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

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

SAMPLE PAPER 8

SECTION-A (MCQ - 1 mark each)

1. Which of the following numbers is divisible by 9:
   a) 783 b) 502 c) 7777 d) 358015

2. What is the digital root of 4710?
   a) 1 b) 2 c) 3 d) 4

3. Which of the following is equal to (a - b)²?
   a) a² + b² b) a² + b² + 2ab c) a² + b² - 2ab d) a² - b²

4. Which of the following in an identity?
   a) (a+b)² = a² + b² b) (a-b)² = a² - b² c) (a-b)² = a² + 2ab - b² d) (a+b)² = a² + 2ab + b²

5. ₹700 is being divided between two friends A and B in the ratio 7:3. How much will B get?
   a) 700 b) 200 c) 210 d) 490

6. The ratio of boys to girls in a class is 3:2. If there are 45 boys, how many girls are there?
   a) 20 b) 25 c) 40 d) 30

7. 6/10 in percentage can be written as:
   a) 90% b) 80% c) 70% d) 60%

8. What is the amount we get back if we invest ₹6000 at an interest rate of 10% p.a. for 2 years?
   a) 1200 b) 3200 c) 5200 d) 7200

9. Which of the following is an example of Baudhayana-Pythagoras triples?
   a) 1, 2, 3 b) 2, 3, 4 c) 6, 8, 10 d) 4, 5, 6

10. Find the diagonal of a square with side length 10 cm:
    a) 2√10 b) 10√2 c) 10√3 d) 10√4

11. If each side of a square is tripled, its area becomes:
    a) Nine times b) Triple c) Four times d) Eight times

12. The diagonal of a square divides it into two triangles. If the square has an area of 40 cm², the area of each triangle is:
    a) 10 cm² b) 20 cm² c) 40 cm² d) 80 cm²

13. If the diagonals of a rhombus are 20 cm and 15 cm then its area:
    a) 200 cm² b) 300 cm² c) 120 cm² d) 150 cm²

SECTION-B (Assertion & Reason)

14. Assertion: The product of (x + 5) and (x - 5) is x² - 25
    Reason: According to the distributive law, a(b + c) = ab + ac

15. Assertion: The fraction 20/15 is equivalent to 4/3.
    Reason: A fraction is in its simplest form if the numerator and denominator have no common factor other than 1.

SECTION-C (Short answer type - 2 marks each)

16. The sum of five consecutive numbers is 35. What are these numbers?

17. A two-digit number is written as 10x + y. If the sum of the original number and its reverse is 66, find the value of x + y.

18. Solve the following using suitable algebraic identities:
    (a) 3874 × 11 (b) 504 × 96
    OR
    A shopkeeper sells 8x boxes of pens. Each box has 5p blue pens and 3q black pens. Find total pens.

19. Reena has 40 marbles, out of which 18 are red. Find the percentage of red marbles.
    OR
    After a discount of 20%, the selling price of an article is ₹12,000. Find its marked price.

20. The hypotenuse of an isosceles right triangle is 10√2 cm. Find the other two sides.

SECTION-D (Short answer type - 3 marks each)

21. Find three consecutive numbers such that the first number is a multiple of 2, the second number is a multiple of 3, and the third number is a multiple of 4. Are there more such numbers? How often do they occur?
    OR
    Draw a Venn diagram which captures the relationship between the multiples of 4, 8, and 32?

22. A hostel has enough food for 180 students for 40 days. How long would the food last if 60 more students join the hostel?

23. The maximum marks in a test are 90. If students score 75% or above in the test, they get an A grade. How much should Zubin score at least to get an A grade?

24. Find the side length of a trapezium whose parallel sides are 10 cm and 14 cm and its area is 96 cm². Find the height.

25. The parallel sides of a trapezium are 10 cm and 14 cm and its area is 96 cm². Find the height.
    OR
    Find the area of the shaded region given that ABCD is a rectangle.

SECTION-E (Long answer type - 4 marks each)

26. A tiny park is coming up in Dhaui. The plan is shown in the figure. The two square plots, each of area g² sq.ft., will have a green cover. All the remaining area is a walking path w ft. wide that needs to be tiled. Write an expression for the area that needs to be tiled.

27. A company planned to complete a road construction project in 50 days using 40 workers. After 20 days, 10 workers left the job. The remaining workers continued to work at the same rate.
    a) How much of the work was completed in the first 20 days?
    b) How many workers were left after 20 days?
    c) How many more days will the remaining workers take to complete the remaining work?
    d) Identify whether this situation is a direct or inverse proportion and justify your answer.

