CBSE Class 6 Mathematics · Exam Practice

Practice Paper — Set 1

CBSE Class 6 Mathematics, covering prime numbers, HCF and LCM, integers, fractions, symmetry, perimeter and data, 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 CBSE Class 6 Mathematics topics on MuskMeadow: Patterns, Lines & Angles, Prime Time, Fractions, The Other Side of Zero, Perimeter & Area, Symmetry 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. Which of the following numbers is prime?

A. 51B. 57C. 53D. 91

2. The LCM of 12 and 18 is

A. 36B. 6C. 72D. 216

3. The prime factorisation of 60 is

A. 2 × 3 × 10B. 2 × 2 × 3 × 5C. 2 × 3 × 3 × 5D. 4 × 15

4. The temperature in a hill town was 4 °C. It then fell by 9 °C. The new temperature is

A. 5 °CB. −13 °CC. 13 °CD. −5 °C

5. Which fraction is equivalent to 3/5?

A. 9/15B. 6/15C. 3/10D. 6/9

6. 1/2 + 1/3 =

A. 2/5B. 2/6C. 5/6D. 1/6

7. How many end-points does a ray have?

A. 0B. 1C. 2D. infinitely many

8. The perimeter of a regular pentagon of side 8 cm is

A. 40 cmB. 32 cmC. 64 cmD. 13 cm

9. The number of lines of symmetry of a square is

A. 1B. 2C. 8D. 4

10. In a pictograph, one symbol stands for 5 books. A row with 7 symbols shows

A. 7 booksB. 35 booksC. 12 booksD. 57 books
8 MARKS

Section B — Fill in the Blanks & True / False

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

11. The number 1 is neither ______ nor composite.

12. Every even number greater than 2 is a composite number. (   )

13. The letter H has ______ lines of symmetry.

14. 0 is a negative number. (   )

15. The area of a square of side 9 cm is ______ cm².

16. The smallest prime number is ______.

17. 4/6 and 2/3 are equivalent fractions. (   )

18. The radius of a circle with diameter 18 cm is ______ cm.

16 MARKS

Section C — Short Answer Questions

Show your working. (2 marks each)

19. List all the factors of 36.

20. Without dividing fully, check whether 3,456 is divisible by 3 and by 4.

21. Arrange in ascending order: −6, 3, −2, 0, −9.

22. Subtract: 5/6 − 1/4.

23. Find the next three numbers in the pattern 3, 7, 11, 15, … and state the rule.

24. A rectangle is 15 cm long and 9 cm wide. Find its perimeter. A square has the same perimeter — what is the side of the square?

25. How many lines of symmetry does an equilateral triangle have? What is its order of rotational symmetry?

26. The table shows the favourite game of the students of Class 6. (a) Which game is the most popular? (b) How many more votes does it get than the least popular game? (c) How many students voted altogether?

GameCricketFootballHockeyKabaddi
Votes12859
16 MARKS

Section D — Problem Solving

Write the complete solution. (4 marks each)

27. Two ropes, 48 m and 72 m long, are to be cut into pieces of equal length, with no rope left over. The pieces should be as long as possible.

  1. What is the length of each piece? [2]
  2. How many pieces are there altogether? [2]

28. A milk container holds 2 litres. Meena drinks 3/4 litre in the morning and 1/2 litre in the evening.

  1. How much milk does she drink in all? [2]
  2. How much milk is left in the container? [2]

29. A rectangle 10 m × 6 m and a square of side 6 m are joined along a 6 m side to form one bigger rectangle.

  1. Find the total area of the combined shape. [2]
  2. Find the perimeter of the combined shape. [2]

30. At 6 a.m. the temperature in Shimla was −4 °C. By noon it had risen by 9 °C, and by night it had fallen by 7 °C from the noon temperature.

  1. Find the temperature at noon. [1]
  2. Find the temperature at night. [2]
  3. By how many degrees is the night temperature higher than the 6 a.m. temperature? [1]

CBSE 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. C. 53

53 is not divisible by 2, 3, 5 or 7 (7 × 7 = 49 and 7 × 8 = 56 straddle it), so its only factors are 1 and 53.

Tempting wrong answer: 51 (= 3 × 17), 57 (= 3 × 19) and 91 (= 7 × 13) all look prime because they are odd and not in the 2, 5 or 10 tables — but each has a smaller factor.

Q2. A. 36

Multiples of 18: 18, 36, … and 36 = 12 × 3 ✓. It is the smallest number that both 12 and 18 divide.

Tempting wrong answer: 6 is their HCF, not LCM. 216 is 12 × 18 — a common multiple, but not the least one because 12 and 18 share the factor 6.

Q3. B. 2 × 2 × 3 × 5

60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5 — every factor is prime.

Tempting wrong answer: 2 × 3 × 10 and 4 × 15 multiply to 60 but 10, 4 and 15 are not prime. 2 × 3 × 3 × 5 = 90.

Q4. D. −5 °C

4 − 9 = −5. Going 4 steps down reaches 0, and 5 more steps take it below zero to −5.

Tempting wrong answer: 5 °C — subtracting the smaller from the larger (9 − 4) and forgetting that the temperature ends up below zero.

Q5. A. 9/15

Multiply the numerator and denominator by the same number: 3 × 3 = 9 and 5 × 3 = 15.

Tempting wrong answer: 6/15 — the numerator is doubled but the denominator is tripled. 3/10 changes only the denominator. Both parts must be multiplied by the same number.

