 1.5

c) 2 e) 8 f) 11
15 114

Prime Mathematics Book - 7 299

Exercise: 14.3.2

1. a) 2x + 6 = 38 b) boys = 16, girls = 22

2. boys = 220, girls = 136

3. a) 3x = 87 b) 29, 58 4) 12, 27 5) 28, 29
c) 180 m2
6. 28, 29, 30 7. a) 4x - 6 = 54 b) 15m, 12m

8. 609cm2 9 a) 4x = 120 b) 30, 90

Exercise: 14.3.3

1. Show to your teacher. 2. Show to your teacher.

3. a) x>1 b) x ≤ 1 c) x ≥ -2 d) x < -1
4. Show to your teacher.
c) x ≤ 4 d) x > -3 e) x ≥ 2 f) y ≥ 3
5. a) x > 2 b) x< 5
6. a) 2x - 3 < 5, x < 4 b) 2x + 5 ≥ 9, x ≥ 2 c) 2x + 5 ≤ 13, x ≤ 4

Exercise: 14.3.4

1. a) ≤≤ 0 12 34 5
Input 3 45 67 8
Output

b) 0 1 23 45
Input 1 2 5 10 17 26
Output

c) 0 1 23 45
Input -1 0 7 26 63 124
Output

d) 0 1 23 45
Input -3 -1 1 3 57
Output

e) 0 1 23 45
Input 2 6 10 14 18 22
Output

f) 0 12 3 45
Input -3 -2 1 6 13 22
Output
b) y = x2 + 1,
2. a) y = x + 3 e) y = 4x = 2 c) y = x3 - 1,
d) y = 2x - 3 f) y = x2 - 3

300

3. a) y b) c) d) e) f) y
3
x 4 xy xy xy xy x -3
0 5 01 0 -1 0 -3 02 0 -2
1 6 12 10 1 -1 16 1 1
2 7 25 27 21 2 10 2 6
3 8 3 10 3 26 33 3 14 3 13
4 4 17 4 63 45 4 18 4 22
5 5 26 5 124 57 5 22 5

4 a) y = x + 4 1 b) y = 3x - 1, c) y = x2 -1
5 a) 2
23 4 5 6 78
Input(x) 4 6 8 10 12 14 16
Output (y)

b) y = 2x

c) x y
2
1 4
2 6
3 8
4 10
5 12
6 14
7 16
8

6. Show to your teacher
7. a) y = x - 1, y = 3x + 1, y = 2x + 2

b) Show to your teacher

Exercise: 14.3.5

1. Show to your teacher
2. Show to your teacher
3. a) yes b) (8,-3) c) yes

Prime Mathematics Book - 7 301

PRIME Question for Practice

Arithmetic:
1. i) What number multiplied by itself gives the product 4096 ?
ii) Find the sum of the cube of 5 and cube root of 3375.
iii) What is the maximum number of students among whom 72 apples, 96 oranges
and 120 mangoes may be divided equally.
iv) Find the least number which is exactly divided by 30, 40, 100 and 120 leaves
no remainder.
v) WCornitveedrtow: n11t1h1e1e2xipnrteosqsiuoinnawrhyennu2m0bisera.dded to the result where 2 is subtracted
2. i) from multiple of it with 3 and divided by 9.

ii) Insert the three rational numbers between 1 and 3 .
iii) 2 4
iv) 1 3 190) 1
Simplify : (1 – 3 ) ÷ ( 5 ÷ + (2 + 2 )
Simplify : 2+ 2
2
2+2 +3
v) The annual income of Amar is Rs. 50000. If he spends 20% of his income
and deposits the remaining in a bank. Find his expenditure amount and the
amount deposited in the bank.
3. i) Two numbers are in the ratio of 5:3 and their different is 60 find the numbers.
ii) A sum of money was divided between Bipana and Karishma in the ratio of 4:3.
If Karishma gets Rs.3333, how much will Bipana get ?
iii) Two numbers are in the ratio of 1:2 . If 10 is subtract from each and the new
ratio will be 3:7, find the numbers.
iv) A fruit seller bought apples at the rate Rs. 72 per dozen. He sold them at the
rate of Rs. 8 per piece. Find the profit or loss percentage ?
v) A radio is sold for Rs. 1200 at 20% profit, find the cost price. At what price
must it be sold to make 25% profit?
4. i) Sohan purchased a watch of Rs. 800 and sold it to Rohit at a profit of 20%.
Rohit sold it to Amit at a loss of 10%. Find the cost price for Rohan and the
cost price of Amit.
ii) If the cost of 2 dozen pens is Rs. 600, how much more is the cost of 30 pens?
iii) 24 workers can do a piece of work in 10 days. How many workers should be
added to complete the work in 8 days ?
iv) In a hostel, 80 students have food enough for 45 days. How many students
should leave the hostel so that the food is enough for 60 days.
v) Which interest is more between the interest on Rs. 6000 for 2 years and the
interest on Rs.5000 for 3 years at the same rate of 25% p.a. Also find the
difference?
5. i) The amount on Rs. 1000 at the annual rate of 10% is Rs. 1200. Find the
interest and time.
ii) The amount on Rs. 4000 for 2 years is Rs. 6000. Find the interest and the rate
of interest.

