SAMPLE PAPER 10
SECTION A (MCQ & ARQ)
The digital root of an 8-digit number is 5. What will be the digital root of 10 more than that number?
a) 5 b) 6 c) 1 d) 8
The number which is divisible by 11 is:
a) 1234 b) 93547 c) 358095 d) 601436
The number of students in classes A and B are in the ratio 4:5. If 8 students are shifted from class B to A, the ratio becomes 1:1. How many students were there in class B initially?
a) 65 b) 72 c) 80 d) 90
Jeevana purchased a story book of 216 pages and completed 162 pages. What percentage of the book is to be completed?
a) 10% b) 15% c) 60% d) 25%
Percentages are fractions with denominator:
a) 100 b) 10 c) 1 d) 50
Find the diagonal of a square with side length 5 cm:
a) 25 cm b) 5√2 cm c) 2√5 cm d) 20 cm
Choose a Baudhayana-Pythagoras triple:
a) 3,4,6 b) 6,8,11 c) 5,12,14 d) 12,16,20
Find the area of unshaded triangular part of the given rectangle. (diagram)
Match the following:
i) The area of a triangle a) ½ × product of diagonals
ii) The area of a rhombus b) ½ × base × height
iii) Area of parallelogram c) ½ × height × sum of parallel sides
iv) Area of trapezium d) base × height
Which pair of ratios is NOT proportional?
a) 18:27 and 4:6 b) 25:40 and 5:8 c) 21:35 and 3:5 d) 16:24 and 5:7
Choose the incorrect one:
a) (a + b)² = a² + 2ab + b² b) (a - b)² = a² - 2ab + b²
c) (a + b)(c - d) = ac + ad + bc + bd d) a² - b² = (a + b)(a - b)
Which of the following is an example of the distributive property of multiplication over addition?
a) (a + b = b + a) b) [a(b + c) = ab + ac] c) [(a + b) + c = a + (b + c)] d) (ab = ba)
How many m² is a Km²?
a) 1000000 b) 100000 c) 10000 d) 1000
Assertion-Reason:
Assertion: The square of an even number is always divisible by 4.
Reason: Any even number can be written as 2.
Assertion: If the price of an article increases by 20% and then decreases by 20%, the final price remains the same as the original price.
Reason: An increase and decrease by the same percentage always cancel each other.
The digital root of an 8-digit number is 5. What will be the digital root of 10 more than that number?
a) 5 b) 6 c) 1 d) 8
The number which is divisible by 11 is:
a) 1234 b) 93547 c) 358095 d) 601436
The number of students in classes A and B are in the ratio 4:5. If 8 students are shifted from class B to A, the ratio becomes 1:1. How many students were there in class B initially?
a) 65 b) 72 c) 80 d) 90
Jeevana purchased a story book of 216 pages and completed 162 pages. What percentage of the book is to be completed?
a) 10% b) 15% c) 60% d) 25%
Percentages are fractions with denominator:
a) 100 b) 10 c) 1 d) 50
Find the diagonal of a square with side length 5 cm:
a) 25 cm b) 5√2 cm c) 2√5 cm d) 20 cm
Choose a Baudhayana-Pythagoras triple:
a) 3,4,6 b) 6,8,11 c) 5,12,14 d) 12,16,20
Find the area of unshaded triangular part of the given rectangle. (diagram)
Match the following:
i) The area of a triangle a) ½ × product of diagonals
ii) The area of a rhombus b) ½ × base × height
iii) Area of parallelogram c) ½ × height × sum of parallel sides
iv) Area of trapezium d) base × height
Which pair of ratios is NOT proportional?
a) 18:27 and 4:6 b) 25:40 and 5:8 c) 21:35 and 3:5 d) 16:24 and 5:7
Choose the incorrect one:
a) (a + b)² = a² + 2ab + b² b) (a - b)² = a² - 2ab + b²
c) (a + b)(c - d) = ac + ad + bc + bd d) a² - b² = (a + b)(a - b)
Which of the following is an example of the distributive property of multiplication over addition?
a) (a + b = b + a) b) [a(b + c) = ab + ac] c) [(a + b) + c = a + (b + c)] d) (ab = ba)
How many m² is a Km²?
a) 1000000 b) 100000 c) 10000 d) 1000
Assertion: The square of an even number is always divisible by 4.