28. If a right-angled triangle has shorter sides of lengths 5 cm and 12 cm, then what is the length of its hypotenuse? First draw the right-angled triangle with these side lengths and measure the hypotenuse, then check your answer using Baudhayana's Theorem.
    OR
    A student has three wooden sticks of lengths 7 cm, 24 cm, and 25 cm.
    (a) Check if these three sticks can form a right-angled triangle.
    (b) State the property or theorem you used to reach your conclusion.

SECTION-F (Case based questions)

29. A school canteen has 600 food packets. 35% are biscuits, 1/3 are chips and the rest are juice.
    (a) Find the number of biscuit packets.
    (b) Find the number of chips packets and express it as a percentage.
    (c) If 10% of juice packets are donated, how many packets are donated?

30. A rectangular garden has length (x + 8) meters and breadth (x - 2) meters. If both the length and breadth are increased by 1 meter.
    (a) Find the area of the original rectangular garden.
    (b) What is the area of the current rectangular garden after increase of 1m?
    (c) How much area increased?

SAMPLE Paper 8 – Section A – MCQs with Explanations

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Q1: Which number is divisible by 9?
a) 783 b) 502 c) 7777 d) 358015
✅ Answer: a) 783
Explanation: Sum of digits: 7+8+3=18 → divisible by 9.

Q2: Digital root of 4710?
a) 1 b) 2 c) 3 d) 4
✅ Answer: c) 3
Explanation: 4+7+1+0=12 → 1+2=3.

Q3: (a−b)² = ?
a) a²+b² b) a²+b²+2ab c) a²+b²−2ab d) a²−b²
✅ Answer: c) a²+b²−2ab

Q4: Which is an identity?
a) (a+b)²=a²+b² b) (a−b)²=a²−b² c) (a−b)²=a²+2ab−b² d) (a+b)²=a²+2ab+b²
✅ Answer: d) (a+b)²=a²+2ab+b²

Q5: ₹700 divided in ratio 7:3 → B’s share?
a) 700 b) 200 c) 210 d) 490
✅ Answer: c) 210
Explanation: B’s share = (3/10)×700 = 210.

Q6: Boys:Girls = 3:2, boys=45 → girls?
a) 20 b) 25 c) 40 d) 30
✅ Answer: d) 30
Explanation: Let girls=2x, boys=3x=45 → x=15 → girls=30.

Q7: 6/10 as percentage = ?
a) 90% b) 80% c) 70% d) 60%
✅ Answer: d) 60%
Explanation: 6/10=0.6=60%.

Q8: Invest ₹6000 at 10% p.a. for 2 years → amount?
a) 1200 b) 3200 c) 5200 d) 7200
✅ Answer: d) 7200
Explanation: Simple interest = 6000×0.10×2=1200 → total=7200.

Q9: Example of Pythagorean triple:
a) 1,2,3 b) 2,3,4 c) 6,8,10 d) 4,5,6
✅ Answer: c) 6,8,10
Explanation: 6²+8²=36+64=100=10².

Q10: Diagonal of square side 10 cm:
a) 2√10 b) 10√2 c) 10√3 d) 10√4
✅ Answer: b) 10√2 cm

Q11: If side of square tripled → area becomes:
a) Nine times b) Triple c) Four times d) Eight times
✅ Answer: a) Nine times
Explanation: Area ∝ side² → (3)²=9.

Q12: Diagonal divides square area 40 cm² into two triangles → each triangle area =
a) 10 cm² b) 20 cm² c) 40 cm² d) 80 cm²
✅ Answer: b) 20 cm²
Explanation: Each triangle = half of square = 20 cm².

Q13: Rhombus diagonals 20 cm and 15 cm → area =
a) 200 cm² b) 300 cm² c) 120 cm² d) 150 cm²
✅ Answer: d) 150 cm²
Explanation: ½×20×15=150.

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Assertion-Reason

Q14:
A: (x+5)(x−5)=x²−25
R: Distributive law a(b+c)=ab+ac
✅ Answer: (b) Both true, R not correct explanation
Explanation: R is distributive, but A uses difference of squares identity.

Q15:
A: 20/15 = 4/3
R: Fraction in simplest form if numerator/denominator have no common factor other than 1.
✅ Answer: (a) Both true, R explains A
Explanation: Dividing numerator/denominator by 5 gives 4/3.