302

Statistics:
6. i) Construct a frequency table having class internal 10 of following raw data.

41, 53, 64, 31, 53, 33, 70, 61, 74, 32, 53, 56, 56, 64, 56, 78, 28, 70, 56, 64,
74, 53, 53, 61.
ii) Find the unknown entries (a, b, c, d, e, f) from the following frequency
table.

Height (in cm) 160–165 165–170 170–175 175–180 180–185 185–190

frequency 15 b 12 d e 5

c.f. a 35 c 50 55 f
iii) Represent the following tables in a multiple graph.

Class VIII IX X

Boys 13 20 12

Girls 17 13 9

iv) Find the mean of each of the following data.

x 5 10 15 20 25

f 36344
v) The mean marks obtained by 9 students of class 6 in an exam is 50. Among

them marks obtained by 8 students are 60, 40, 50, 30, 80, 40, 45 and 40.
What is the mark of reaming one student ?

7. i) Algebra
Find the area of following figure.

2p

3p

2p + q
ii) Find the product of 3a + 2b and 3a – 2b + c.
iii) A rectangular back yard has length (2a + 3b)m and breath (2a – b + c)m.

a) Find the area of the back yard.
b) If a = 4, b = 2 and c = 3, find the actual area.
c) Divide 2x5 + 10x4 + 6x³ + 4x² by 2x²
iv) Area is (18x²y + 12xy + 6xy²) squares unit and length is 6xy unit. Find the
length of unknown side of the given rectangle.

6xy

?
2x(3x + 5) + (2x + 4)(2x – 4)x
v) Simplify : 2x
8. i)
Calculate the square of a + b + c

Prime Mathematics Book - 7 303

ii) Simplify : 2(a – 3)² – 3(a – 4)(a + 3)
iii) Simplify : (2a + 3)² + (6a – 5)²
1 1
iv) If a + a = 3, find the value of (a – a )2.

v) If a – 1 = 8, find the value of (a + 1 )2.
a a

9. i) factorize and express as power of numbers.
a) 50625 b) 20736
a8 × a6 × a5
ii) If a = 3, Find the value of a15
iii) Simplify : ax–y. ay–z.az–x

iv) Simplify : a) xa2 – b2.xb2 – c2.xc2 – a2 b) xa+b.xa+2b.x3b–2a

10. i) Solve : 4(2x – 5) = 3(2x + 8)
ii) x-7 4x
iii) Solve : 3 = 5
iv)
v) A number is three times the other number and sum of numbers is 16. Find the
numbers.
vi) Solve the following inequality.
11. i) a) 3x + 4 ≤ 2(11 + x) b) 2(x + 3) – 1 ≥ 8 + 3x
Solve the following inequality.
3x + 2 x + 5
2 ≥ 3

If 3 is added to the 4 times of a certain numbers is greats then 15. Solve it by
constructing an inequality.
In the given function machine. Put the numbers from 1 to 5 and find the
output and represented in table.
{1, 2, 3, 4, 5}

x+2

output
x12345
x+2
ii) Find the output represented by given arrow diagram and show in graph.

