Annual practice question paper- class 7

CLASS VII – MATHEMATICS ANNUAL EXAMINATION 

Time: 2 hours 15 minutes
Maximum Marks: 80

SECTION A – OBJECTIVE (1 × 15 = 15)

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1. If ( 3x - 5 = 2x + 7 ), then x =
   a) 12 b) -12 c) 2 d) 7

2. ( 2^3 × 4^2 = )
   a) 64 b) 128 c) 32 d) 256

3. Increase ₹400 by 25%:
   a) 425 b) 500 c) 480 d) 450

4. Which is NOT a perfect square?
   a) 441 b) 529 c) 625 d) 650

5. If two angles of a triangle are 45° and 65°, third angle is:
   a) 70° b) 80° c) 90° d) 100°

6. Number of lines of symmetry in a rhombus:
   a) 1 b) 2 c) 4 d) 0

7. A shopkeeper gives 20% discount on ₹1000 and still gains 20%. CP =
   a) 600 b) 700 c) 800 d) 900

8. ( (3^2)^3 = )
   a) 9 b) 27 c) 729 d) 81

9. Area of a triangle = 1/2 × base × height. If base doubles, area:
   a) doubles b) halves c) same d) quadruples

10. Number of edges in a cuboid:
    a) 8 b) 12 c) 6 d) 10

11. Congruent triangles must have:
    a) equal area only
    b) equal sides and angles
    c) equal perimeter only
    d) same shape only

12. Mean of 2, 4, 6, 8 is:
    a) 4 b) 5 c) 6 d) 8

13. The smallest 3-digit perfect square is:
    a) 100 b) 121 c) 144 d) 169

14. ( 10² ÷ 10⁰ = )
    a) 100 b) 0.01 c) 10 d) -100

15. A parallelogram has rotational symmetry of order:
    a) 1 b) 2 c) 3 d) 4

SECTION B – (10 × 3 = 30)

16. Simplify:
    ( 8 - { 3 + 2[5 - (3 - 1)] } )

17. Solve and check:     

    
    
    

18. After two successive discounts of 10% and 20%, find the final price of ₹1000.

19. Evaluate:
    
    

    
    
    

20. The base of an isosceles triangle is half the other two equal sides. The perimeter of the triangle is 30cm. What is the length of each side of the triangle.

21. A bag contains 25 cards numbered from 1 to 25. A card is drawn at random 

    from the bag. Find the probability that the number on the drawn card is:

    (i) divisible by 3 or 5.                 (ii) A perfect square number.

22. Complete the table:

Polygon	Lines of symmetry	Order of rotation
Regular pentagon	?	?
Parallelogram Equilateral triangle	?                     ?	?                         ?

23. In Fig., QX bisects ∠PQR as well as ∠PSR. State the three facts needed to ensure that △QRS = △QPS.Give reasons for each statement.

    
    
    

24. Construct a triangle ABC  with sides AB= 5 cm, BC = 6 cm and angle B = 60 ⁰ with a pair of compasses amd a ruler.

25. Find the distance covered by the wheel of a truck in 100 rotations if the diameter of the wheel is 49 cm.

SECTION C – (5 × 4 = 20)

26. If ( 2^x × 4^{x+1} = 128 ), find x.

27. In ΔABC, AB = AC. D is midpoint of BC. Prove that AD ⟂ BC.

28. Find the value of a, b, and c 

    
    
    

29. In what time will Rs. 1600 amount to Rs. 1768 at 6% per annum simple interest?

30. From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed (as shown in the following figure.) Find the area of the remaining sheet. (take π = 22/7)                                                                       

SECTION D – (3 × 5 = 15)

31. A ladder of length 25 m reaches a wall at 7 m height.
    If the base is moved 8 m away, find the new height reached.

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32. Following data gives total marks (out of 600) obtained by six children of a particular class. 

    Represent the data on a bar graph.

    
    
    

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33. In the following figures, find the area of the shaded portions: (i)