7th Class PSEB Math Final Model/Sample Paper with Solution 2023

Model Test Paper
Class : 7th
Subject : Math
Time : 3hrs
M.M : 80
Part – A
Note: Each question carries 1 mark each.
Question 1: Multiple choice Questions
i) The product of 3 × -1 is :
(a) 3
(b) – 3
(c) 1
(d) -1.
Ans: (b) – 3
ii) Place value of 5 in 17.56 is :
(a) 5
(b) 5/10
(c) 5/100
(d) 50
Answer: (b) 5/10
iii) A cricketer scored 38, 79, 25, 52, 0, 8, 100 runs in seven innings, the range of the runs scored is :
(a) 100
(b) 92
(c) 52
(d) 38.
Ans: (a) 100
iv) In equation 5x = 25 the value of x is :
(a) 0
(b) 5
(c) -5
(d) 1
Ans: (b) 5
v) Supplementary angle of 100° is :
(a) 80°
(b) 100°
(c) 90°
(d) 180°
Ans: (d) 180°

vi) The number of median a triangle has, is:
(a) Two
(b) One
(c) Three
(d) Four
Ans: (c) Three
vii) Out of two congruent angles measure of one angle is 70°, then the measure of other angle is :
(a) 70°
(b) 110°
(c) 90°
(d) 140°
Answer:
(a) 70°
viii) Convert 12.35 into percent.
(a) 12.35%
(b) 123.5%
(c) 1235%
(d) 1.235%
Ans: (c) 1235%
ix) Which of the following is not an natural number ?
(a) 0
(b) 2
(c) 10
(d) 105.
Ans: (a) 0
x) The angles of a triangle are 30° and 50°, third angle is :
(a) 100°
(b) 60°
(c) 80°
(d) 50°.
Ans: (a) 100°
xi) Circumference of a circle = …………….
(a) πr
(b) 2πr
(c) πr²
(d) 2πr².
Ans: (b) 2πr
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xii) If a = 2, b = – 2, the value of a² + b² is :
(a) 0
(b) 4
(c) 8
(d) 10
Ans: (c) 8
xiii) Find the value of 2⁶ will be :
(a) 32
(b) 64
(c) 16
(d) 8
Ans: (b) 64
xiv) The number of lines of symmetry for an equilater triangle is :
(a) One
(b) Two
(c) Three
(d) Four
Ans: (c) Three
xv) What cross-section is made by vertical cut in a cuboid
(a) Square
(b) Rectangle
(c) Circle
(d) Triangle
Ans: (b) Rectangle
xvi) A polygon is said to be a regular polygon if its :
(a) All sides are equal
(b) All angles are equal
(c) Both (A) and (B)
(d) None of these.
Ans: (c) Both (A) and (B)
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Question: 2 True/False.
i) 1 ÷ a = 1 (True/False)
Ans: False
ii) The value of 1.5 × 8 is 12 (True/False)
Ans: True
iii) A triangle is possible with angle 60°, 70°, 80°. (True/False)
Ans: False
iv) The complement of a right angle is also a right angle. (True/False)
Ans: False
v) Two opposite sides of a rectangle are always congruent. (True/False)
Ans: True
vi) 1/10 not a rational number. (True/False)
Ans: True
vii) The value of 2⁰ × 3⁰ × 4⁰ will be 24. (True/False)
Ans: False
viii) 7 and 12xy are like terms. (True/False)
Ans: False
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Question: 3 Fill in the blanks
i) 369 ÷ ……… = 369 ( 0, 1, 369 , 2)
Ans: 1
ii) 2/3 of 18 is …………. ( 10 , 12 , 26, 24)
Ans: 12
iii) The angle which is equal to its complement is_______ ( 50°, 45°, 60°,90°)
Ans: 45°
iv) If 8x – 4 = 28, then x is equal to ……………. ( x = 4 , 4=x , x=2,x=6)
Ans: x = 4
v) When we write ∠A = ∠B, there we really means…….
Ans: m∠A = m∠B
vi) Area of a square = __________ (side × side /4× side / 3× side / 4+ side)
Ans. side × side
vii) On subtracting 5 from x we get ……………
Ans: x – 5
viii) The exponential form of 5 × 5 × 5 × 5 × 5 × 5 is ……………… (56,65,75,85)
Ans : 56
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Part-B
Each question carries 2 marks each
4. Find the median of the following data :
3, 1, 5, 6, 3, 4, 5
Ans.: We arrange the data in ascending order.
1, 3, 3, 4, 5, 5, 6
Here, 3 and 5 both occur twice.
Therefore, both the numbers 3 and 5 are modes of the given data.
5. Find the value of x in the following figures.