Q6. C. 5/6

Common denominator 6: 3/6 + 2/6 = 5/6.

Tempting wrong answer: 2/5 — adding the tops and the bottoms separately. The denominators tell the size of the pieces and must be made equal first.

Q7. B. 1

A ray starts at one point and goes on forever in one direction, so it has exactly one end-point.

Tempting wrong answer: 2 — that is a line segment. 0 — that is a line, which extends in both directions.

Q8. A. 40 cm

A regular pentagon has 5 equal sides: 5 × 8 = 40 cm.

Tempting wrong answer: 32 cm — using 4 sides (a square's perimeter). Always count the sides of the shape.

Q9. D. 4

A square folds onto itself along 2 diagonals and 2 lines through the mid-points of opposite sides: 4 lines in all.

Tempting wrong answer: 2 — students remember the two diagonals but forget the horizontal and vertical fold lines.

Q10. B. 35 books

Each symbol is worth 5 books, so 7 symbols = 7 × 5 = 35 books.

Tempting wrong answer: 7 — counting the symbols without reading the scale. 12 — adding 7 + 5 instead of multiplying.

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

A prime number has exactly two factors. The number 1 has only one factor (itself), so it is neither prime nor composite.

Q12. True

An even number is divisible by 2. If it is greater than 2, it has at least the factors 1, 2 and itself, so it is composite. (2 is the only even prime.)

Q13. 2

One vertical line (down the middle) and one horizontal line (across the crossbar).

Q14. False

Zero is neither positive nor negative; it separates the positive numbers from the negative ones on the number line.

Q15. 81

Area = side × side = 9 × 9 = 81 cm².

Q16. 2

1 is not prime, and 2 has exactly two factors (1 and 2). It is also the only even prime.

Q17. True

Dividing the numerator and denominator of 4/6 by 2 gives 2/3.

Q18. 9

Radius = diameter ÷ 2 = 18 ÷ 2 = 9 cm.

Section C — Short Answer Questions (16 marks)
Q19. 1, 2, 3, 4, 6, 9, 12, 18, 36
  1. Look for pairs that multiply to 36: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.
  2. Write the numbers in order (6 is listed once): 1, 2, 3, 4, 6, 9, 12, 18, 36 — nine factors.
Q20. Divisible by both 3 and 4
  1. By 3: digit sum = 3 + 4 + 5 + 6 = 18, and 18 is a multiple of 3 ✓.
  2. By 4: the last two digits form 56, and 56 = 4 × 14 ✓.
Q21. −9, −6, −2, 0, 3
  1. On the number line, numbers increase from left to right.
  2. The most negative number is the smallest: −9 < −6 < −2 < 0 < 3.
  3. Common slip: thinking −9 is greater than −2 because 9 is greater than 2.
Q22. 7/12
  1. LCM of 6 and 4 = 12.
  2. 5/6 = 10/12 and 1/4 = 3/12.
  3. 10/12 − 3/12 = 7/12.
Q23. 19, 23, 27; add 4 each time
  1. Differences: 7 − 3 = 4, 11 − 7 = 4, 15 − 11 = 4. The rule is 'add 4'.
  2. 15 + 4 = 19, 19 + 4 = 23, 23 + 4 = 27.
Q24. 48 cm; 12 cm
  1. Perimeter of the rectangle = 2 × (15 + 9) = 48 cm.
  2. Perimeter of a square = 4 × side, so side = 48 ÷ 4 = 12 cm.
Q25. 3 lines; order 3
  1. Each line joins a vertex to the mid-point of the opposite side: 3 lines of symmetry.
  2. Turning it through 120° (a third of a full turn) fits it back onto itself, so it looks the same 3 times in one full turn: order 3.
Q26. (a) Cricket (b) 7 (c) 34
  1. (a) The highest number of votes is 12, for Cricket.
  2. (b) The lowest is 5 (Hockey): 12 − 5 = 7 more votes.
  3. (c) Total = 12 + 8 + 5 + 9 = 34 students.
Section D — Problem Solving (16 marks)
Q27. (a) 24 m (b) 5 pieces
  1. The longest equal length that divides both 48 and 72 is their HCF. 48 = 2⁴ × 3 and 72 = 2³ × 3², so HCF = 2³ × 3 = 24 m.
  2. First rope: 48 ÷ 24 = 2 pieces. Second rope: 72 ÷ 24 = 3 pieces. Total = 2 + 3 = 5 pieces.
Q28. (a) 1¼ litres (b) ¾ litre
  1. 3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1¼ litres.
  2. 2 − 5/4 = 8/4 − 5/4 = 3/4, so ¾ litre is left.
Q29. (a) 96 m² (b) 44 m
  1. Area = area of rectangle + area of square = 10 × 6 + 6 × 6 = 60 + 36 = 96 m².
  2. The joined 6 m sides are now inside the shape and are not part of the perimeter. The new rectangle is (10 + 6) m × 6 m = 16 m × 6 m.
  3. Perimeter = 2 × (16 + 6) = 44 m.
Q30. (a) 5 °C (b) −2 °C (c) 2 °C
  1. Noon: −4 + 9 = 5 °C.
  2. Night: 5 − 7 = −2 °C (5 steps down reach 0, two more reach −2).
  3. Difference: −2 − (−4) = −2 + 4 = 2 °C. On the number line, −2 is 2 steps to the right of −4.
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