Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-3 WITH ANSWERS
SAMPLE Paper 3
SECTION A
How many cm² is 1 m²: a) 100 b) 1000 c) 10000 d) 100000
Area of rhombus diagonals 12 cm and 14 cm: a) 64 b) 74 c) 84 d) 94
Simplest form of 48/72: a) 6/9 b) 4/6 c) 2/3 d) 12/18
Ratio of ₹5 to 50 paise: a) 1:10 b) 5:50 c) 1:1 d) 10:1
Which shows proportional relationship: a) Age & height b) Speed & distance (time constant) c) Marks & roll no d) Shoe size & marks
Sum of first (n−1) odd numbers: a) 3n b) n² c) n³ d) 4n
How many inches in 1 ft: a) 142 b) 145 c) 144 d) 146
If 3/5 = y/35, y = ? a) 15 b) 21 c) 25 d) 30
Equation aโฟ+bโฟ=cโฟ has no solution in positive integers when: a) n=2 b) n>2 c) n<2 d) n>0
Sum of first 10 natural numbers: a) 45 b) 50 c) 55 d) 60
Number divisible by 2 and 3: a) 15 b) 16 c) 18 d) 21
a(b+c)=ab+ac is: a) associative b) closure c) distributive d) all
Cost of 5 pencils=₹30, cost of 7 pencils: a) 6 b) 12 c) 14 d) 21
Assertion-Reason (14-15)
14. A: Product of two naturals always greater than both. R: Multiplication always increases value.
15. A: 5/10=1/2 R: Fraction unchanged when numerator/denominator divided by same nonzero number.
SECTION B (2 marks)
16. Diagonal of square side 5 cm.
17. Digital root of 8-digit number is 5. Digital root of number+10?
18. Compute 96² using identity OR Multiply 3874×101.
19. If 3a7b8 divisible by 44, list possible values of a,b.
20. TV bought at ₹21,000 depreciates 5% yearly → value after 2 years OR Shopkeeper sells pencils: SP of 3 = CP of 5 → profit/loss %?
SECTION C (3 marks)
21. Scooter: 120 km in 3h, train: 120 km in 2h → ratio of speeds OR Parking: 115 cycles, 75 scooters, 45 bikes → ratio cycles:total.
22. Isosceles right triangle hypotenuse=√72 → find other sides.
23. Manju: ₹12,500 at 12% p.a. simple for 3 years; Anju: same at 10% p.a. compounded annually → who pays more interest and by how much?
24. a) Simplify (am+bn)²−(am−bn)² b) If a+b=8, a−b=4 → find a²+b²
25. Find area of ฮXDC if AB=5 cm, AD=4 cm OR Area of trapezium parallel sides 6 in, 14 in, distance 10 in.
SECTION D (4 marks)
26. Side of rhombus diagonals 24 cm & 70 cm OR Area of equilateral triangle side 6 m.
27. Number remainder 3 when ÷7, another remainder 5 when ÷7 → remainder of sum ÷7 OR Newspapers: 312 total, 216 English → ratio English:Hindi & Hindi:Total.
28. Population reduces 10% per decade, current 1250 → after 4 decades.
SECTION E (Case-Based)
29. Hexagonal cake side 4 cm, 10 friends share equally → each gets? Perimeter?
30. Deepa earns ₹150,000/month, spends 1/10 on food, 1/4 on shopping, 1/5 of remaining on kids' education, rest saved.
a) Food expense b) Education expense c) Savings
SAMPLE Paper 3 – Complete Solutions with Explanations
Section A – MCQs with Explanations
Q1: How many cm² in 1 m²?
a) 100 b) 1000 c) 10000 d) 100000
✅ Answer: c) 10000
Explanation: 1 m² = (100 cm)² = 10000 cm².
Q2: Area of rhombus with diagonals 12 cm and 14 cm?
a) 64 b) 74 c) 84 d) 94
✅ Answer: c) 84
Explanation: Area = ½ × d₁ × d₂ = ½ × 12 × 14 = 84 cm².
Q3: Simplest form of 48/72?
a) 6/9 b) 4/6 c) 2/3 d) 12/18
✅ Answer: c) 2/3
Explanation: Divide numerator and denominator by 24 → 48/72 = 2/3.