Reason: Any even number can be written as 2.
Assertion: If the price of an article increases by 20% and then decreases by 20%, the final price remains the same as the original price.
Reason: An increase and decrease by the same percentage always cancel each other.
SECTION B (VSA - 2 marks each)
Find four consecutive numbers whose sum is 94.
A sports coach buys 24 kits. Each kit has 2 pairs of shoes and 3 T-shirts. Each boy is given a pair of shoes and a T-shirt. In that afternoon the coach has distributed shoes & T-shirt to 20 boys. How much T-shirt are left?
A TV is bought at a price of ₹21,000. After 1 year, the value of the TV depreciates by 5%. Find the value of the TV after one year.
If a = 8 cm and b = 12 cm are the sides of a right triangle, find the length of hypotenuse.
If 3p7q8 is divisible by 6, list any two pairs of values for 'p' and 'q'.
Find four consecutive numbers whose sum is 94.
A sports coach buys 24 kits. Each kit has 2 pairs of shoes and 3 T-shirts. Each boy is given a pair of shoes and a T-shirt. In that afternoon the coach has distributed shoes & T-shirt to 20 boys. How much T-shirt are left?
A TV is bought at a price of ₹21,000. After 1 year, the value of the TV depreciates by 5%. Find the value of the TV after one year.
If a = 8 cm and b = 12 cm are the sides of a right triangle, find the length of hypotenuse.
If 3p7q8 is divisible by 6, list any two pairs of values for 'p' and 'q'.
SECTION C (SA - 3 marks each)
Explain the divisibility test for 11 using place value with an example.
Percentage calculations: (question incomplete in PDF)
Find the area of the shaded region given that ABCD is a rectangle. (diagram)
Find the side length of a rhombus whose diagonals are of 24 units and 70 units.
Simplify a) 72 : 108 (b) 20 : 30 (c) Check whether the two ratios are proportional.
Explain the divisibility test for 11 using place value with an example.
Percentage calculations: (question incomplete in PDF)
Find the area of the shaded region given that ABCD is a rectangle. (diagram)
Find the side length of a rhombus whose diagonals are of 24 units and 70 units.
Simplify a) 72 : 108 (b) 20 : 30 (c) Check whether the two ratios are proportional.
SECTION D (LA - 4 marks each)
A shopkeeper has a set of (21 + x) pens and the cost of each pen is ₹(21 - x)
a) What is the total cost all his pens?
b) Find the cost pens in the above case if x = 4
A four days scout and guide camp were arranged by the school for class 8 students.
i) The school arranged 6 buses to take 150 students to the camp. If 75 more students are joined, how many buses are required in all?
ii) In the camp, they assigned some jobs to the students. 45 students complete a job in 20 minutes. How many minutes will 30 students take to complete the same job?
Find the area of an equilateral triangle with side length 6 units. (Hint: Show that an altitude bisects the opposite side. Use this to find the height)
A shopkeeper has a set of (21 + x) pens and the cost of each pen is ₹(21 - x)
a) What is the total cost all his pens?
b) Find the cost pens in the above case if x = 4
A four days scout and guide camp were arranged by the school for class 8 students.
i) The school arranged 6 buses to take 150 students to the camp. If 75 more students are joined, how many buses are required in all?
ii) In the camp, they assigned some jobs to the students. 45 students complete a job in 20 minutes. How many minutes will 30 students take to complete the same job?
Find the area of an equilateral triangle with side length 6 units. (Hint: Show that an altitude bisects the opposite side. Use this to find the height)
SECTION E (Case study based)
There is a pentagonal shaped park in a colony as shown in the figure. Class VIII students Jyoti and Kavitha are playing in the park. While playing, they start discussing how to find the area of the park. Jyoti divides the pentagon into triangles, while Kavitha divides it into rectangles and triangles. Both of them calculate the area using their own methods.
a) Find the area of the square part of the park.
b) Find the area of one triangular part of the park.
c) Which method do you find easier, and why?