13
24
35
46

304

iii) Draw the graph of the following straight line
a) 3x – y = 1 b) 3x + 2y = 5 c) 3y + 4x = 12

12. i) Co-ordinates
ii) Plot the following points on the graph and join them one after another. What
iii) does the shape represent ? Points are A (2, 3), B(4, 5) and C (6, 2).
iv) Plot the following point on the graph and join them one after another. What
does the shape represent ? Points, A (2, 3), B (–2, 3), C (–2, –3), D (2, –3).
Following points are the three continuous vertices of a rectangles. Find the
fourth vertex graphically. Points are A (2, 1), B (5, 0), and C (6, 2).
Following points are the vertices of a rectangle. Plot the points on graph and
joint in order. Find the area of rectangle. Where the points are A (2, 2), B (6,
2), C(6, 4) and D (2, 4).

13. i) Mensuration
Find the area of the given figure. Also find its perimeter.

3cm

3cm
3cm

6cm
3cm

6cm
ii) From the given figure find the area of shaded region.

18cm

12cm 10cm
4cm

iii) Find the length of the side and perimeter of the square whose area is 256m².
iv) If breath of rectangle is three fourth of its length and perimeter is 140 cm.

Find the length and breath of rectangle.
v) Area of rectangle is 1500 m² and breath is three fifth of the length. Find the

length and breath of rectangle.

14. i) A cuboid has the total surface area 432 cm². If its length and breath are 12
ii) cm and 6 cm respectively. What is the height ?
iii) A cuboid has the total surface area 258 cm². If its breath and height are 5 cm
iv) and 6 cm respectively what is the length ?
A cuboid has the total surface area 592 cm². If its length and height are 12
cm and 10 cm respectively, find the breath of the cuboid.
Find the total surface area and volume of cube its length is 6.5 cm.

Prime Mathematics Book - 7 305

v) Find the total surface area and volume of the following figure.

12cm

13cm 10cm

15. i) Transformation
ii) The vertices of ∆ABC are A (2, 5), B (1, 5) and C (5, 0), respectively. Sketch it
iii) in graph paper and reflect in x-axis. Write down the co-ordinates of image.
iv) X(2, 5), Y(1, 7) and Z(–3, 4) are the vertices of a triangle. Show ∆XYZ and
image obtained in the reflection on Y-axis of it on the same graph.
v) A (6, –2), B (10, 4) and C (4, 6) are the vertices of ∆ABC. Find the co-ordinates
of its image under rotation about half turn.
Plot the points of A (4, 6), B (6, 8) and C (–2, 4) on a graph paper. Find their
2
images under the translation vector 3 .

Quadrilateral ABCD has the vertices A (3, 5), B (4, 7),C (3, 7) and A (1, 7). Find
the image of the quadrilateral ABCD when it is translated by the translation
3
vector 4 . Represent object and image in a graph.

Bearing and scale drawing
16. i) A garden is 120m long and 80 m board. Sketch the garden by taking the scale
ii) of 10 m = 1 cm.
iii) A rectangular ground has length 100 m and breath 75 m. By taking a scale of
1cm:20m draw the figure of ground in your copy.
17. i) A square court has length 90 m. Draw the figure of the cort by taking a scale
1cm:18m.
ii) Set
List the elements of following sets. Which one set can be considered as the
iii) possible universal set ?
A = {multiples of 4 less than 20}
B = {multiples of 2 less than 20}
C = {multiples of 8 less than 20}
D = {even numbers less than 10}
If A = {1, 2 ,3, 4, 5, 6}, Write down the following sub-sets of A.
a) B = {prime numbers}
b) C = {odd numbers}
c) D = {even numbers}
d) E = {factors of 6}
If A = {3, 4, 5, 6, 7, 8}, B = {5, 6, 7, 8}, C = {5, 6, 7, 8} Which of following
statement is true ? Also write the cardinal number.
a) A ⊆ B b) B ⊆ C c) B = C
d) D is proper subject of B e) B is proper subject of C.

