VI MAT SP 1

KENDRIYA VIDYALAYA STEEL PLANT - CLASS VI MATHEMATICS SAMPLE PAPER

SET - 01 | Total Marks: 40

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

1. Which of the following is the smallest prime number?

A) 1
B) 2
C) 3
D) 4

Answer: B) 2

2. What is the perimeter of a square with a side of 1 m?

A) 1 m
B) 2 m
C) 4 m
D) 8 m

Answer: C) 4 m

3. How is the fraction 'one half' written?

A) 1/4
B) 1/2
C) 2/1
D) 1/3

Answer: B) 1/2

4. Which of these numbers is a multiple of 3?

A) 16
B) 25
C) 43
D) 9

Answer: D) 9

5. If 56 = 4 × 14, which of these are factors of 56?

A) Only 4
B) Only 14
C) Both 4 and 14
D) Neither

Answer: C) Both 4 and 14

6. A number that has only two factors (1 and itself) is called:

A) Composite number
B) Perfect number
C) Prime number
D) Even number

Answer: C) Prime number

7. In the fraction 5/6, what is the number 5 called?

A) Denominator
B) Divisor
C) Numerator
D) Remainder

Answer: C) Numerator

8. What is the area of a square with side 3 m?

A) 6 sq m
B) 9 sq m
C) 12 sq m
D) 3 sq m

Answer: B) 9 sq m

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

9. Find the common factors of 20 and 28.

Solution:
1. Factors of 20: 1, 2, 4, 5, 10, 20.
2. Factors of 28: 1, 2, 4, 7, 14, 28.
3. Common factors: 1, 2, 4.

10. Find the missing breadth if Perimeter of a rectangle = 12 m and length = 3 m.

Solution:
1. Perimeter = 2 × (length + breadth).
2. 12 = 2 × (3 + breadth).
3. 6 = 3 + breadth.
4. Breadth = 3 m.

11. Write the mixed fraction 2 2/3 as a regular fraction.

Solution:
1. Multiply whole number by denominator: 2 × 3 = 6.
2. Add numerator: 6 + 2 = 8.
3. Result: 8/3.

12. Identify if the numbers 18 and 35 are co-prime.

Solution:
1. Find factors of 18: 1, 2, 3, 6, 9, 18.
2. Find factors of 35: 1, 5, 7, 35.
3. Since they have no common factor other than 1, they are co-prime.

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

13. Express 36/60 in its lowest terms.

Solution:
1. Divide both by 2: 36/60 = 18/30.
2. Divide both by 2 again: 18/30 = 9/15.
3. Divide both by 3: 9/15 = 3/5.
4. Lowest terms: 3/5.

14. Find the sum of 1/4 and 1/3 using Brahmagupta’s method.

Solution:
1. Find common denominator (4 × 3 = 12).
2. Convert 1/4 to 3/12.
3. Convert 1/3 to 4/12.
4. Add numerators: 3 + 4 = 7.
5. Result: 7/12.

15. A rectangular field has length 230 m and breadth 160 m. What is the length of rope needed for 3 rounds of fencing?

Solution:
1. Perimeter = 2 × (230 + 160) = 780 m.
2. Length for 3 rounds = 3 × 780 m.
3. Total length = 2340 m.

16. Find all multiples of 40 that lie between 310 and 410.

Solution:
1. List multiples of 40 near 310: 40 × 8 = 320.
2. 40 × 9 = 360.
3. 40 × 10 = 400.
4. Multiples are 320, 360, 400.

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

17. Find the prime factorisation of 1728.

Solution:
1. 1728 ÷ 2 = 864.
2. 864 ÷ 2 = 432.
3. 432 ÷ 2 = 216.
4. 216 ÷ 2 = 108.
5. 108 ÷ 2 = 54.
6. 54 ÷ 2 = 27.
7. 27 ÷ 3 = 9.
8. 9 ÷ 3 = 3.
9. 3 ÷ 3 = 1.
10. Factorisation: 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3.

18. A floor is 5 m long and 4 m wide. A square carpet of side 3 m is laid. Find the area not carpeted.

Solution:
1. Area of floor = 5 m × 4 m = 20 sq m.
2. Area of square carpet = 3 m × 3 m = 9 sq m.
3. Area not carpeted = 20 sq m - 9 sq m.
4. Result = 11 sq m.

19. Compare the fractions 3/4 and 7/10 to find which is larger.

Solution:
1. Find a common denominator: 4 × 10 = 40.
2. 3/4 = 30/40.
3. 7/10 = 28/40.
4. Since 30/40 > 28/40, then 3/4 > 7/10.