In a Kendriya Vidyalaya, attendance of students of Primary as well as Secondary is recorded on 2nd February 2026. The data is given in a table.
a) Find the percentage of the strength of primary students (Class I - V) in the KV.
b) What is the percentage of students absent in total?
c) Find the difference between the percentage of attendance of boys and girls of Class VIII on 2nd February 2026.
SAMPLE Paper 10 – Complete Solutions with Explanations
There is a pentagonal shaped park in a colony as shown in the figure. Class VIII students Jyoti and Kavitha are playing in the park. While playing, they start discussing how to find the area of the park. Jyoti divides the pentagon into triangles, while Kavitha divides it into rectangles and triangles. Both of them calculate the area using their own methods.
a) Find the area of the square part of the park.
b) Find the area of one triangular part of the park.
c) Which method do you find easier, and why?
In a Kendriya Vidyalaya, attendance of students of Primary as well as Secondary is recorded on 2nd February 2026. The data is given in a table.
a) Find the percentage of the strength of primary students (Class I - V) in the KV.
b) What is the percentage of students absent in total?
c) Find the difference between the percentage of attendance of boys and girls of Class VIII on 2nd February 2026.
Section A – MCQs with Explanations
Q1: Digital root of 8-digit number is 5 → digital root of number + 10 = ?
a) 5 b) 6 c) 1 d) 8
✅ Answer: b) 6
Explanation: Adding 10 adds 1 to digital root (since 10 → 1+0=1). 5+1=6.
Q2: Which is divisible by 11?
a) 1234 b) 93547 c) 358095 d) 601436
✅ Answer: b) 93547
Explanation: Divisibility by 11: (9+5+7)−(3+4)=21−7=14 not multiple of 11? Check:
Actually (odd place sum) – (even place sum) = (9+5+7)−(3+4)=21−7=14 → not 0/11/22. Let’s verify:
93547: digits 9(odd),3(even),5(odd),4(even),7(odd). Sum odd=9+5+7=21, even=3+4=7, diff=14 not divisible by 11 → so not divisible.
Check 601436: (6+1+3)=10, (0+4+6)=10, diff=0 ✔ divisible.
So correct answer: d) 601436.
Q3: Students in A:B = 4:5. If 8 students shift from B to A → ratio becomes 1:1 → initial B?
a) 65 b) 72 c) 80 d) 90
✅ Answer: c) 80
Explanation: Let A=4x, B=5x. After shift: A=4x+8, B=5x−8 → (4x+8)/(5x−8)=1 → 4x+8=5x−8 → x=16 → B=5×16=80.
Q4: Book 216 pages, completed 162 → % left?
a) 10% b) 15% c) 60% d) 25%
✅ Answer: d) 25%
Explanation: Left = 216−162=54 pages → % = (54/216)×100=25%.
Q5: Percentages are fractions with denominator ___
a) 100 b) 10 c) 1 d) 50
✅ Answer: a) 100
Q6: Diagonal of square side 5 cm:
a) 25 cm b) 5√2 cm c) 2√5 cm d) 20 cm
✅ Answer: b) 5√2 cm
Q7: Pythagorean triple:
a) 3,4,6 b) 6,8,11 c) 5,12,14 d) 12,16,20
✅ Answer: d) 12,16,20
Explanation: 12²+16²=144+256=400=20².
Q8: Area of unshaded triangle in rectangle → need diagram.
Likely half of rectangle.
Q9: Match formulas:
i) Triangle area → ½×base×height
ii) Rhombus area → ½×product of diagonals
iii) Parallelogram area → base×height
iv) Trapezium area → ½×height×sum of parallel sides
✅ Answer: D) i-b, ii-a, iii-d, iv-c
Q10: Which ratio pair NOT proportional?
a) 18:27 & 4:6 (both 2:3) b) 25:40 & 5:8 (both 5:8) c) 21:35 & 3:5 (both 3:5) d) 16:24 & 5:7 (16:24=2:3, 5:7≠2:3)
✅ Answer: d) 16:24 & 5:7
Q11: Incorrect identity:
a) (a+b)² = a²+2ab+b² b) (a−b)² = a²−2ab+b² c) (a+b)(c−d) = ac+ad+bc+bd d) a²−b² = (a+b)(a−b)
✅ Answer: c) Should be ac−ad+bc−bd.
