Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-5 WITH ANSWERS

 Class 8 SESSION ENDING EXAMINATION (2026)  SAMPLE PAPER-5 WITH ANSWERS

SAMPLE Paper 5

SECTION A

1. Sum of any four consecutive integers is always: a) odd b) prime c) even d) multiple of 3

2. Numbers remainder 3 when ÷5 are of form: a) 3k b) 5k+3 c) 5k−3 d) 3k+5

3. Algebraic: Two more than square number: a) 2+s b) (s+2)² c) s²+2 d) s²+4

4. Correct: a) 1 mL=10 cc b) 1 mL=1 cc c) 1 L=100 cc d) 1 L=10 cc

5. Diagonal of square produces square with area: a) half b) same c) double d) four times original

6. Triangle base same, height doubled → area: a) half b) double c) triple d) unchanged

7. Mobile ₹8250 + 18% GST → final price expression: a) 8250+18 b) 8250+0.18 c) 8250×1.8 d) 8250+0.18×8250

8. Pythagorean triple: a) (2,3,4) b) (4,5,6) c) (3,4,5) d) (5,6,7)

9. Area of rhombus formula: a) base×height b) side² c) ½×product of diagonals d) diagonal²

10. Twice sum of squares of a,b = a) (a+b)² b) (a−b)² c) (a+b)²+(a−b)² d) a²+b²

11. True proportion: a) 4:7::12:21 b) 8:3::24:6 c) 7:12::12:7 d) 12:18::28:12

12. Cutting figure and rearranging to same area: a) rotation b) reflection c) dissection d) translation

13. Jasmine invests p at 6% p.a. for 4 years no compounding → total amount expression: a) p×6×4 b) p×0.6×4 c) p×0.06×4 d) p×1.06×4

Assertion-Reason (14-15)
14. A: Square of even number multiple of 4, square of odd number 1 more than multiple of 8. R: Even=2n, odd=2n+1
15. A: 15% of 60 = 60% of 15. R: x% of y = y% of x since multiplication commutative.

SECTION B (2 marks)
16. If 3p7q8 divisible by 44 → list possible p,q pairs.
17. A) Expand (a+ab−3b²)(4+b) OR B) 98×102 using identity.
18. Hypotenuse of isosceles right triangle equal sides=12.
19. A) 25% of 160 B) Express as %: i) 3/5 ii) 5/11
20. Product of two consecutive integers always multiple of 2? Why?

SECTION C (3 marks)
21. A) Tea: 200g for ₹200, 1kg for ₹800 → proportional? Which expensive? OR B) Prashanti invested ₹75,000, Bhuvan ₹25,000, profit ₹4000 → share in investment ratio.
22. Cyclist completed 40% = 92 km → remaining distance to Agra.
23. A) Solve cryptarithms: i) EF×E=GGG ii) WOW×5=MEOW OR B) Sreelatha's number divisible by 9, reversed still divisible by 9 → examine conjecture.
24. A) ZYXW trapezium, A midpoint of XY → show area trapezium = area ΔZWB OR B) Parallelograms on same base → compare areas & perimeters.
25. Side of rhombus diagonals 24 & 70 units.

SECTION D (4 marks)
26. Expand: i) (a−b)(a+b) ii) (a−b)(a²+ab+b²) iii) (a−b)(a³+a²b+ab²+b³) → identify pattern, next identity.
27. ¥10 coin mass 7.74g, Cu:Ni=3:1, Cu=¥906/kg, Ni=¥1341/kg → a) mass of Cu,Ni b) cost of metals in coin.
28. A) Prove √2 irrational OR B) Find missing side in right triangles.

SECTION E (Case-Based)
29. Shops A,B,C deals same as Paper 4 Q29 → effective price & % discount.

30. Rectangular path problem same as Paper 4 Q30.

SAMPLE Paper 5 – Complete Solutions with Explanations

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Section A – MCQs with Explanations

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Q1: The sum of any four consecutive integers is always:
a) odd b) prime c) even d) a multiple of 3
✅ Answer: c) even
Explanation: Let n, n+1, n+2, n+3 → sum = 4n+6 = 2(2n+3) → always even.

