ICSE Class 7 Mathematics · Exam Practice

Practice Paper — Set 1

ICSE Class 7 Mathematics, covering number work, algebra, geometry, mensuration, data and probability, with a full answer key and worked solutions.

🎯 Full Marks: 50 ⏱️ Time: 1½ Hours 📝 Questions: 30
SectionType of questionsQsMarks
AMultiple Choice Questions1010
BFill in the Blanks & True / False88
CShort Answer Questions816
DProblem Solving416
Total3050
Before you start
  • This paper draws on Class 7 chapters on MuskMeadow: Integers, Fractions, Decimals, Exponents, Rational Numbers, Percent, Profit & Loss, Simple Interest, Linear Equations, Lines & Angles, Triangles, Congruency, Pythagoras Theorem, Symmetry, Mensuration, Data Handling and Probability.
  • Attempt the paper first, without looking at the answer key at the bottom of the page.
  • Show your working for Sections C and D — method marks are given even if the final answer is wrong.
10 MARKS

Section A — Multiple Choice Questions

Choose the correct option. (1 mark each)

1. (−6) × (−4) ÷ (−3) =

A. 8B. −72C. −8D. 72

2. 2/3 ÷ 4/9 =

A. 8/27B. 3/2C. 2/3D. 9/4

3. 0.36 ÷ 0.06 =

A. 0.6B. 60C. 0.06D. 6

4. 2⁵ × 2³ is equal to

A. 2⁸B. 2¹⁵C. 4⁸D. 4¹⁵

5. Which of the following rational numbers is the greatest?

A. −1/2B. −2/3C. −3/4D. −1/3

6. 35% of 240 is

A. 8.4B. 84C. 156D. 840

7. A shopkeeper buys an article for ₹ 800 and sells it for ₹ 680. His loss per cent is

A. 85%B. 17.6%C. 15%D. 120%

8. The simple interest on ₹ 5,000 at 6% per annum for 2 years is

A. ₹ 600B. ₹ 300C. ₹ 3,000D. ₹ 5,600

9. If 3x − 7 = 11, then x =

A. 4/3B. 18C. 6D. 1

10. Two angles are supplementary. If one of them is 112°, the other is

A. 78°B. 68°C. 22°D. 248°
8 MARKS

Section B — Fill in the Blanks & True / False

Fill in each blank, or write True / False. (1 mark each)

11. An exterior angle of a triangle is equal to the sum of its two interior opposite angles. (   )

12. In a right-angled triangle the two shorter sides are 6 cm and 8 cm. The hypotenuse is ______ cm.

13. A triangle with sides 3 cm, 4 cm and 6 cm is right-angled. (   )

14. When a fair coin is tossed once, the probability of getting a head is ______.

15. A regular pentagon has ______ lines of symmetry.

16. Two triangles whose corresponding angles are equal are always congruent. (   )

17. Taking π = 22/7, the circumference of a circle of radius 7 cm is ______ cm.

18. The median of 3, 7, 5, 13, 9 is ______.

16 MARKS

Section C — Short Answer Questions

Show your working. (2 marks each)

19. Simplify: (−3/4) + (5/6).

20. Simplify: (2³ × 2⁴) ÷ 2⁵.

21. 12 pencils cost ₹ 84. Find the cost of 20 pencils.

22. What per cent of 250 is 40?

23. The marked price of a bag is ₹ 1,200. A discount of 15% is given. Find the selling price.

24. Solve: 5(x − 2) = 3x + 4.

25. The angles of a triangle are in the ratio 2 : 3 : 4. Find the angles.

26. A cuboid measures 12 cm × 5 cm × 4 cm. Find (a) its volume (b) its total surface area.

16 MARKS

Section D — Problem Solving

Write the complete solution. (4 marks each)

27. A 10 m ladder leans against a wall and reaches a window 8 m above the ground.

  1. How far is the foot of the ladder from the wall? [2]
  2. A second ladder has its foot 12 m from a wall and reaches a point 16 m up the wall. What is its length? [2]

28. Rohan borrows ₹ 8,000 at 7.5% per annum for 3 years. Find (a) the simple interest [3] (b) the total amount he must repay [1].

