Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-2 WITH ANSWERS
SAMPLE Paper 2
General Instructions: All questions compulsory. Sections A-F.
SECTION A (1 mark each)
Which statement of proportion is true:
a) 4:7::12:21 b) 8:3::24:6 c) 2:3::5:7 d) 7:12::12:71 Hectare =
a) 10,000 m b) 10,000 sq m c) 1000 sq m d) 1 km9/20 in % is:
a) 45% b) 90% c) 9% d) 80%Nandini has 25 marbles, out of which 15 are white. What % is white:
a) 15% b) 25% c) 100% d) 60%Smallest multiple of 9 with no odd digits is:
a) 288 b) 504 c) 902 d) 348A number that has a remainder of 3 when divided by 5 is:
a) 15 b) 9 c) 13 d) 2If area of rectangle is 44 and breadth is 4, what is the length:
a) 8 b) 11 c) 48 d) 40Area of right triangle with perpendicular sides 3 and 4 is:
a) 12 b) 7 c) 24 d) 6Fill appropriate sign: 50/10 ___ 50%
5w² + 6w =
a) 11w² b) 11w c) 30w³ d) 5w²+6wArea of isosceles triangle SUB is 48 sq m. What is area of triangle SEB? (diagram needed)
Two more than square a number:
a) 2+s b) s²+2 c) (s+2)² d) 2s²HCF of 72 and 96 is:
a) 32 b) 24 c) 72 d) 2
Assertion-Reason Questions (14-15):
14. Assertion: (a−b)² = (b−a)² for any integers a,b
Reason: Square of any integer is positive
15. Assertion: Population of tigers increased by 5% last decade
Reason: Population now is 0.05m
SECTION B (2 marks each)
16. Sum of 4 consecutive numbers is 34. Find them.
17. What will be digital root of 9a + 36b + 13?
18. Express 100 as difference of two squares.
19. Maximum marks=75, need 80% for A grade. How much to score?
20. Is 10% of a day longer than 1% of a week? Justify.
SECTION C (3 marks each)
21. Anagh mixes 600 mL orange juice with 900 mL apple juice. Write ratio in simplest form.
22. Solve cryptarithm: MEOW (diagram needed)
23. In parallelogram, AM=12 cm, CN=8 cm, DC=10 cm. Find AD.
24. Samson bought car for ₹4,40,000 after 15% discount. Find original price.
25. Find side lengths of rhombus whose diagonals are 24 cm and 70 cm.
SECTION D (4 marks each)
26. Right triangle has sides 5 cm and 12 cm. Find hypotenuse by drawing and then verify by Pythagoras theorem.
27. Compute using identity: a) 43×45 using (a+b)(a−b) b) Earth travels 940 million km/year → km/week.
SECTION E (Case-Based)
29. Giridhar borrows ₹12,500 at 12% p.a. simple interest for 3 years; Raghu borrows same at 10% p.a. compounded annually.
a) Who pays more interest?
b) Difference in amount paid after 3 years?
c) Who incurs loss?
Varun's toy looks like two trapeziums + rectangle in middle (diagram).
a) Height of trapezium
b) Total area of toy
c) Length and breadth of rectangle part
SAMPLE Paper 2 – Complete Solutions with Explanations
Section A – MCQs with Explanations
Q1: Which proportion is true?
a) 4:7 :: 12:21 b) 8:3 :: 24:6 c) 2:3 :: 5:7 d) 7:12 :: 12:7
✅ Answer: a) 4:7 :: 12:21
Explanation: Check cross products: 4×21 = 84, 7×12 = 84 → Equal → Proportional.
Q2: 1 Hectare =
a) 10,000 m b) 10,000 sq m c) 1000 sq m d) 1 km
✅ Answer: b) 10,000 sq m
Explanation: 1 hectare = 10,000 m².
Q3: 9/20 in % is
a) 45% b) 90% c) 9% d) 80%
✅ Answer: a) 45%
Explanation: 9/20 = 0.45 = 45%.
Q4: Nandini has 25 marbles, 15 white. % white?
a) 15% b) 25% c) 100% d) 60%
✅ Answer: d) 60%
Explanation: (15/25)×100 = 60%.
Q5: Smallest multiple of 9 with no odd digits is
a) 288 b) 504 c) 902 d) 348
✅ Answer: a) 288
Explanation: 288 digits: 2,8,8 (all even). Multiples of 9: sum of digits divisible by 9. 2+8+8=18 ✔. Check others: 504 has 5 (odd), 902 has 9 (odd), 348 sum=15 not divisible by 9.
Q6: A number remainder 3 when divided by 5 is
a) 15 b) 9 c) 13 d) 2
✅ Answer: c) 13
Explanation: 13 ÷ 5 = 2 remainder 3.
Q7: Area of rectangle = 44, breadth = 4, length = ?
a) 8 b) 11 c) 48 d) 40
✅ Answer: b) 11
Explanation: Area = l × b → 44 = l × 4 → l = 11.
Q8: Area of right triangle with perpendicular sides 3 and 4 is
a) 12 b) 7 c) 24 d) 6
✅ Answer: d) 6
Explanation: Area = ½ × 3 × 4 = 6.