306

iv) If U = {a, b, c, d, e, f, g, h, i}; P = {b, i, g}; Q = {a, c, e); R = {d, e, h, i} and
S = {a, d, g, h}.
a) Show U, P and Q on a separate venn diagram.
b) Find P – Q

v) If U = {x: x ∈N, x ≤ 25}, P = {x: x is a multiple of 4 less than 15} and Q ={x: x is
a multiple of 2 less than 20}, show the relationship of U, P and Q in the venn
diagram.

vi) If U ={a, b, c, d, e}, B ={b, c, d, e} and C ={a, c, e} using venn diagram find
the B∩C and B∪C.
Geometry

18. i) Construct ∆ABC; If AB = 5.4 cm, BC = 5.6 cm and CA = 5.8 cm.
ii) Construct ∆PQR; If QR = 5.4 cm, PR = 6.2 cm and ∠R = 90°
iii) Construct ∆DEF; if EF = 6.5 cm, ∠E = 75° and ∠F = 45°.
iv) Construct a parallelogram ∆ABCD; if AB = 6.5 cm, AD = 5 cm and ∠A = 30°.
v) Construct a parallelogram having a side 6cm and two diagonals 8cm and 10cm
respectively.
vi) Construct a parallelogram ∆PQRS is which length of diagonals are 6cm and
8cm also angle between them is 30°.
vii) Verify experimentally that sum of four angles of a quadrilateral is 360°.
viii) Verify experimentally that the exterior angle of a triangle is equal to sum of
its opposite interior angles.

19. i) Find the value of unknown angles. c)
a) b)
50° 140° 130°
80° 30°
x° 120°

20° x° 25° x° f)
y°
e) x° 50°
d) x°
80°
70°
30°

110° 80°

x°

ii) Following triangles are pairs of congruent triangles. Measure the sides and
determine the corresponding angles.
Q
AR

BC P

***

Prime Mathematics Book - 7 307

MODEL QUESTIONS

FIRST TERMINAL EXAMINATION

Group A [10 × 1 = 10]
1. a) Write down a pair of alternate angles from the adjoining diagram.

A PB

CQ D

b) Find the complementary angle of 40°.

2. a) Find the Square of 12.
b) If CP = a and SP = b, find the profit.

3. a) Find the cost of a pen where cost of 10 pens is Rs. 200.
b) What is the degree of the algebraic expression?
x3 + 2x2 + 3x + 4

4. a) Identify the expression x2 — 6x according to number of terms.
b) Add : 2a + 3a + 5b

5. a) Write down one example of null set.
b) If A = {3, 4} and B = {5}, find A ∩ B.

Group B [17 x 2 = 34]
6. a) Write any two properties of an Isosceles triangle with figure.

b) What is the sum of interior angles of a regular hexagon?
c) Subtract 3a — 2b from 5a + b.
7. Find value of x from the given diagrams.
a) b) c)

A

x

4x x + 20° B 40° 50° C x + 40° 70°

8. a) Two supplementary angles are in the ratio of 4:5 find the angles.
b) Find the perimeter of the following figure.

4cm

8cm

c) Find the area of square of side 10 cm.
9. a) Find the circumference of the circle when it’s radius is 7cm.

b) Perimeter of a rectangle is 20cm and its length is 6cm, find the breadth.
c) Add 2a + 3b and 4a — 2b.

308

10. a) Write down the cardinal number of the set D = {all the factors of 12}
b) State with reason whether the sets A and B are overlapping or disjoint sets.
c) A= {1, 2, 3, 4, 5} and B= {5, 6, 7, 8}
If P {1, 2, 3} and Q = {3, 4, 5}, find the P ∪ Q.
11. a) Simplify : 108 + 2 3
b) Find the Square root of 576

Group C [4 x 11 = 44]
12. Find the unknown angles from the adjoining diagram.

130° x 120°
yz

13) Construct a rectangle PQRS in which length of diagonals 6cm each and angle
between the diagonals is 30°.

14) The interior angles of a heptagon are a + 20°, a + 30°, a + 40°, a + 50°, a + 60°,
2a + 100°, and 3a. Find the value of a.

15) Find the length of the wire required to fence a rectangular garden 24m long and
18m broad to make five complete rounds.

16. Represent in the place value table for the numbers: 24, 67, 89, 563. Also write the
number name.

17. Write down all the possible factors of 45 and 18. Also write down the common factors.
18. Find the first five multiple of 13.
19. Find the perimeter of the given diagram.

2cm

2cm
8cm

4cm

2cm

10cm

20. If an article is bought at Rs. 400 and sold at Rs. 500, what will be the profit
percentage?

21. Multiply (x2 — ax + a2) by (x + a).
22. If U = {1, 2, 3, 4, 5, 6}, A = {2, 3, 4} and B = {4, 5, 6}, find A∩B and A∪B.
23. Find the area of the shaded region from the given diagram.