29. A bag contains 5 red, 3 blue and 2 green marbles. One marble is drawn at random. Find the probability that it is

  1. red
  2. blue
  3. not green
  4. yellow

30. A wire in the shape of a circle of radius 21 cm is straightened and bent into a square (take π = 22/7). Find

  1. the length of the wire [1]
  2. the side of the square [1]
  3. the area of the square [2]

ICSE Class 7 Mathematics · Practice Paper — Set 1 · Answer Key

Answers & Worked Solutions

Mark your own paper, then read the solution for every question you got wrong. For the multiple-choice questions, the note in pink shows the answer most students pick by mistake, and why.

Section A — Multiple Choice Questions (10 marks)
Q1. C. −8

Work left to right: (−6) × (−4) = +24 (two negatives give a positive), then 24 ÷ (−3) = −8 (unlike signs give a negative).

Tempting wrong answer: 8 — students notice the first sign change and forget the second one. Count the negative signs: three negatives → the answer is negative.

Q2. B. 3/2

Dividing by a fraction = multiplying by its reciprocal: 2/3 × 9/4 = 18/12 = 3/2.

Tempting wrong answer: 8/27 — multiplying straight across without turning the second fraction upside down.

Q3. D. 6

Multiply both numbers by 100 to make the divisor whole: 36 ÷ 6 = 6.

Tempting wrong answer: 0.6 — the decimal point is copied from the dividend. When both numbers have two decimal places, the point cancels out.

Q4. A. 2⁸

Same base, so add the powers: aᵐ × aⁿ = aᵐ⁺ⁿ. 2⁵ × 2³ = 2⁵⁺³ = 2⁸ = 256.

Tempting wrong answer: 2¹⁵ — multiplying the powers (5 × 3). 4⁸ — multiplying the bases (2 × 2). Neither rule exists: the base stays the same and the powers are added.

Q5. D. −1/3

On the number line, the negative number closest to zero is the greatest. Over 12: −6/12, −8/12, −9/12, −4/12 — the greatest is −4/12 = −1/3.

Tempting wrong answer: −3/4 — it 'looks' biggest because 3/4 is the largest fraction, but among negative numbers the largest fraction is the smallest number.

Q6. B. 84

35% of 240 = (35 ÷ 100) × 240 = 84.

Tempting wrong answer: 156 — that is 65% of 240 (the amount remaining after taking 35% away).

Q7. C. 15%

Loss = 800 − 680 = ₹ 120. Loss % = (loss ÷ cost price) × 100 = (120 ÷ 800) × 100 = 15%.

Tempting wrong answer: 17.6% — dividing the loss by the selling price (120 ÷ 680). Profit and loss per cent are always found on the cost price.

Q8. A. ₹ 600

SI = (P × R × T) ÷ 100 = (5,000 × 6 × 2) ÷ 100 = ₹ 600.

Tempting wrong answer: ₹ 300 — forgetting to multiply by the 2 years. ₹ 5,600 is the amount (P + SI) for 1 year, not the interest.

Q9. C. 6

Add 7 to both sides: 3x = 18. Divide both sides by 3: x = 6. Check: 3 × 6 − 7 = 11 ✓.

Tempting wrong answer: 4/3 — subtracting 7 from 11 instead of adding it. To undo '− 7' you must do the opposite: '+ 7'.

Q10. B. 68°

Supplementary angles add up to 180°: 180° − 112° = 68°.

Tempting wrong answer: 22° — mixing up 'supplementary' (180°) with 'complementary' (90°) and doing 112° − 90°.

Section B — Fill in the Blanks & True / False (8 marks)
Q11. True

If the interior angles are a, b and c, the exterior angle at c is 180° − c = a + b, because a + b + c = 180°.

Q12. 10

Hypotenuse² = 6² + 8² = 36 + 64 = 100, so the hypotenuse = √100 = 10 cm.

