Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-9 WITH ANSWERS
SAMPLE
PAPER 9
SECTION A
Which of the following Venn diagrams captures the relationship between the multiples of 4, 8 and 32?
If 8 exactly divides two numbers separately it must exactly divide their sum:
a) Always true b) sometimes true c) never true d) noneBy how much does the product increase in 23 × 27, if 23 is increased by 1?
a) 1 b) 23 c) 27 d) 21The sum of the squares of the two consecutive numbers:
a) m² + n² b) (m + n)² c) m² + (m + 1)² d) (m + (m + 1))²120:15::80:?
a) 5 b) 10 c) 15 d) 2025°C is equal to:
a) 70°F b) 75°F c) 77°F d) 79°FCompounding is an example of:
a) linear growth b) exponential growth c) both d) noneWhat is the amount we get back for the amount 'p' at an interest rate of 'r%' p.a. for 't' years?
a) p(1 + rt) b) p + t c) p + (1 + rt) d) p - (1 + rt)The longest side of a right angled triangle is called:
a) diagonal b) hypotenuse c) height d) adjacent sideWhat is the sum of the first n odd numbers?
a) 2n b) 2 + n c) 2 - n d) n²How many m² is a km²?
a) 1000000 m² b) 1000 m² c) 100 m² d) 1000 m²Find the area of the rhombus whose diagonals are 20 cm and 15 cm:
a) 150 cm² b) 140 cm² c) 200 cm² d) 300 cm²How many cm² is 1 in²?
a) 2.34² b) 2.44² c) 2.54² d) 2.64²
Assertion-Reason:
50% discount is not equal to 30% + 20%.
x% + y% means compounding.(a+b)(a-b) = a² - b²
dcab × (10 + 1) = (dcab × 10) + dcab
SECTION B (2 marks each)
Riddle: "I'm made of digits, each tiniest and odd, No shared ground with root #1-how odd! My digits count, their sum, my root- All point to one bold number's pursuit- The largest odd single-digit I proudly claim. What's my number? What's my name?"
If 31Z5 is a multiple of 9, where Z is a digit, what is the value of Z? Explain why there are two answers to this problem?
Which is greater: (a-b)² or (b-a)²? Justify your answer.
OR
Express 100 as the difference of two squares.1600 people voted in an election and the winner got 500 votes. What percent of the total votes did the winner get? Can you guess the minimum number of candidates who stood for elections?
OR
A TV is bought at a price of ₹21,000. After 1 year, the value of the TV depreciates by 5%. Find the value of the TV after one year?Is √2 less than or greater than 2?
SECTION C (3 marks each)
"I hold some pebbles, not too many, When I group them in 3's, one stays with me. Try pairing them up - it simply won't do, A stubborn odd pebble remains in my view. Group them by 5, yet one's still around, But grouping by seven, perfection is found. More than one hundred would be far too bold, Can you tell me the number of pebbles I hold?"
OR
"I take a number that leaves a remainder of 8 when divided by 12. I take another number which is 4 short of a multiple of 12. Their sum will always be a multiple of 8", claims Snehal. Examine his claim and justify your conclusion.To make soft idlis, you need to mix rice and urad dal in the ratio of 2:1. If you need 6 cups of this mixture to make idlis tomorrow morning, how many cups of rice and urad dal will you need?
What is 5% of 40? What is 40% of 5? What is 25% of 12? What is 12% of 25? What is 15% of 60? What is 60% of 15? What do you notice? Can you make a general statement and justify it using algebra, comparing x% of y and y% of x?
What fraction of the total area of the rectangle is the area of the dark shaded region? (diagram)
SECTION D (4 marks each)
Profit and Loss: Kishanlal (retailer) buys sweaters from a wholesaler at a price of ₹300 per sweater. The marked price he quotes his customers is ₹480. After bargaining, he sells this sweater at ₹430.
(i) Find out the profit Kishanlal made on this sweater.
(ii) Find out the profit percentage Kishanlal made in the above deal.
(iii) After few months to clear the old stock Kishanlal sells the same variety of sweater for ₹250. Find out the loss/profit percentage in this case.In the Sulba-SΕ«tras, consider two copies of the given trapezium in which AB||CD. Rotate the second copy as shown.
i) What figure will we get when the two trapeziums are joined along BC?
ii) What type of quadrilateral is this?
iii) Find the area of the following figure.
SAMPLE Paper 9 – Complete Solutions with Explanations
Section A – MCQs with Explanations
Q1: Which Venn diagram captures the relationship between multiples of 4, 8, and 32?
No options given, but explanation:
Multiples of 32 are inside multiples of 8, which are inside multiples of 4.
So: Multiples of 32 ⊂ Multiples of 8 ⊂ Multiples of 4.
Q2: If 8 divides two numbers separately, it must divide their sum:
a) Always true b) Sometimes true c) Never true d) None
✅ Answer: a) Always true
Explanation: If a and b divisible by 8, then a=8m, b=8n → a+b=8(m+n) divisible by 8.
