VI MAT SP 2

KENDRIYA VIDYALAYA STEEL PLANT - CLASS VI MATHEMATICS SAMPLE PAPER

SET - 02 | Total Marks: 40

Section A: Multiple Choice Questions (8 x 1 = 8 Marks)

1. Which number is neither prime nor composite?

A) 0
B) 1
C) 2
D) 4

Answer: B) 1

2. A number is divisible by 10 if it ends with:

A) 5
B) 0
C) 2
D) Any even number

Answer: B) 0

3. What is the perimeter of an equilateral triangle with side 4 cm?

A) 8 cm
B) 16 cm
C) 12 cm
D) 4 cm

Answer: C) 12 cm

4. Fractions that denote the same length or share are called:

A) Unit fractions
B) Mixed fractions
C) Equivalent fractions
D) Simple fractions

Answer: C) Equivalent fractions

5. Which of the following is a composite number?

A) 17
B) 19
C) 4
D) 13

Answer: C) 4

6. What is the perimeter of a rectangle with length 12 cm and breadth 8 cm?

A) 20 cm
B) 40 cm
C) 96 cm
D) 100 cm

Answer: B) 40 cm

7. A mixed fraction contains a whole part and a:

A) Greater part
B) Fractional part
C) Even part
D) Composite part

Answer: B) Fractional part

8. Which jump sizes will land on both 14 and 36?

A) 7
B) 3
C) 2
D) 4

Answer: C) 2

Section B: Short Answer Questions (4 x 2 = 8 Marks)

9. Find any three numbers that are multiples of 25 but not multiples of 50.

Solution:
1. List multiples of 25: 25, 50, 75, 100, 125, 150, 175...
2. Remove multiples of 50: 50, 100, 150...
3. Numbers: 25, 75, 125.

10. Find the side of a square if its perimeter is 20 cm.

Solution:
1. Perimeter of a square = 4 × length of a side.
2. 20 = 4 × side.
3. Side = 20 ÷ 4 = 5 cm.

11. Write the fraction 9/2 as a mixed fraction.

Solution:
1. Divide 9 by 2: Quotient is 4, Remainder is 1.
2. Mixed fraction = 4 1/2.

12. What are twin primes? Give one example.

Solution:
1. Twin primes are pairs of primes having a difference of 2.
2. Example: (3, 5) or (17, 19).

Section C: Long Answer Questions (4 x 3 = 12 Marks)

13. Find the prime factorisation of 1000.

Solution:
1. 1000 = 10 × 100.
2. 10 = 2 × 5.
3. 100 = 10 × 10 = (2 × 5) × (2 × 5).
4. Factorisation: 2 × 2 × 2 × 5 × 5 × 5.

14. Subtract 5/9 from 7/9.

Solution:
1. The fractional units are the same (1/9).
2. Subtract numerators: 7 - 5 = 2.
3. Result: 2/9.

15. Is 8536 divisible by 4? Explain using the divisibility test.

Solution:
1. Check the last two digits: 36.
2. Check if 36 is divisible by 4: 36 ÷ 4 = 9.
3. Since 36 is divisible by 4, the original number 8536 is divisible by 4.

16. Find the length of the third side of a triangle with perimeter 55 cm and two sides of 20 cm and 14 cm.

Solution:
1. Perimeter = Sum of all three sides.
2. 55 = 20 + 14 + third side.
3. 55 = 34 + third side.
4. Third side = 55 - 34 = 21 cm.

Section D: Very Long Answer Questions (3 x 4 = 12 Marks)

17. Find the smallest number whose prime factorisation has four different prime numbers.

Solution:
1. Identify the first four prime numbers: 2, 3, 5, 7.
2. Multiply them: 2 × 3 × 5 × 7.
3. Calculate: 6 × 35 = 210.
4. Result: 210.

18. Rahim mixes 2/3 litres of yellow paint with 3/4 litres of blue paint. What is the total volume?

Solution:
1. Common denominator for 3 and 4 is 12.
2. 2/3 = 8/12.
3. 3/4 = 9/12.
4. Add: 8/12 + 9/12 = 17/12.
5. Convert to mixed fraction: 1 5/12 litres.

19. Four flower beds (4m side) are in corners of a land (12m x 10m). Find the area of remaining part.

Solution:
1. Total land area = 12m × 10m = 120 sq m.
2. Area of one flower bed = 4m × 4m = 16 sq m.
3. Area of 4 beds = 4 × 16 = 64 sq m.
4. Remaining area = 120 - 64 = 56 sq m.