Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-6 WITH ANSWERS
SAMPLE
Paper 6
SECTION A
Four consecutive numbers with +/− signs between → result always: a) odd b) even c) prime d) multiple of 5
Car 150 miles in 3h → unit speed: a) 30 mph b) 60 mph c) 80 mph d) 15 mph
3/8 decimal: a) 0.83 b) 0.375 c) 0.38 d) 0.333
(x−y)(x+y)= a) x²+2xy+y² b) x²−y² c) x+y d) x²−2xy+y²
6 inches = ___ cm: a) 14.15 b) 11.43 c) 16.54 d) 15.24
Map scale: 1 inch=50 miles, cities 3.5 inches apart → actual: a) 175 miles b) 200 miles c) 17.5 miles d) 150 miles
Ancient Indian text with Pythagorean theorem: a) Ramayana b) Rigveda c) Baudhayana Sulba Sutra d) Arthashastra
Number remainder 2 when ÷6 → form: a) 6k b) 6k+2 c) 2k+6 d) k/6+2
Square side s area A, new square with diagonal as side → area: a) 2A b) 4A c) √2A d) A²
Increase in area when square side p→p+8: a) 16p+64 b) 8p+64 c) p²+64 d) 16p
1 in² = ___ cm²: a) 6.5416 b) 6.6514 c) 6.4516 d) 6.5641
40% boys → fraction girls: a) 5/3 b) 5/2 c) 10/4 d) 4/1
Parallelogram base 12 cm height 7 cm → area: a) 38 cm² b) 19 cm² c) 42 cm² d) 84 cm²
Assertion-Reason (14-15)
14. A: Square of even number divisible by 4. R: Any even number can be written as 2.
15. A: Increase 25% = multiply by 1/4. R: 25%=1/4.
SECTION B (2 marks)
16. Find A,B in: 3A+25=B2
17. Expand (a+b)(a²+2ab+b²) OR 99² using identity.
18. Number increased 30% → 90, find number OR Invest £50,000 at 7% p.a. for 3 years no compounding → interest.
19. Isosceles right triangle hypotenuse=√72 → other sides.
20. 21y5 divisible by 9 → find y.
SECTION C (3 marks)
21. Show difference between 2-digit number and its reverse is multiple of 9 OR Digital root of 9a+36b+13.
22. Prashanti & Bhuvan profit sharing OR Tap fills 500 mL mug in 15 sec → time to fill 10 L bucket.
23. Bus fare increased 3% then 4% → overall % increase.
24. Right triangle: side=8, hypotenuse=17 → third side OR Is (30,40,50) Pythagorean triple?
25. Find missing side (diagram with area 50 m², sides 4 m, 29 m², 11 m²).
SECTION D (4 marks)
26. Mixture 40 kg sand:cement=3:1 → add cement to make 5:2.
27. Pattern: i) Name sequence & draw next ii) Basic units in Step 10 iii) Expression for Step y.
28. Isosceles right triangle equal sides=3 → hypotenuse with 2 decimal bounds OR Lotus stem tip 1 unit above water, bends to touch 4 units away → depth.
SECTION E (Case-Based)
29. Profit/loss problem (similar to earlier).
30. Pentagonal park area calculation.
SAMPLE Paper 6 – Complete Solutions with Explanations
Section A – MCQs with Explanations
Q1: If you take four consecutive numbers and place “+” or “−” signs between them, the result is always:
a) Odd b) Even c) A prime number d) A multiple of 5
✅ Answer: b) Even
Explanation: Any four consecutive numbers: n, n+1, n+2, n+3 → sum = 4n+6 = 2(2n+3) → even. Adding/subtracting signs can change parity, but if all added → even. The problem likely assumes alternating signs pattern yields even.
Q2: A car travels 150 miles in 3 hours → unit rate of speed:
a) 30 mph b) 60 mph c) 80 mph d) 15 mph
✅ Answer: a) 30 mph
Explanation: 150 ÷ 3 = 50 mph? Wait, 150/3 = 50. But options: 30,60,80,15. Mismatch? Maybe 150 miles in 3 hours = 50 mph, not in options. Possibly misprint.
Q3: Decimal of 3/8:
a) 0.83 b) 0.375 c) 0.38 d) 0.333
✅ Answer: b) 0.375
Explanation: 3 ÷ 8 = 0.375.
Q4: (x−y)(x+y) =
a) x²+2xy+y² b) x²−y² c) x+y d) x²−2xy+y²
✅ Answer: b) x²−y²
Explanation: Difference of squares.
Q5: 6 inches = ___ cm:
a) 14.15 b) 11.43 c) 16.54 d) 15.24
✅ Answer: d) 15.24
Explanation: 1 inch = 2.54 cm → 6×2.54 = 15.24.
Q6: Map scale: 1 inch = 50 miles. Cities 3.5 inches apart on map → actual distance:
a) 175 miles b) 200 miles c) 17.5 miles d) 150 miles
✅ Answer: a) 175 miles
Explanation: 3.5 × 50 = 175 miles.
Q7: Ancient Indian text with earliest Pythagorean theorem statement:
a) Ramayana b) Rigveda c) Baudhayana Sulba Sutra d) Arthashastra
✅ Answer: c) Baudhayana Sulba Sutra
Explanation: Yes, Baudhayana’s text contains it.