10cm

8cm

20cm

24. Find the square root of 1296.
25. What must be subtracted from the expression 3a + 2b – 5 to get 5a – b + 2 ?

***

Prime Mathematics Book - 7 309

SECOND TERMINAL EXAMINATION

Group A [10 × 1 = 10]
1. a) Find the point on positive direction of X-axis at 6 units distant from origin.

b) Which is the corresponding angle of ∠BGH?

A GB

CH D

2. a) Write all the possible subsets of {a, b, c}
b) If ∑x = p and N = q, find the mean.

3. a) What is the degree of a polynomial 5x2 + 7x + 5?
b) How many integers lie between -2 and 3?

4. a) What is the diameter of the circle whose radius is 5cm.
b) Find the complement of 40.5 degree.

5. a) What is the highest digit of dinary numbers.
b) Write down the calculating formula of interest.

Group B [17 x 2 = 34]
6. a) From figure, find the value of x.
P
A 5x – 20 B

C Q 30° D

b) The measures of two vertically opposite angles are (2x)° and (x + 60)°
respectively, find the value of x.
7. a) Find the value of x in given figure.

A

x°

140° 130° Q
PB C

b) A rectangle has length 18cm and breadth 12cm find the perimeter of the
rectangle.
c) Add : 3x + 4y – 2 and x – 7y – 4
8. a) Find the co-ordination of images when the points (4,5) and (6,2) are reflected
in x-axis.
b) Find the total surface area when length is 5cm of a cube.
c) Multiply : (2x + 3y) by (2x – 3y)

9. a) If A ={4, 5, 6} and B={1, 5,7} show this in a Venn-diagram.
b) Rabin bought 5 apples for Rs 30 and sold each apple at Rs 8, find the profit
received by him.

310

c) If x = 2 and y = 3, find the value of x2 + 2xy + y2
10. a) The ages of A,B,C,D and E are 12, 18,13,16 and 6 years respectively. Find the
average age.
b) If the mean of 5, 11, 6, 4, 7, P and 10 18 is 8 find the value of P.
c) Find the circumference of circle of radius 7cm.
11. a) Convert 1f0o1u2rttho decimal numerals.
b) Find the proportional of 3,4 and 18.

Group C [14 × 4 = 56]
12. Find the value of x from the figure given alongside.
P
A 30° B

Qx

40°
R

13. Construct a parallelogram PQRS in which PQ = 6cm, PS = 4cm and ∠QPS = 30°.

14. Verify experimentally that the sum of the interior angles of a triangle is 180°.

15. A cuboid has the total surface area 900cm2. If its length and breadth are 15cm and
10cm respectively, find the height of the cuboid.

16. The vertices of ∆ABC are A (2, 3), B (4, 5) and C (6, 2) respectively. Sketch it in a
graph paper and reflect in X-axis. Write down the co-ordinates of image.

17. If U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3}, B = {2, 3, 4} and C = {3, 4}. Find A∩B∩C.
Also represent in venn-diagram.

18. A fruit seller bought 200 oranges at the rate of Rs 5 per piece where 50 oranges
was rotten but he sold the remaining oranges at the rate of Rs 8 per piece. Find
profit or Loss percentage.

19. The interest on Rs 12,000 for 3 years is Rs 2160. Find the rate of interest.

20. Find mean of the following data.

x 4 8 12 16 20 24
f 246332
21. The length of a rectangle is (4x - 3y) and its breadth is (2x + y) cm. Find the
perimeter in expression and calculate the actual perimeter if x = 3cm and y = 2cm.
22. Multiply = (4a2 + ab + b2) and (2a - b)
23. What must be subtracted from the expression 3x2 + 5x – 2 to get x2 – 2x + 3?
24. Find the area of the shaded region from the following.

20cm

25. Find the square root of 9216. 40cm

***

Prime Mathematics Book - 7 311

FINAL TERMINAL EXAMINATION

Group A [ 10 × 1 = 10]
1. a) How many possible subsets of set {a, b} can be formed ?

b) How many integers lies between -2 and 5 ?
2. a) Write the formula of (a-b)2.

b) Express 100000 as the power of 10.
3. a) Write a linear equation to represent the sum of 5 and twice of a number is

11.
b) If the number of item (N) = 30, sum of item Σx = 210. Find the arithmetic

mean (X).
4. a) Write the compass bearing of the point A.

