ICSE Class 6 Mathematics · Exam Practice

Practice Paper — Set 1

ICSE Class 6 Mathematics, covering all chapters, 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 covers all eight ICSE Class 6 chapters on MuskMeadow: Number System, Playing with Numbers, Fractions & Decimals, Ratio & Proportion, Algebra Basics, Basic Geometrical Ideas, Perimeter & Area and Data Handling.
  • 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. The value of −7 + 12 − 8 is

A. 3B. −3C. −27D. −13

2. The greatest 6-digit number that can be made using the digits 4, 0, 7, 2, 9 and 5 once each is

A. 9,75,402B. 9,74,520C. 9,54,720D. 9,75,420

3. Which of the following numbers is divisible by 9?

A. 5,238B. 4,326C. 7,231D. 6,104

4. The HCF of 36 and 48 is

A. 6B. 24C. 12D. 144

5. 3/4 + 2/3 =

A. 5/7B. 17/12C. 5/12D. 1/12

6. 4.5 × 0.6 =

A. 27B. 0.27C. 2.7D. 2.07

7. The ratio 18 : 24 in its simplest form is

A. 3 : 4B. 9 : 12C. 6 : 8D. 4 : 3

8. The value of 3x + 5 when x = 4 is

A. 39B. 12C. 9D. 17

9. A triangle has angles of 50°, 60° and 70°. It is a(n)

A. right-angled triangleB. acute-angled triangleC. obtuse-angled triangleD. equilateral triangle

10. The area of a rectangle 12 cm long and 7 cm wide is

A. 84 cm²B. 38 cm²C. 19 cm²D. 84 cm
8 MARKS

Section B — Fill in the Blanks & True / False

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

11. The LCM of 6 and 8 is ______.

12. The additive inverse of −15 is ______.

13. 91 is a prime number. (   )

14. 2 and 9 are co-prime numbers. (   )

15. The ratio 20 minutes : 1 hour in its simplest form is ______.

16. The mean of 4, 8, 6, 10 and 2 is ______.

17. An angle measuring 200° is a reflex angle. (   )

18. The mode of 3, 5, 5, 7, 9, 5, 3 is ______.

16 MARKS

Section C — Short Answer Questions

Show your working. (2 marks each)

19. Evaluate: (−12) + 7 − (−5).

20. Find the HCF of 48 and 72 by the division method.

21. Multiply: 2½ × 1⅕.

22. Divide: 12.6 ÷ 0.9.

23. Check whether 3 : 5 and 12 : 20 are in proportion.

24. Write an algebraic expression for: '5 less than three times a number n'.

25. Two angles of a triangle are 65° and 48°. Find the third angle and say whether the triangle is acute-, right- or obtuse-angled.

26. The perimeter of a square is 40 cm. Find its area.

16 MARKS

Section D — Problem Solving

Write the complete solution. (4 marks each)

27. A tailor has 7.5 m of cloth. One shirt needs 2.25 m of cloth.

  1. How many complete shirts can he make?
  2. How much cloth is left over?

28. Asha and Bina share ₹ 1,800 in the ratio 5 : 4. Find the amount each gets.

29. The marks obtained by 7 students in a test are: 12, 20, 11, 9, 16, 7, 9. Find the (a) mean [2] (b) median [1] (c) mode [1].

30. A rectangular field is 30 m long and 20 m wide. A square flower bed of side 6 m is inside it.

  1. Find the perimeter of the field. [1]
  2. Find the cost of fencing the field at ₹ 12 per metre. [1]
  3. Find the area of the field that is not covered by the flower bed. [2]

ICSE Class 6 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. B. −3

−7 + 12 = 5, and 5 − 8 = −3.

Tempting wrong answer: 3 — students work out 8 − 5 = 3 and forget that the larger number (8) is being subtracted, so the answer must be negative.

Q2. D. 9,75,420

For the greatest number, write the digits in descending order: 9, 7, 5, 4, 2, 0 → 9,75,420.

Tempting wrong answer: 9,75,402 — it looks right at a glance, but 4 and 2 are swapped at the end; 4 > 2, so 4 must come first.

Q3. A. 5,238

A number is divisible by 9 if its digit sum is a multiple of 9. 5 + 2 + 3 + 8 = 18 ✓. The others give 15, 13 and 11.

Tempting wrong answer: 4,326 — its digit sum is 15, which is a multiple of 3, so the number is divisible by 3 — but 15 is not a multiple of 9.

Q4. C. 12

36 = 2 × 2 × 3 × 3 and 48 = 2 × 2 × 2 × 2 × 3. Common prime factors: 2 × 2 × 3 = 12.

Tempting wrong answer: 144 — that is the LCM, not the HCF. 6 is a common factor, but not the highest one.

Q5. B. 17/12

LCM of 4 and 3 is 12: 3/4 = 9/12 and 2/3 = 8/12, so 9/12 + 8/12 = 17/12 = 1 5/12.

Tempting wrong answer: 5/7 — adding the numerators (3 + 2) and the denominators (4 + 3) is the classic mistake. Fractions must have a common denominator first.

Q6. C. 2.7

Multiply as whole numbers: 45 × 6 = 270. There is 1 decimal place in each factor, so 2 in the answer: 2.70 = 2.7.

Tempting wrong answer: 0.27 or 27 — the digits 27 are right, but the decimal point is put in the wrong place. Count the decimal places (1 + 1 = 2) and then simplify 2.70.