Q4: Ratio of ₹5 to 50 paise?
a) 1:10 b) 5:50 c) 1:1 d) 10:1
✅ Answer: d) 10:1
Explanation: ₹5 = 500 paise. Ratio = 500:50 = 10:1.
Q5: Which shows proportional relationship?
a) Age and height b) Speed and distance (time constant) c) Marks and roll no d) Shoe size and marks
✅ Answer: b) Speed and distance (time constant)
Explanation: If time constant, distance ∝ speed (proportional).
Q6: Sum of first (n−1) odd numbers?
a) 3n b) n² c) n³ d) 4n
✅ Answer: b) n²
Explanation: Sum of first k odd numbers = k². Here k = n−1 → (n−1)². But options don’t match? Wait, they say first (n−1) odd numbers sum = (n−1)². But given options: n² is for first n odds. This seems mismatch. Likely answer: n² if they meant first n−1 odds sum = (n−1)² not in options, so maybe misprint.
Q7: How many inches in 1 ft?
a) 142 b) 145 c) 144 d) 146
✅ Answer: None match — actually 1 ft = 12 inches. But maybe they meant in cm? 1 ft = 30.48 cm ≈ 30.5 cm. Not matching. Possibly misprint.
Q8: If 3/5 = y/35, y = ?
a) 15 b) 21 c) 25 d) 30
✅ Answer: b) 21
Explanation: y = (3/5)×35 = 21.
Q9: Equation aโฟ + bโฟ = cโฟ has no solution in positive integers when:
a) n=2 b) n>2 c) n<2 d) n>0
✅ Answer: b) n>2
Explanation: Fermat’s Last Theorem: no integer solutions for n>2.
Q10: Sum of first 10 natural numbers?
a) 45 b) 50 c) 55 d) 60
✅ Answer: c) 55
Explanation: Sum = n(n+1)/2 = 10×11/2 = 55.
Q11: Number divisible by 2 and 3?
a) 15 b) 16 c) 18 d) 21
✅ Answer: c) 18
Explanation: Divisible by 6: 18/6=3.
Q12: a(b+c) = ab + ac → property?
a) associative b) closure c) distributive d) all
✅ Answer: c) distributive
Explanation: Distributive property of multiplication over addition.
Q13: Cost of 5 pencils = ₹30, cost of 7 pencils?
a) 6 b) 12 c) 14 d) 21
✅ Answer: c) 42 but not in options — recalc: Cost per pencil = 30/5=6, so 7 pencils = 42. Options wrong? They have 6,12,14,21. Possibly misprint.
Assertion-Reason
Q14:
A: Product of two natural numbers always greater than both.
R: Multiplication always increases value.
✅ Answer: (d) A false, R true
Explanation: If one number is 1, product equals the other. So A false. R: multiplication by number >1 increases, but not always.
Q15:
A: 5/10 = 1/2
R: Fraction unchanged if numerator/denominator divided by same nonzero number.
✅ Answer: (a) Both true, R explains A
Explanation: 5/10 ÷ 5/5 = 1/2.
Section B – Short Answers (2 marks)
Q16: Diagonal of square with side 5 cm.
✅ Answer: Diagonal = side√2 = 5√2 cm ≈ 7.07 cm.
Q17: Digital root of 8-digit number is 5. Digital root of number + 10?
✅ Answer: Adding 10 adds 1 to digital root sum → new digital root = 5+1 = 6 (since 10 ≡ 1 mod 9).
Q18: Compute 96² using identity.
✅ Answer: 96² = (100−4)² = 10000 − 800 + 16 = 9216.
OR Multiply 3874 × 101 = 3874 × (100+1) = 387400 + 3874 = 391,274.
Q19: If 3a7b8 divisible by 44, find possible a,b.
✅ Explanation: Divisible by 44 means divisible by 4 and 11.
Divisible by 4: last two digits b8 divisible by 4 → b=0,2,4,6,8.
Divisible by 11: (3+7+8) − (a+b) = multiple of 11 → 18 − (a+b) = 0 or 11 or… Try values.
Let’s solve: 18 − (a+b) = 0 ⇒ a+b=18 (max digit 9+9=18).
If 18 − (a+b) = 11 ⇒ a+b=7.
If 18 − (a+b) = −11 ⇒ a+b=29 (not possible).
So a+b=18 or 7. With b even from step 1.
Test b=0 → a=18 or 7 (a digit so ≤9) → a=7 works for a+b=7.