Q2: Numbers leaving remainder 3 when divided by 5 are of the form:
a) 3k b) 5k+3 c) 5k−3 d) 3k+5
✅ Answer: b) 5k+3
Explanation: That’s the general form.

Q3: Algebraic expression for “Two more than a square number”:
a) 2+s b) (s+2)² c) s²+2 d) s²+4
✅ Answer: c) s²+2
Explanation: Square first (s²), then add 2.

Q4: Which is correct?
a) 1 mL = 10 cc b) 1 mL = 1 cc c) 1 L = 100 cc d) 1 L = 10 cc
✅ Answer: b) 1 mL = 1 cc
Explanation: 1 cm³ = 1 mL.

Q5: The diagonal of a square produces a square whose area is:
a) Half the original b) Same as original c) Double the original d) Four times the original
✅ Answer: c) Double the original
Explanation: If original side = a, area = a². Diagonal = a√2 → new square side = a√2 → area = 2a² → double.

Q6: If base of triangle remains same and height is doubled, area becomes:
a) Half b) double c) triple d) unchanged
✅ Answer: b) double
Explanation: Area = ½ × base × height → height doubles → area doubles.

Q7: Price of mobile = ₹8250, GST 18% added → final price = ?
a) 8250+18 b) 8250+0.18 c) 8250×1.8 d) 8250+0.18×8250
✅ Answer: d) 8250+0.18×8250
Explanation: GST amount = 0.18×8250, so final = 8250 + that.

Q8: Which is a Pythagorean triplet?
a) (2,3,4) b) (4,5,6) c) (3,4,5) d) (5,6,7)
✅ Answer: c) (3,4,5)
Explanation: 3²+4²=9+16=25=5².

Q9: Formula for area of rhombus is:
a) base × height b) side² c) ½ × product of diagonals d) diagonal²
✅ Answer: c) ½ × product of diagonals
Explanation: Standard formula.

Q10: If two natural numbers a and b, then twice the sum of their squares is:
a) (a+b)² b) (a−b)² c) (a+b)²+(a−b)² d) a²+b²
✅ Answer: c) (a+b)²+(a−b)²
Explanation: Expand: (a+b)²+(a−b)² = a²+2ab+b² + a²−2ab+b² = 2a²+2b² = 2(a²+b²).

Q11: Which proportion is true?
a) 4:7 :: 12:21 b) 8:3 :: 24:6 c) 7:12 :: 12:7 d) 12:18 :: 28:12
✅ Answer: a) 4:7 :: 12:21
Explanation: Cross-check: 4×21=84, 7×12=84.

Q12: Cutting a figure and rearranging to get same area is called:
a) Rotation b) reflection c) dissection d) translation
✅ Answer: c) dissection
Explanation: Dissection and rearrangement.

Q13: Jasmine invests p at 6% p.a. for 4 years, no compounding → total amount = ?
a) p×6×4 b) p×0.6×4 c) p×0.06×4 d) p×1.06×4
✅ Answer: d) p×1.06×4 is wrong — correct from options: c) p×0.06×4? No, that’s interest only.
Simple interest total = p + p×0.06×4.
Given options, none correct fully, but likely they mean interest only: c) p×0.06×4.

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Assertion-Reason

Q14:
A: Square of even number multiple of 4, square of odd number 1 more than multiple of 8.
R: Even = 2n, odd = 2n+1, n integer.
✅ Answer: (a) Both true, R explains A
Explanation: From 2n: (2n)²=4n² (multiple of 4). From 2n+1: (2n+1)²=4n²+4n+1=4n(n+1)+1, n(n+1) even → 8m+1.

Q15:
A: 15% of 60 = 60% of 15.
R: x% of y = y% of x since multiplication commutative.
✅ Answer: (a) Both true, R explains A
Explanation: x% of y = (x/100)×y = (y/100)×x = y% of x.

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Section B – Short Answers (2 marks)

Q16: If 3p7q8 divisible by 44 → find possible p,q.
✅ Explanation: Divisible by 44 = divisible by 4 and 11.

• By 4: last two digits q8 divisible by 4 → q=0,2,4,6,8.