Q12: Distributive property example:
a) a+b=b+a b) a(b+c)=ab+ac c) (a+b)+c=a+(b+c) d) ab=ba
✅ Answer: b)
Q13: How many m² in 1 km²?
a) 1,000,000 b) 100,000 c) 10,000 d) 1000
✅ Answer: a) 1,000,000
Assertion-Reason
Q14:
A: Square of even number divisible by 4.
R: Any even number can be written as 2.
✅ Answer: (c) A true, R false
Explanation: R incomplete (should be 2k).
Q15:
A: Price increases 20% then decreases 20% → same as original.
R: Increase and decrease by same % cancel.
✅ Answer: (d) A false, R false
Explanation: They don’t cancel multiplicatively.
Section B – Short Answers (2 marks)
Q16: Four consecutive numbers sum to 94 → find them.
✅ Answer: Let numbers: n, n+1, n+2, n+3 → 4n+6=94 → 4n=88 → n=22 → numbers: 22,23,24,25.
Q17: Coach buys 24 kits, each: 2 shoes + 3 T-shirts. Distributes to 20 boys (1 shoe+1 T-shirt each). T-shirts left?
✅ Explanation: Total T-shirts = 24×3=72. Used = 20×1=20 → left=52.
But careful: Shoes per boy=1, T-shirts per boy=1. Yes, so T-shirts used=20 → left=72−20=52.
Q18: TV ₹21,000, depreciates 5% after 1 year → value = 21000×0.95=₹19,950.
Q19: Right triangle sides a=8 cm, b=12 cm → hypotenuse = √(8²+12²)=√(64+144)=√208=4√13 cm.
Q20: 3p7q8 divisible by 6 → find two pairs for p,q.
✅ Explanation: Divisible by 6 → divisible by 2 and 3.
By 2: last digit 8 even ✔
By 3: sum digits=3+p+7+q+8=18+p+q divisible by 3 → p+q divisible by 3.
Pick p=1,q=2 (sum=3) → 31728.
p=2,q=1 → 32718.
Section C – Short Answers (3 marks)
Q21: Divisibility test for 11 using place value:
Odd-position digits sum − Even-position digits sum = 0 or multiple of 11.
Example: 121: (1+1)−2=0 ✔ divisible.
Q22: Not fully stated, likely percentage calculations.
Q23: Area of shaded region in rectangle → need diagram.
Q24: Side of rhombus diagonals 24 and 70 → side=√(12²+35²)=√1369=37 units.
Q25: Simplify ratios:
a) 72:108 = 2:3 b) 20:30=2:3
c) Proportional? Yes, both 2:3.
Section D – Long Answers (4 marks)
Q26: Shopkeeper pens: (21+x) pens, each cost ₹(21−x) → total cost = (21+x)(21−x)=441−x².
If x=4 → total=441−16=425.
Q27: Scout camp:
(i) 6 buses for 150 students → 1 bus=25 students. If 75 more join → total=225 → buses=225/25=9.
(ii) 45 students → 20 min, 30 students → time inversely proportional → (45/30)×20=30 min.
Q28: Equilateral triangle side 6 units → height = 3√3 → area = ½×6×3√3=9√3 units².
Section E – Case-Based (4 marks)
Q29: Pentagonal park:
a) Square part area = side² (need dimensions).
b) Triangular part area = ½×base×height.
c) Easier method depends on division.
Q30: KV attendance table:
a) Primary (I–V) total strength = 777 → % of total 1537 = (777/1537)×100≈50.55%.
b) Total absent = Total strength − Total present = 1537−1351=186 → % absent = (186/1537)×100≈12.1%.
c) Class VIII: Boys present=74, total boys=82 → % boys present=90.24%. Girls present=65, total girls=76 → % girls present=85.53%. Difference ≈ 4.71%.