Q13. False

The longest side is 6 cm: 3² + 4² = 25 but 6² = 36. Since 25 ≠ 36 the Pythagoras relation fails. (3, 4, 5 would work.)

Q14. 1/2

There are 2 equally likely outcomes (head, tail) and 1 favourable outcome: 1/2.

Q15. 5

A regular polygon with n sides has n lines of symmetry. Each line joins a vertex to the middle of the opposite side.

Q16. False

Equal angles only guarantee the same shape; one triangle can be a bigger copy of the other. For congruency you also need matching sides (SSS, SAS, ASA, RHS).

Q17. 44

C = 2πr = 2 × 22/7 × 7 = 44 cm.

Q18. 7

Arrange in order: 3, 5, 7, 9, 13. The middle value is 7.

Section C — Short Answer Questions (16 marks)
Q19. 1/12
  1. LCM of 4 and 6 = 12.
  2. −3/4 = −9/12 and 5/6 = 10/12.
  3. −9/12 + 10/12 = 1/12.
Q20. 4
  1. Numerator: 2³ × 2⁴ = 2⁷.
  2. 2⁷ ÷ 2⁵ = 2⁷⁻⁵ = 2².
  3. 2² = 4.
Q21. ₹ 140
  1. Cost of 1 pencil = 84 ÷ 12 = ₹ 7.
  2. Cost of 20 pencils = 20 × 7 = ₹ 140.
Q22. 16%
  1. Per cent = (part ÷ whole) × 100.
  2. (40 ÷ 250) × 100 = 16%.
Q23. ₹ 1,020
  1. Discount = 15% of 1,200 = 0.15 × 1,200 = ₹ 180.
  2. Selling price = marked price − discount = 1,200 − 180 = ₹ 1,020.
Q24. x = 7
  1. Expand the bracket: 5x − 10 = 3x + 4.
  2. Move the x-terms to one side: 5x − 3x = 4 + 10 → 2x = 14.
  3. x = 7.
  4. Check: LHS = 5 × (7 − 2) = 25; RHS = 3 × 7 + 4 = 25 ✓.
Q25. 40°, 60°, 80°
  1. Total parts = 2 + 3 + 4 = 9, and the angles add up to 180°.
  2. One part = 180° ÷ 9 = 20°.
  3. Angles = 2 × 20° = 40°, 3 × 20° = 60°, 4 × 20° = 80°.
Q26. (a) 240 cm³ (b) 256 cm²
  1. Volume = l × b × h = 12 × 5 × 4 = 240 cm³.
  2. Total surface area = 2(lb + bh + hl) = 2(60 + 20 + 48) = 2 × 128 = 256 cm².
Section D — Problem Solving (16 marks)
Q27. (a) 6 m (b) 20 m
  1. The ladder is the hypotenuse: distance² = 10² − 8² = 100 − 64 = 36, so distance = 6 m.
  2. Length² = 12² + 16² = 144 + 256 = 400, so length = √400 = 20 m.
Q28. (a) ₹ 1,800 (b) ₹ 9,800
  1. SI = (P × R × T) ÷ 100 = (8,000 × 7.5 × 3) ÷ 100 = ₹ 1,800.
  2. Amount = P + SI = 8,000 + 1,800 = ₹ 9,800.
Q29. (a) 1/2 (b) 3/10 (c) 4/5 (d) 0
  1. Total marbles = 5 + 3 + 2 = 10.
  2. (a) P(red) = 5/10 = 1/2.
  3. (b) P(blue) = 3/10.
  4. (c) Not green = red or blue = 8 marbles, so P = 8/10 = 4/5.
  5. (d) There are no yellow marbles, so it is an impossible event: P = 0.
Q30. (a) 132 cm (b) 33 cm (c) 1,089 cm²
  1. Length of wire = circumference = 2πr = 2 × 22/7 × 21 = 132 cm.
  2. Perimeter of the square = 132 cm, so side = 132 ÷ 4 = 33 cm.
  3. Area = 33 × 33 = 1,089 cm².
← All ICSE Class 7 Exams