Ans. By exterior angle property of a triangle
Sum of interior opp. angles = Exterior angle
40° + x = 120°
x = 120° – 40°
x = 80°.
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6. Find the product of :
(-8) × 0 + [(-5) × (-4)]
Ans. (-8) × 0 + [(-5) × (-4)]
= [(-8) × 0] + [(-5) × (-4)]
= 0 + 20 = 20.
7.Find the value of x, y and z

Ans. In fig (i)
x = 100°
(Vertically opposite angles)
y = 80°
(Vertically opposite angles)
8. Using laws of exponents , Simplify the following
5² × 3²
Ans.
5² × 3² = 5 × 5 × 3 × 3
= 25 × 9
= 225
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9. If ΔPQR as ΔOMN under the correspondence PQR ↔ OMN, write all the corresponding congruent parts of the triangle.
Ans. The correspondence is PQR → OMN
This means vertices P ↔ O, Q ↔ M, R ↔ N
Sides : PQ ↔ OM, QR ↔ MN, RP ↔ NO
and Angles: ∠PQR ↔ ∠OMN, ∠QRP ↔ ∠MNO, ∠RPQ ↔ ∠NOM
10.Write two equivalent rational numbers of the 4/5
Ans. 4/5 = 4/5 × 2/2
= 8/10
4/5 = 4/5 × 3/3
= 12/15
∴ Equivalent rational numbers of 4/5 are 8/10 and 12/15
11.If 7 is added to five times a number, the result is 57. Find the number.
Ans. Let the required number = x
Five times the number = 5x
7 added to five times the number = 5x + 7
According to the problem
5x + 7 = 57
5x = 57 – 7
5x = 50
x = 505
So, x = 10
Hence the required number is 10.
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Part-C
Note: Each question carries 4 marks each 12
12.In a triangle ABC, ZB = 50°, ∠C = 62°. Find ∠A.
Ans. In a ΔABC, ∠B = 50°, ∠C = 62°
By angle sum property of a triangle
∠A + ∠B + ∠C = 180°
∠A + 50° + 62° = 180°
∠A + 112° = 180°
∠A = 180° – 112°
∠A = 68°
13. In the following figure AB || CD and EF || GH, find the measure of ∠x and ∠y.

14. A batsman scored the following number of runs in six innings :
36, 35, 50, 46, 60, 55
Calculate the mean runs scored by him in an inning.
Ans:
Mean runs
= 36+35+50+46+60+55/6
= 282/6
Hence, the mean runs scored by batsman in an innings = 47
OR
A bag contains 3 red and 7 green balls. One ball is drawn at random from the bag. Find the probability of getting (i) a red ball (ii) a green ball.
Ans.: Total number of balls in the bag = 3 + 7 = 10
(i) The event is getting a red ball.
Probability (getting a red ball) = 3/10
(ii) The event is getting a green ball.
Probability (getting a green ball) = 7/10
15.Raju’s father’s age is 4 years more than five times Raju’s age. Raju’s father is 54 years old.
Ans: Let x years be Raju’s age
Five times Raju’s age is 5x years
His father’s age will be 4 years more than five times
Raju’s age = 5x + 4
But 4 years more han five times Raju’s age = Raju’s father’s age
Therefore 5x + 4 = 54
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OR

In a class test containing 10 questions, 5 marks are awarded for every correct answer and (-2) marks awarded for every incorrect answer and 0 for questions not attempted. Reshma gets five correct answers and five incorrect answers. What is her score?

16.There are two teams A and B. A coin is flipped to decide which team starts the game. What is the probability that team A will start ?
Ans.: When a coin is tossed once. The number of possible outcomes is head or tail
Sample space : [H, T]
The probability of getting head or tail is equal and is 1/2 for each.
∴ The probability that team A will start = 1/2
OR
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Part-D
Note: Each question carries 6 mark .
17. Two hundred students of 6th and 7th class were asked to name their favourite colour so as to decide upon what should be the colour of their school building. The results are shown in the table :

Ans. i) Choose a suitable scale as follows :
Start the scale at 0. The greatest value in data is 55, so end the scale at a value greater than 55, such as 60.
Ans. ii) Use equal divisions along the vertical axis, such as increments = 10. All the bars would between 0 and 60. We choose the scale such that the length between 0 and 60 is neither too long nor too small. Here we take 1 unit for 10 students.
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OR
Consider the following data collected from a survey of a colony :

Ans.Take different sports along X = axis and number of persons watching and participating favourite sports Y-axis.
Scale. Take 1 unit height along Y-axis = 200 persons. The double bar graphs representing the given data is shown below.

18. The length of a rectangle is 3 units more than its breadth and the perimeter is 22 units. Find the breadth and length of a rectangle.
Ans. Let breadth of rectangle (l)
= x units
∵ length of rectangle (b) = (x + 3) units
∴ Perimeter of rectangle = 2(l + b)
= 2 (x + x + 3) units
= 2(2x + 3) units
According to the question
Perimeter = 22 units
2 (2x + 3) =22
2(2x+3)2=222
2x + 3 = 11
2x = 11 – 3
or 2x = 8
Dividing both sides by 2 we get
2×2=82
x = 4
∴ breadth = 4 units
Length = (4 + 3) units
= 7 units
OR
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Irfan says that he has 7 marbles more than five times the marbles Pannit has. Irfan has 37 marbles. How many marbles does Pannit have ?
Ans. Let marbles Parmit has = x
Marbles Irfan has = 5x + 7
But Marbles Irfan has = 37
∴ 5x + 7 = 37
5x = 37 – 7
5x = 30
x = 305 = 6
Therefore Parmit has 6 marbles.
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