• By 11: (3+7+8)−(p+q) = multiple of 11 → 18−(p+q)=0 or 11 or −11.
  18−(p+q)=0 → p+q=18.
  18−(p+q)=11 → p+q=7.
  Possible pairs: For sum=7: (7,0),(5,2),(3,4),(1,6) with q even.
  For sum=18: (9,9) but q=9 not even.
  So possible: (7,0),(5,2),(3,4),(1,6).

Q17(A): Expand (a+ab−3b²)(4+b).
✅ Answer: = a(4+b) + ab(4+b) − 3b²(4+b)
= 4a+ab + 4ab+ab² − 12b²−3b³
= 4a + 5ab + ab² − 12b² − 3b³.
OR
Q17(B): 98×102 = (100−2)(100+2) = 100²−2² = 10000−4=9996.

Q18: Hypotenuse of isosceles right triangle with equal sides 12.
✅ Answer: Hypotenuse = side√2 = 12√2.

Q19(A): 25% of 160 = 40.
Q19(B): 3/5 = 60%, 5/11 ≈ 45.45%.

Q20: Is product of two consecutive integers always multiple of 2? Why?
✅ Answer: Yes. One of two consecutive integers is even → product even.

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Section C – Short Answers (3 marks)

Q21(A): Tea: 200 g for ₹200 → ₹1/g.
1 kg for ₹800 → ₹0.8/g. Ratios not proportional (price per gram different). More expensive: first one.
OR
Q21(B): Prashanti: ₹75,000, Bhuvan: ₹25,000 → ratio 3:1.
Profit ₹4000 → shares: Prashanti = ¾×4000=₹3000, Bhuvan=₹1000.

Q22: Cyclist completes 40% = 92 km → total journey = 92/0.4 = 230 km.
Remaining = 230−92=138 km.

Q23(A): Cryptarithms:
(i) EF×E = GGG → Try E=3, F=7? 37×3=111 (G=1). Works.
(ii) WOW×5 = MEOW → trial needed.
OR
Q23(B): Sreelatha’s number divisible by 9 → sum digits divisible by 9. Reverse digits → sum same → still divisible by 9.
Any digit shuffle keeps sum same → still divisible by 9.

Q24(A): ZYXW trapezium, A midpoint of XY → show area trapezium = area ΔZWB.
Diagram needed: likely by splitting shapes.

Q24(B): Parallelograms on same base, between parallels → areas equal.
Perimeters vary; longest side → larger perimeter.

Q25: Side of rhombus diagonals 24 and 70 units → side = √(12²+35²)=√1369=37 units.

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Section D – Long Answers (4 marks)

Q26: Expand:
(i) (a−b)(a+b) = a²−b².
(ii) (a−b)(a²+ab+b²) = a³−b³.
(iii) (a−b)(a³+a²b+ab²+b³) = a⁴−b⁴.
Pattern: (a−b)(aⁿ⁻¹ + aⁿ⁻²b + ... + bⁿ⁻¹) = aⁿ−bⁿ. Next: n=5 → a⁵−b⁵.

Q27: ¥10 coin mass 7.74 g, Cu:Ni = 3:1.
Cu mass = ¾×7.74=5.805 g, Ni=1.937 g.
Cost Cu=¥906/kg → cost=5.805×0.906=¥5.26.
Cost Ni=¥1341/kg → cost=1.937×1.341=¥2.60.
Total metal cost ≈ ¥7.86.

Q28(A): Prove √2 irrational.
Classic proof: assume √2=m/n in lowest terms → m²=2n² → m even → n even → contradiction.
OR
Q28(B): Find missing side in right triangles (diagram needed).

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Section E – Case-Based (4 marks)

Q29: Shops A,B,C deals:
A: Buy1 Get1 → effective price/item = 50% of marked.
B: Buy2 Get1 → pay for 2 get 3 → per item = (2/3) of marked.
C: Buy3 Get1 → pay for 3 get 4 → per item = (3/4) of marked.
Price=100.
(a) A=50, B≈66.67, C=75.
(b) % discount: A=50%, B≈33.33%, C=25%.
Cheapest to costliest: A, B, C.

Q30: Rectangular path:
a) Rectangles: ABCD (outer), EFGH (inner).
b) Area path = Area(ABCD)−Area(EFGH).
If park 20×12 m, path width 2 m → outer 24×16 m → path area=144 m².
c) If outer shifted but inner fixed, area path changes if outer dimensions change.