South Point High School, Annual Question Paper, Mathematics, Class 7, 2025-26

South Point High School (CBSE)

Annual Examination 2025–26

Class VII – Mathematics

Full Marks: 80

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GROUP A (MCQs)

This group comprises 10 MCQ of 2 marks each.

1. If m = 2, then the value of 3m − 5 is:
   (A) 1 (B) 3 (C) 5 (D) 6
2. −1 is NOT a solution of the equation:
   (A) x + 1 = 0
   (B) 3x + 4 = 1
   (C) 5x + 7 = 2
   (D) x − 1 = 2
3. In the figure below, CD || AB. The value of x is:
   
   
   
   (A) 220 (B) 140 (C) 100 (D) 40
4. If in an isosceles triangle, each base angle is 40°, then the triangle is:
   (A) Right-angled triangle
   (B) Acute-angled triangle
   (C) Obtuse-angled triangle
   (D) Equilateral triangle
5. The probability of selecting a vowel from the word "ALPHABET" is:
   (A) 1/2 (B) 1/7 (C) 2/7 (D) 3/8
6. By selling an article for ₹900, a person lost 10%. The cost price is:
   (A) ₹990 (B) ₹1000 (C) ₹750 (D) ₹910
7. If ΔABC ≅ ΔDEF and AB = 5 cm, BC = 6 cm, CA = 7 cm, DE = 5 cm, DF = 7 cm, then EF = ?
   (A) 18 cm (B) 11 cm (C) 6 cm (D) 2 cm
8. The number of edges of a cone is:
   (A) 1 (B) 2 (C) 3 (D) 5
9. The area of a circle of diameter d is:
   (A) 2πd² (B) πd² (C) πd²/2 (D) πd²/4
10. The number of lines of symmetry of the letter "Z" is:
    (A) 1 (B) 2 (C) 3 (D) None of these

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GROUP B (Very Short Answer)

This group comprises of 6 Very Short Answer Type questions of 2 marks each.

11. Simplify: 2(x² − 3x) − 5(7x − 4). Also find value when x = −2.
12. Two equal sides of an isosceles triangle are (3x − 1) units and (2x + 2) units. Third side is 2x units. Find x and perimeter of triangle.
13. Two poles of height 6 m and 11 m stand on a pole ground. If the distance between their feet is 12 m, find the distance between their tops. Explain with a diagram
14. A die is thrown. Find probability of getting an odd number or a multiple of 3.
15. A person bought 10 dozen pens at the rate of ₹40 per dozen. On checking, he found that 20 pens were not working and discarded them. To earn 25% profit, at what price should he sell each pen?
16. Find the mean age from the data:

Age (years)	14	15	16	17	18
No. of Students	2	6	5	4	3

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GROUP C (Short Answer)

This group comprises of 6 Short Answer Type questions of 3 marks each.

17. I have some 5-rupee coins and some 2-rupee coins. Number of 2-rupee coins is 4 times the 5-rupee coins. If I have ₹117 in all. Find the number of coins of each denomination.
18. Find x, y, z in the figure where n || m . 
    
    
    
    
19. In the following figure, BD and CE are altitudes of ΔABC such that BD = CE:
    • (i) State three pairs of equal parts in ΔCBD and ΔBCE
    • (ii) Are ΔCBD and ΔBCE congruent? Give reason
    • (iii) Prove ∠DCB = ∠EBC
      
      
      
      
20. With a compass and a ruler construct ΔABC in which BC = 6.2 cm, ∠B = 60° and ∠C = 45°.
21. The inner circumference of a circular track is 220 m and the width of the track is 7 m. Calculate the cost of putting up a fence along the outer circle of the track at the rate of ₹50 per m.

22. The following table shows the number of books which are meant for only reference in the library:

    Subject	Languages	Mathematics	Science	Social Science
    Number of Books	300	450	500	175

    Draw a bar graph for the above data, choosing an appropriate scale.

GROUP D (Long Answer)

This group comprises 6 Long Answer type questions of 5 marks each.

23. Prove that the sum of three interior angles of a triangle is 180°.
24. A sells an article to B at a profit of 5%. B sells the same to C for ₹3213, thereby making a profit of 2%. What did A pay for it?
25. With a compass and a ruler construct a ΔABC in which AB = AC = 5.2 cm and ∠A = 120°. Construct AD ⟂ BC.

26. In a certain school, a bus service is provided for the students who reside more than 1 km away from the school. The distances (in km) from the school to the homes of 10 students are as follows:

    0, 1/2, 1/2, 1, 1, 1, 1, 1½, 3½, 10

    1. For this data, find the (a) mean, (b) median, and (c) mode.
    2. How many of these 10 students are eligible for the bus service?
    3. Explain why the mean is not an appropriate representative of the data in this case.

27. The performance of a student in TERM I and TERM II is given below:

    Subject	English	Hindi	Mathematics	Science	Social Science
    TERM I	67	72	88	81	73
    TERM II	70	65	95	85	75

    Represent this data using a double bar graph, choosing an appropriate scale.

28. A garden ABCD in the shahpe of a parallelogram with AB=40m, BC=32m, and DM=18m has a circular pond at its centre. The diameter of the circular pond is 14 metres.
    

    
    1. Find the circumference of circular pond.
    2. Caalculate the area of the garden not occupied by the pond.
    3. The owner wants to put a fence along the outer perimeter of the garden. it costs Rs. 45 per metre for the fening. How much will it cost to fence the garden?