Q7. A. 3 : 4

Divide both terms by their HCF, 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4.

Tempting wrong answer: 9 : 12 and 6 : 8 are both equivalent to 18 : 24 but can still be reduced — 'simplest form' means no common factor is left.

Q8. D. 17

3x means 3 × x. Put x = 4: 3 × 4 + 5 = 12 + 5 = 17.

Tempting wrong answer: 39 — reading 3x as 'three-four' (34) instead of 3 × 4. In algebra, a number next to a letter means multiplication.

Q9. B. acute-angled triangle

The angles add up to 180°, and all three are less than 90°, so it is an acute-angled triangle.

Tempting wrong answer: Equilateral — that needs three equal angles (60° each) or three equal sides. Here the angles are all different.

Q10. A. 84 cm²

Area = length × breadth = 12 × 7 = 84 cm².

Tempting wrong answer: 38 comes from the perimeter formula 2 × (12 + 7). '84 cm' has the right number but the wrong unit — area is always in square units.

Section B — Fill in the Blanks & True / False (8 marks)
Q11. 24

Multiples of 8: 8, 16, 24; 24 is also a multiple of 6 (6 × 4). Prime-factor check: 2 × 2 × 2 × 3 = 24.

Q12. 15

The additive inverse is the number that adds to give 0: −15 + 15 = 0.

Q13. False

91 = 7 × 13, so it has more than two factors. It looks prime because it is not divisible by 2, 3 or 5.

Q14. True

Their only common factor is 1 (HCF = 1). Co-prime numbers do not have to be prime themselves — 9 is composite.

Q15. 1 : 3

Bring both to the same unit first: 1 hour = 60 minutes. 20 : 60 = 1 : 3.

Q16. 6

Sum = 4 + 8 + 6 + 10 + 2 = 30. Mean = 30 ÷ 5 = 6.

Q17. True

A reflex angle is more than 180° and less than 360°.

Q18. 5

5 occurs three times; 3 occurs twice; the others once. The mode is the value that occurs most often.

Section C — Short Answer Questions (16 marks)
Q19. 0
  1. Subtracting −5 is the same as adding 5: (−12) + 7 + 5.
  2. −12 + 7 = −5.
  3. −5 + 5 = 0.
Q20. 24
  1. Divide the larger number by the smaller: 72 ÷ 48 → quotient 1, remainder 24.
  2. Divide the old divisor by the remainder: 48 ÷ 24 → quotient 2, remainder 0.
  3. The last divisor is the HCF: 24.
Q21. 3
  1. Convert to improper fractions: 2½ = 5/2 and 1⅕ = 6/5.
  2. Multiply: (5 × 6) / (2 × 5) = 30/10.
  3. Simplify: 30/10 = 3.
Q22. 14
  1. Multiply both numbers by 10 so the divisor is a whole number: 126 ÷ 9.
  2. 126 ÷ 9 = 14.
Q23. Yes, they are in proportion
  1. Product of extremes = 3 × 20 = 60.
  2. Product of means = 5 × 12 = 60.
  3. The two products are equal, so 3 : 5 :: 12 : 20.
Q24. 3n − 5
  1. 'Three times a number n' is 3n.
  2. '5 less than' 3n means take 5 away from it: 3n − 5.
  3. Common slip: writing 5 − 3n, which means 3n less than 5.
Q25. 67°; acute-angled
  1. Sum of the angles of a triangle = 180°.
  2. 65° + 48° = 113°, so the third angle = 180° − 113° = 67°.
  3. All three angles (65°, 48°, 67°) are less than 90°, so the triangle is acute-angled.
Q26. 100 cm²
  1. Perimeter of a square = 4 × side, so side = 40 ÷ 4 = 10 cm.
  2. Area = side × side = 10 × 10 = 100 cm².
Section D — Problem Solving (16 marks)
Q27. (a) 3 shirts (b) 0.75 m
  1. 7.5 ÷ 2.25 = 750 ÷ 225 = 3.33… — only whole shirts count, so he can make 3 shirts.
  2. Cloth used = 3 × 2.25 = 6.75 m.
  3. Cloth left = 7.5 − 6.75 = 0.75 m (not enough for a fourth shirt).
Q28. Asha ₹ 1,000; Bina ₹ 800
  1. Total number of parts = 5 + 4 = 9.
  2. Value of one part = 1,800 ÷ 9 = ₹ 200.
  3. Asha = 5 × 200 = ₹ 1,000; Bina = 4 × 200 = ₹ 800.
  4. Check: 1,000 + 800 = 1,800 ✓.
Q29. Mean 12; median 11; mode 9
  1. Mean = (12 + 20 + 11 + 9 + 16 + 7 + 9) ÷ 7 = 84 ÷ 7 = 12.
  2. Arrange in order: 7, 9, 9, 11, 12, 16, 20. The middle (4th) value is 11, so the median = 11.
  3. 9 appears twice and every other value once, so the mode = 9.
Q30. (a) 100 m (b) ₹ 1,200 (c) 564 m²
  1. Perimeter = 2 × (30 + 20) = 100 m.
  2. Cost = 100 × 12 = ₹ 1,200.
  3. Area of field = 30 × 20 = 600 m²; area of flower bed = 6 × 6 = 36 m²; area left = 600 − 36 = 564 m².
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