Q9: Fill sign: 50/10 ___ 50%
✅ Answer: >
Explanation: 50/10 = 5, 50% = 0.5 → 5 > 0.5.
Q10: 5w² + 6w =
a) 11w² b) 11w c) 30w³ d) 5w²+6w
✅ Answer: d) 5w²+6w
Explanation: Cannot combine unlike terms.
Q11: Area of isosceles triangle SUB is 48 m². Area of triangle SEB?
Image needed. If SEB is half or congruent, may be 24 m².
Q12: Algebraic expression: Two more than square a number
a) 2+s b) s²+2 c) (s+2)² d) 2s²
✅ Answer: b) s²+2
Explanation: Square first: s², then add 2.
Q13: HCF of 72 and 96 is
a) 32 b) 24 c) 72 d) 2
✅ Answer: b) 24
Explanation: 72=2³×3², 96=2⁵×3 → HCF=2³×3=24.
Assertion-Reason
Q14:
A: (a−b)² = (b−a)² for any integers a,b.
R: Square of any integer is positive.
✅ Answer: (b) Both true but R not correct explanation
Explanation: Equality holds because (a−b)² = (b−a)² due to squaring, not because squares are positive.
Q15:
A: Tiger population was m, increased by 5% in last decade.
R: Population now is 0.05m.
✅ Answer: (d) A true, R false
Explanation: Increase 5% → new population = m + 0.05m = 1.05m, not 0.05m.
Section B – Short Answers (2 marks)
Q16: Sum of 4 consecutive numbers = 34. Find them.
✅ Answer: Let numbers: n, n+1, n+2, n+3.
Sum = 4n+6 = 34 ⇒ 4n=28 ⇒ n=7 → 7,8,9,10.
Q17: Digital root of 9a + 36b + 13.
✅ Answer: Digital root = sum digits mod 9.
9a divisible by 9, 36b divisible by 9, 13 → digital root 1+3=4.
Q18: Express 100 as difference of two squares.
✅ Answer: 100 = 26² − 24²? Check: 26²=676, 24²=576, difference=100 ✔. Also 10²−0².
Q19: Max marks=75, need 80% for A grade. Marks needed?
✅ Answer: 80% of 75 = 0.8×75 = 60 marks.
Q20: Is 10% of a day longer than 1% of a week? Justify.
✅ Answer:
10% of day = 0.1×24h = 2.4h.
1% of week = 0.01×168h = 1.68h.
2.4h > 1.68h → Yes, longer.
Section C – Short Answers (3 marks)
Q21: Orange juice 600 mL, apple juice 900 mL → ratio in simplest form.
✅ Answer: Orange:Apple = 600:900 = 2:3.
Q22: Solve cryptarithm: MEOW? Image needed.
If typical, e.g., W=... Usually involves digit assignment.
Q23: Parallelogram: AM=12 cm, CN=8 cm, DC=10 cm → Find AD.
Area using base DC×AM = base AD×CN → 10×12 = AD×8 → AD=15 cm.
Q24: Car bought ₹4,40,000 after 15% discount. Original price?
✅ Answer: SP = 85% of MP → 4,40,000 = 0.85×MP → MP = 4,40,000 / 0.85 ≈ ₹5,17,647.
Q25: Rhombus diagonals 24 cm and 70 cm → side length.
✅ Answer: Side = √[(d1/2)² + (d2/2)²] = √(12² + 35²) = √(144+1225) = √1369 = 37 cm.
Section D – Long Answers (4 marks)
Q26: Right triangle sides 5 cm, 12 cm → hypotenuse.
✅ Answer: Hypotenuse = √(5²+12²) = √(25+144) = √169 = 13 cm.
Q27(a): Compute 43×45 using (a+b)(a−b) identity.
✅ Answer: 43×45 = (44−1)(44+1) = 44²−1² = 1936−1 = 1935.
Q27(b): Earth travels 940 million km/year → km/week.
✅ Answer: 1 year = 52 weeks → 940/52 ≈ 18.08 million km/week.
Section E – Case-Based (4 marks)
Q29: Giridhar: loan ₹12,500 at 12% p.a. simple interest for 3 years.
Raghu: same loan at 10% p.a. compound annually.
(a) Who pays more interest?
✅ Simple interest for Giridhar = P×r×t = 12500×0.12×3 = ₹4500.
Compound for Raghu: A = P(1+r)α΅ = 12500×(1.1)³ = 12500×1.331 = ₹16637.5, Interest = 16637.5−12500 = ₹4137.5.
Giridhar pays more (4500 > 4137.5).
(b) Difference in amount paid after 3 years?
✅ Giridhar amount = 12500+4500 = ₹17000. Raghu = ₹16637.5. Difference = 17000−16637.5 = ₹362.5.
(c) Who incurs loss?
✅ Neither loses; but Giridhar pays more interest, so borrower’s perspective: Giridhar has higher cost.
Q30: Toy: two trapeziums + rectangle in middle.
(a) Height of trapezium? Need dimensions from diagram. If given parallel sides and area, solve.
(b) Total area of toy?
✅ Area = 2 × area of trapezium + area of rectangle.
(c) Length and breadth of rectangle? From diagram.