Q3: By how much does product increase in 23×27 if 23 is increased by 1?
a) 1 b) 23 c) 27 d) 21
✅ Answer: c) 27
Explanation: 23×27=621, 24×27=648 → increase=27.
Q4: Sum of squares of two consecutive numbers:
a) m²+n² b) (m+n)² c) m²+(m+1)² d) (m+(m+1))²
✅ Answer: c) m²+(m+1)²
Q5: 120:15 :: 80:?
a) 5 b) 10 c) 15 d) 20
✅ Answer: b) 10
Explanation: 120/15=8, so 80/?=8 → ?=10.
Q6: 25°C = ?°F
a) 70°F b) 75°F c) 77°F d) 79°F
✅ Answer: c) 77°F
Explanation: °F = (9/5)×°C + 32 = (9/5)×25+32=45+32=77°F.
Q7: Compounding is an example of:
a) Linear growth b) Exponential growth c) Both d) None
✅ Answer: b) Exponential growth
Q8: Amount for principal p at r% p.a. for t years:
a) p(1+rt) b) p+t c) p+(1+rt) d) p−(1+rt)
✅ Answer: a) p(1+rt)
Explanation: Simple interest formula.
Q9: Longest side of right triangle:
a) Diagonal b) Hypotenuse c) Height d) Adjacent side
✅ Answer: b) Hypotenuse
Q10: Sum of first n odd numbers:
a) 2n b) 2+n c) 2−n d) n²
✅ Answer: d) n²
Q11: How many m² in 1 km²?
a) 1,000,000 m² b) 1000 m² c) 100 m² d) 1000 m²
✅ Answer: a) 1,000,000 m²
Q12: Area of rhombus diagonals 20 cm and 15 cm:
a) 150 cm² b) 140 cm² c) 200 cm² d) 300 cm²
✅ Answer: a) 150 cm²
Explanation: ½×20×15=150.
Q13: How many cm² in 1 in²?
a) 2.34² b) 2.44² c) 2.54² d) 2.64²
✅ Answer: c) 2.54² ≈ 6.4516 cm²
Assertion-Reason
Q14:
A: 50% discount ≠ 30%+20% discount.
B: x% + y% means compounding.
✅ Answer: Need full R statement — likely both true.
Q15:
A: (a+b)(a−b)=a²−b²
R: dcab×(10+1) = (dcab×10)+dcab
✅ Answer: (b) Both true, R not explanation
Explanation: R shows distributive property, not difference of squares.
Section B – Short Answers (2 marks)
Q16: Riddle: “Digits all odd, no shared ground with root #1, largest odd single-digit number” → ?
✅ Answer: 9
Explanation: Largest odd single digit = 9, digits all odd, digital root=9.
Q17: 31Z5 divisible by 9 → Z=? Why two answers?
✅ Answer: Sum digits=3+1+Z+5=9+Z divisible by 9 → Z=0 or 9 (since Z digit 0–9). Two answers possible.
Q18: Which greater: (a−b)² or (b−a)²? Justify.
✅ Answer: Equal because square of a number is same regardless of sign.
OR Express 100 as difference of two squares: 26²−24²=100.
Q19: 1600 votes, winner got 500 → % of total = (500/1600)×100=31.25%.
Minimum candidates? At least 2.
OR TV ₹21,000, depreciates 5% after 1 year → value=21000×0.95=₹19,950.
Q20: Is √2 less than or greater than 2?
✅ Answer: √2 ≈ 1.414 < 2.
Section C – Short Answers (3 marks)
Q21: Riddle: Pebbles → remainder 1 when divided by 3, by 5, but divisible by 7, <100.
✅ Answer: Let N=7k, N≡1 mod 3, N≡1 mod 5 → N≡1 mod 15 → N=15m+1=7k.
Test: 15×4+1=61 (not multiple of 7), 15×6+1=91=7×13 ✔.
So 91 pebbles.
OR Snehal’s claim: One number remainder 8 mod 12, another 4 short of multiple of 12 (remainder 8) → sum remainder=16 mod 12=4, not necessarily multiple of 8 → claim false.
Q22: Rice:Urad dal = 2:1, total 6 cups → rice= (2/3)×6=4 cups, urad dal=2 cups.
Q23:
5% of 40 = 2
40% of 5 = 2
25% of 12 = 3
12% of 25 = 3
15% of 60 = 9
60% of 15 = 9
Observation: x% of y = y% of x.
Algebra: (x/100)×y = (y/100)×x.
Q24: Figure area problem:
Dark shaded fraction = ? Need diagram.
Likely ¼ or ⅓.
Section D – Long Answers (4 marks)
Q29: Profit and loss:
Kishanlal: CP=₹300, MP=₹480, SP=₹430.
(i) Profit = SP−CP=430−300=₹130.
(ii) Profit % = (130/300)×100≈43.33%.
(iii) Later sells at ₹250 → Loss=300−250=₹50 → Loss%=(50/300)×100≈16.67%.
Q30: Two trapeziums joined along BC → forms a parallelogram.
(i) Quadrilateral type = Parallelogram.
(ii) Area = 2 × area of trapezium.
Need dimensions for exact.
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