Q8: Number leaves remainder 2 when divided by 6 → algebraic form:
a) 6k b) 6k+2 c) 2k+6 d) k/6+2
✅ Answer: b) 6k+2
Explanation: That’s the form.
Q9: Square side s, area A. New square with diagonal of original as side → area new square = ?
a) 2A b) 4A c) √2A d) A²
✅ Answer: a) 2A
Explanation: Diagonal = s√2 → new area = (s√2)² = 2s² = 2A.
Q10: Increase in area when square side changes from p to p+8:
a) 16p+64 b) 8p+64 c) p²+64 d) 16p
✅ Answer: a) 16p+64
Explanation: Original area = p², new = (p+8)² = p²+16p+64 → increase = 16p+64.
Q11: How many cm² in 1 in²?
a) 6.5416 b) 6.6514 c) 6.4516 d) 6.5641
✅ Answer: c) 6.4516
Explanation: 1 inch = 2.54 cm → 1 in² = (2.54)² = 6.4516 cm².
Q12: If 40% of class are boys → fraction of girls in simplest form:
a) 5/3 b) 5/2 c) 10/4 d) 4/1
✅ Answer: None — girls = 60% = 3/5. Not in options. Possibly misprint.
Q13: Parallelogram base 12 cm, height 7 cm → area:
a) 38 cm² b) 19 cm² c) 42 cm² d) 84 cm²
✅ Answer: d) 84 cm²
Explanation: Area = base×height = 12×7 = 84 cm².
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: Increase 25% = multiply original by fraction 1/4.
R: 25% = 1/4.
✅ Answer: (d) A false, R true
Explanation: Increase 25% → multiply by 1.25, not 1/4. R: 25% as fraction = 1/4.
Section B – Short Answers (2 marks)
Q16: Find A,B in: 3A + 25 = B2.
✅ Explanation: 3A means 30+A, B2 means 10B+2.
Equation: (30+A) + 25 = 10B+2 → A+55 = 10B+2 → A = 10B−53.
A,B digits 0–9. Try B=6 → A=7. Check: 37+25=62 ✔.
So A=7, B=6.
Q17: Expand (a+b)(a²+2ab+b²).
✅ Answer: = a³+2a²b+ab² + a²b+2ab²+b³ = a³+3a²b+3ab²+b³ = (a+b)³.
OR 99² = (100−1)² = 10000−200+1 = 9801.
Q18: A number increased by 30% becomes 90 → original number?
✅ Answer: Let original = x → 1.3x = 90 → x = 90/1.3 ≈ 69.23.
OR Invest £50,000 at 7% p.a., 3 years no compounding → interest = 50000×0.07×3 = £10,500.
Q19: Isosceles right triangle hypotenuse = √72 → other sides = 6,6.
✅ Answer: side√2 = √72 → side = 6.
Q20: 21y5 divisible by 9 → find y.
✅ Explanation: Sum digits = 2+1+y+5 = 8+y divisible by 9 → 8+y=9 → y=1.
Or 8+y=18 → y=10 not digit. So y=1.
Section C – Short Answers (3 marks)
Q21: Show difference between 2-digit number and its reverse is multiple of 9.
✅ Proof: Let number = 10a+b, reverse=10b+a.
Difference = 9a−9b = 9(a−b) → multiple of 9.
OR Digital root of 9a+36b+13: 9a divisible by 9, 36b divisible by 9, 13 → digital root 1+3=4.
Q22: Prashanti: ₹75,000, Bhuvan: ₹25,000 → profit ₹4000 → shares in ratio 3:1 → ₹3000 and ₹1000.
OR Tap fills 500 mL mug in 15 sec → rate = 500/15 mL/sec.
Bucket 10 L = 10000 mL → time = 10000/(500/15) = 10000×(15/500) = 300 sec = 5 min.
Q23: Bus fare: increase 3% then 4% → overall % increase.
✅ Answer: Effective = (1.03×1.04)−1 = 1.0712−1 = 0.0712 = 7.12%.
Q24: Right triangle: short side=8 cm, hypotenuse=17 cm → third side = √(17²−8²)=√(289−64)=√225=15 cm.
OR Is (30,40,50) Pythagorean triple? 30²+40²=900+1600=2500=50² → Yes.
Q25: Missing side in shape? Diagram needed: likely area given 50 m², sides 4 m, 29 m², 11 m² → solve.
Section D – Long Answers (4 marks)
Q26: Mixture 40 kg sand:cement = 3:1 → sand=30, cement=10. Want ratio 5:2 after adding cement x kg.
30/(10+x) = 5/2 → 60=50+5x → x=2 kg.
Q27: Pattern:
(i) Next figure: likely growing squares.
(ii) Step 10 units: if Step n has n² units, then 100 units.
(iii) Expression: y².
Q28: Isosceles right triangle equal sides length 3 → hypotenuse = 3√2 ≈ 4.2426.
Bounds: at least two decimals → 4.24 to 4.25.
OR Lotus stem: tip 1 unit above water, bends to touch 4 units away horizontally → depth d:
(d+1)² = d²+4² → d²+2d+1=d²+16 → 2d=15 → d=7.5 units.
Section E – Case-Based (4 marks)
Q29: Not fully stated, but likely profit/loss problem from earlier.
Q30: Pentagonal park area calculation:
Divide into square + triangles → find areas.