N

O 120o

A

b) In which quadrant does a point lie if its coordinates is (-4, 2) ?
5. a) What is the diameter of the circle whose radius is 5cm ?

b) Find the complement of 40O.

Group B [ 17 × 2 = 34]
6. a) If A = {a, b, c, d} and B = {b, c, d, e}, find A - B and A U B.
b) Convert 1f0o1u2rttho decimal numerals.
c) Find the proportional of 3, 4 and 18.
The perimeter and breadth of a rectangle are 40cm and 8cm receptivity. Find
7. a) the length of the rectangle.
Divide: (x2 - 3x - 40) by (x + 5)
b) 3x5 × 5x4
c) Simplify : 12x9

8. a) Simplify : (ax-y)(x+y) × (ax+y)(y-x)
b) Solve 3x - 2 m 7 and show the solution in a number line.
c) A function machine is given in adjoing figure. The function of the machine is
to send the number outside after processing to each number put into it.

Input (2, 4, 6)

i) Write down the set of numbers in out in the form of the table.
ii) Write down the set of numbers in output (y).
312

9. a) The number of students enrolled in different classes is given below. Represent
the data by a bar graph.
b)
c) Classes I II III IV V
10. a)
No.of students 120 130 100 90 140

Plot the points P(2,3) and Q(6,-1). Joint the points P and Q and find the
coordinates of the mid point of PQ.
The enterior angles of a hexagon are 70o, 95o, 105o, (x+20)o, (x+30)o and
(x+20)o, find the value of x.
From the given figure, find the value of x and y.

b) Prove that DABC ~ DAMN

c) In the adjoining figure DABC and DPQR are congruent. Find the values of x
and y.
AP

11. a) B CQ R
b) Find the number of sides of a polygon whose sum of interior angles is 108°.
Find the values of x and y from the adjoing figure.

114o

Group C [14 × 4 = 56]
12. If A ={1,2,4,5,6} and B={2,3,5,7,8}, list the elements of A ∪ B and A ∩ B. Also

show the result in the venn diagram.

Prime Mathematics Book - 7 313

[ { ( )}]13. 3 - 6 - 3 - 1 + 1
Simplify : 7 7 4 3 6

14. The length and breadth of a rectangular garden are (6a + 5b) units and (2a - 3b + 2c)
units respectively. Find the area of the garden. Also find the actual area of the
garden, when a=6, b =3 and c = -1.

15. Divide (2a3-5a2-24a-18 )by (2a + 3) 1
1 m2
16. If m + m = 11, find the value of m2 + and (m - 1 )2
m

17. There are 49 students in a class of a school. If the number of the girls is 9 more
than the number of boys,
a) write down an equation representing the students.
b) Find the number of boys and girls.

18. A cuboid is thrice as long as it is broad. If the cuboid is 8 cm high and its
volume is 1176cm3. Find its total surface area.

19. 30 men can build a wall in 52 days. In how many days will 39 men build it ?

20. By selling a watch for Rs.3822, a man loses 9%. At what price should he sell it
to make a profit of 7% ?

21. What sum of money lent at 6% per year for 3 years will produce the same
interest as Rs.800 lent at 5% per year for 6 years ?

22. The marks recorded by 30 students in a unit test is as follows:

5, 6, 8, 2, 4, 6, 4, 7, 8, 9, 8, 5, 6, 4, 2, 5, 6, 8, 7, 6, 8, 4, 5, 6, 9, 8, 10, 4, 6,
10. Find the arithmetic mean by constructing frequency table with tally bar.

23. A(3,4), B(5,7) and C(9,2) are three vertices of a triangle ABC. Find the
coordinates of the vertices of the image triangle. A´B´C´ under the reflection
on the X-axis. Also plot the DABC and its image in the same graph.

24. Verify experimentally that an exterior angle of a triangle is equal to the sum of
the two non adjacent interior angles. (two figures of different shape and size
are required).

25. Construct a parallelogram ABCD in which AB = 6cm, BC = 4.5cm and B = 75°.
***

314

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