List pairs:
(a,b) = (7,0), (5,2), (3,4), (1,6), (8,8) for sum=7? Wait sum=7 cases:
(7,0),(5,2),(3,4),(1,6) yes.
Also sum=18: (9,9) but b=9 not even → no.
So possible: (7,0),(5,2),(3,4),(1,6).
Q20: TV bought ₹21,000, depreciates 5% yearly → value after 2 years?
✅ Answer: After 1 year: 21000×0.95 = ₹19,950.
After 2 years: 19950×0.95 = ₹18,952.5.
OR Profit/loss: SP of 3 pencils = CP of 5 pencils → Let CP per pencil = ₹1, CP of 5 = ₹5 = SP of 3 → SP per pencil = 5/3 ≈ 1.67 → Profit % = (0.67/1)×100 = 67%.
Section C – Short Answers (3 marks)
Q21: Scooter: 120 km in 3h → speed 40 km/h.
Train: 120 km in 2h → speed 60 km/h.
Ratio of speeds = 40:60 = 2:3.
OR Parking: cycles=115, scooters=75, bikes=45, total=235.
Ratio cycles:total = 115:235 = 23:47.
Q22: Isosceles right triangle hypotenuse = √72 → other sides?
✅ Answer: side√2 = √72 = 6√2 → side = 6. So sides 6,6.
Q23: Manju: ₹12,500 at 12% p.a. simple interest for 3 years.
Anju: same at 10% p.a. compound annually.
Who pays more interest and by how much?
✅ Answer:
Manju SI = 12500×0.12×3 = ₹4500.
Anju CI: A = 12500×(1.1)³ = 12500×1.331 = ₹16,637.5 → Interest = 16637.5−12500=4137.5.
Manju pays more by 4500−4137.5=₹362.5.
Q24(a): Simplify (am + bn)² − (am − bn)².
✅ Answer: = (a²m²+2abmn+b²n²) − (a²m²−2abmn+b²n²) = 4abmn.
(b): If a+b=8, a−b=4 → find a²+b².
✅ Answer: Add: 2a=12 → a=6, b=2.
a²+b² = 36+4 = 40.
Q25: Given ฮXDC in figure: AB=5 cm, AD=4 cm. Find area ฮXDC.
Need diagram. Likely rectangle ABCD, X on BC, triangle base DC=5, height=4 → Area = ½×5×4 = 10 cm².
OR Trapezium: parallel sides 6 in, 14 in, distance 10 in → Area = ½×10×(6+14) = 5×20 = 100 in².
Section D – Long Answers (4 marks)
Q26: Side of rhombus diagonals 24 cm and 70 cm.
✅ Answer: Side = √[(24/2)² + (70/2)²] = √(12²+35²) = √(144+1225) = √1369 = 37 cm.
OR Equilateral triangle side 6 m → height = 3√3 m, area = ½×6×3√3 = 9√3 m² ≈ 15.588 m².
Q27: Number remainder 3 when ÷7, another remainder 5 when ÷7. Remainder of sum ÷7?
✅ Answer: Sum remainder = (3+5) mod 7 = 8 mod 7 = 1.
OR Newspapers: English=216, Hindi=312−216=96.
Ratio English:Hindi = 216:96 = 9:4.
Ratio Hindi:Total = 96:312 = 8:26 = 4:13.
Q28: Population reduces 10% per decade. Current 1250 → after 4 decades?
✅ Answer: After each decade = 90% of previous. After 4 decades = 1250×(0.9)⁴ = 1250×0.6561 ≈ 820.
Section E – Case-Based (4 marks)
Q29: Hexagonal cake side 4 cm, 10 friends, equal pieces. Quantity each? Perimeter?
✅ Answer:
Area of hexagon = (3√3/2)×side² = (3√3/2)×16 = 24√3 cm² ≈ 41.57 cm².
Each friend gets ≈ 4.157 cm².
Perimeter = 6×4 = 24 cm.
Q30: Deepa earns ₹150,000/month.
Spends:
Food: 1/10 = ₹15,000.
Shopping: 1/4 = ₹37,500.
Remaining = 150,000 − (15,000+37,500) = ₹97,500.
Education: 1/5 of remaining = ₹19,500.
Savings = 97,500 − 19,500 = ₹78,000.
(a) Food = ₹15,000.
(b) Education = ₹19,500.
(c) Savings = ₹78,000.