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Section B – Short Answers (2 marks)

Q16: Sum of five consecutive numbers = 35 → find them.
✅ Answer: Let numbers: n−2, n−1, n, n+1, n+2 → sum=5n=35 → n=7 → numbers: 5,6,7,8,9.

Q17: Two-digit number = 10x+y. Original + reverse = 66 → find x+y.
✅ Explanation: (10x+y)+(10y+x)=66 → 11x+11y=66 → x+y=6.

Q18: Solve using identities:
(a) 3874×11 = 3874×(10+1)=38740+3874=42614.
(b) 504×96 = 504×(100−4)=50400−2016=48384.
OR Shopkeeper sells 8x boxes, each with 5p blue + 3q black → total pens = 8x×(5p+3q)=40px+24qx.

Q19: Reena: 40 marbles, 18 red → % red = (18/40)×100=45%.
OR After 20% discount, SP=₹12,000 → MP=12000/0.8=₹15,000.

Q20: Isosceles right triangle hypotenuse = 10√2 cm → other sides = 10 cm each.
✅ Explanation: side√2 = 10√2 → side=10.

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Section C – Short Answers (3 marks)

Q21: Three consecutive numbers: first multiple of 2, second multiple of 3, third multiple of 4. Find such numbers.
✅ Answer: Let numbers: 2n, 2n+1, 2n+2. But 2n+1 multiple of 3, 2n+2 multiple of 4.
Test: n=2 → 4,5,6 (5 not multiple of 3).
n=5 → 10,11,12 (11 no).
n=8 → 16,17,18 (17 no).
Better approach: Let numbers be a,a+1,a+2. Conditions: a even, a+1 multiple of 3, a+2 multiple of 4.
Try a=2 → 2,3,4 ✔ (2 multiple of 2, 3 multiple of 3, 4 multiple of 4).
Next: a=14 → 14,15,16 ✔. So they occur every 12 numbers.

OR Venn diagram for multiples of 4,8,32:
Multiples of 32 inside multiples of 8 inside multiples of 4.

Q22: Hostel food for 180 students for 40 days. If 60 more join → food lasts how long?
✅ Explanation: Total “student-days” = 180×40=7200.
New students=240 → days=7200/240=30 days.

Q23: Max marks=90, need 75% for A grade → Zubin needs at least 0.75×90=67.5 → 68 marks.

Q24: Trapezium parallel sides 10 cm and 14 cm, area=96 cm² → height = ?
✅ Answer: Area = ½×h×(10+14)=12h=96 → h=8 cm.

Q25: Same as Q24? Possibly repeat.
OR Area of shaded region in rectangle ABCD → need diagram.

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Section D – Long Answers (4 marks)

Q26: Tiny park with two square plots area g² sq ft each, walking path width w ft → tiled area expression.
✅ Answer: Total area − green area.
If squares side = g, total area = (g+2w)²×? Need full figure.

Q27: Road project: 40 workers, 50 days total. After 20 days, 10 workers leave.
(a) Work in first 20 days: 20/50=2/5 of work.
(b) Workers left = 30.
(c) Remaining work = 3/5, with 30 workers:
Original rate: 40 workers do 1/50 per day → 1 worker does 1/2000 per day.
30 workers do 30/2000=3/200 per day → days for 3/5 work = (3/5)/(3/200)=40 days.
(d) Inverse proportion: fewer workers → more days.

Q28: Right triangle sides 5 cm, 12 cm → hypotenuse = 13 cm (Pythagoras).
OR Sticks 7 cm, 24 cm, 25 cm → Check: 7²+24²=49+576=625=25² → Yes, right triangle.

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Section E – Case-Based (4 marks)

Q29: School canteen: 600 packets.
35% biscuits → 0.35×600=210.
1/3 chips → 600/3=200.
Rest juice = 600−(210+200)=190.
(a) Biscuits=210.
(b) Chips=200 → % = (200/600)×100≈33.33%.
(c) 10% of juice donated → 0.10×190=19 packets.

Q30: Rectangular garden: length=(x+8) m, breadth=(x−2) m.
Both length and breadth increased by 1 m.
(a) Original area = (x+8)(x−2) = x²+6x−16.
(b) New area = (x+9)(x−1) = x²+8x−9.
(c) Increase = (x²+8x−9)−(x²+6x−16) = 2x+7 m².