Monday, February 9, 2026

Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-10 WITH ANSWERS

 

SAMPLE PAPER 10

SECTION A (MCQ & ARQ)

  1. The digital root of an 8-digit number is 5. What will be the digital root of 10 more than that number?
    a) 5 b) 6 c) 1 d) 8

  2. The number which is divisible by 11 is:
    a) 1234 b) 93547 c) 358095 d) 601436

  3. The number of students in classes A and B are in the ratio 4:5. If 8 students are shifted from class B to A, the ratio becomes 1:1. How many students were there in class B initially?
    a) 65 b) 72 c) 80 d) 90

  4. Jeevana purchased a story book of 216 pages and completed 162 pages. What percentage of the book is to be completed?
    a) 10% b) 15% c) 60% d) 25%

  5. Percentages are fractions with denominator:
    a) 100 b) 10 c) 1 d) 50

  6. Find the diagonal of a square with side length 5 cm:
    a) 25 cm b) 5√2 cm c) 2√5 cm d) 20 cm

  7. Choose a Baudhayana-Pythagoras triple:
    a) 3,4,6 b) 6,8,11 c) 5,12,14 d) 12,16,20

  8. Find the area of unshaded triangular part of the given rectangle. (diagram)

  9. Match the following:
    i) The area of a triangle a) ½ × product of diagonals
    ii) The area of a rhombus b) ½ × base × height
    iii) Area of parallelogram c) ½ × height × sum of parallel sides
    iv) Area of trapezium d) base × height

  10. Which pair of ratios is NOT proportional?
    a) 18:27 and 4:6 b) 25:40 and 5:8 c) 21:35 and 3:5 d) 16:24 and 5:7

  11. Choose the incorrect one:
    a) (a + b)² = a² + 2ab + b² b) (a - b)² = a² - 2ab + b²
    c) (a + b)(c - d) = ac + ad + bc + bd d) a² - b² = (a + b)(a - b)

  12. Which of the following is an example of the distributive property of multiplication over addition?
    a) (a + b = b + a) b) [a(b + c) = ab + ac] c) [(a + b) + c = a + (b + c)] d) (ab = ba)

  13. How many m² is a Km²?
    a) 1000000 b) 100000 c) 10000 d) 1000

Assertion-Reason:

  1. Assertion: The square of an even number is always divisible by 4.
    Reason: Any even number can be written as 2.

  2. Assertion: If the price of an article increases by 20% and then decreases by 20%, the final price remains the same as the original price.
    Reason: An increase and decrease by the same percentage always cancel each other.

SECTION B (VSA - 2 marks each)

  1. Find four consecutive numbers whose sum is 94.

  2. A sports coach buys 24 kits. Each kit has 2 pairs of shoes and 3 T-shirts. Each boy is given a pair of shoes and a T-shirt. In that afternoon the coach has distributed shoes & T-shirt to 20 boys. How much T-shirt are left?

  3. 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.

  4. If a = 8 cm and b = 12 cm are the sides of a right triangle, find the length of hypotenuse.

  5. If 3p7q8 is divisible by 6, list any two pairs of values for 'p' and 'q'.

SECTION C (SA - 3 marks each)

  1. Explain the divisibility test for 11 using place value with an example.

  2. Percentage calculations: (question incomplete in PDF)

  3. Find the area of the shaded region given that ABCD is a rectangle. (diagram)

  4. Find the side length of a rhombus whose diagonals are of 24 units and 70 units.

  5. Simplify a) 72 : 108 (b) 20 : 30 (c) Check whether the two ratios are proportional.

SECTION D (LA - 4 marks each)

  1. A shopkeeper has a set of (21 + x) pens and the cost of each pen is ₹(21 - x)
    a) What is the total cost all his pens?
    b) Find the cost pens in the above case if x = 4

  2. A four days scout and guide camp were arranged by the school for class 8 students.
    i) The school arranged 6 buses to take 150 students to the camp. If 75 more students are joined, how many buses are required in all?
    ii) In the camp, they assigned some jobs to the students. 45 students complete a job in 20 minutes. How many minutes will 30 students take to complete the same job?

  3. Find the area of an equilateral triangle with side length 6 units. (Hint: Show that an altitude bisects the opposite side. Use this to find the height)

SECTION E (Case study based)

  1. There is a pentagonal shaped park in a colony as shown in the figure. Class VIII students Jyoti and Kavitha are playing in the park. While playing, they start discussing how to find the area of the park. Jyoti divides the pentagon into triangles, while Kavitha divides it into rectangles and triangles. Both of them calculate the area using their own methods.
    a) Find the area of the square part of the park.
    b) Find the area of one triangular part of the park.
    c) Which method do you find easier, and why?

  2. In a Kendriya Vidyalaya, attendance of students of Primary as well as Secondary is recorded on 2nd February 2026. The data is given in a table.
    a) Find the percentage of the strength of primary students (Class I - V) in the KV.
    b) What is the percentage of students absent in total?
    c) Find the difference between the percentage of attendance of boys and girls of Class VIII on 2nd February 2026.

SAMPLE Paper 10 – Complete Solutions with Explanations

Section A – MCQs with Explanations

Q1: Digital root of 8-digit number is 5 → digital root of number + 10 = ?
a) 5 b) 6 c) 1 d) 8
✅ Answer: b) 6
Explanation: Adding 10 adds 1 to digital root (since 10 → 1+0=1). 5+1=6.

Q2: Which is divisible by 11?
a) 1234 b) 93547 c) 358095 d) 601436
✅ Answer: b) 93547
Explanation: Divisibility by 11: (9+5+7)−(3+4)=21−7=14 not multiple of 11? Check:
Actually (odd place sum) – (even place sum) = (9+5+7)−(3+4)=21−7=14 → not 0/11/22. Let’s verify:
93547: digits 9(odd),3(even),5(odd),4(even),7(odd). Sum odd=9+5+7=21, even=3+4=7, diff=14 not divisible by 11 → so not divisible.
Check 601436: (6+1+3)=10, (0+4+6)=10, diff=0 ✔ divisible.
So correct answer: d) 601436.

Q3: Students in A:B = 4:5. If 8 students shift from B to A → ratio becomes 1:1 → initial B?
a) 65 b) 72 c) 80 d) 90
✅ Answer: c) 80
Explanation: Let A=4x, B=5x. After shift: A=4x+8, B=5x−8 → (4x+8)/(5x−8)=1 → 4x+8=5x−8 → x=16 → B=5×16=80.

Q4: Book 216 pages, completed 162 → % left?
a) 10% b) 15% c) 60% d) 25%
✅ Answer: d) 25%
Explanation: Left = 216−162=54 pages → % = (54/216)×100=25%.

Q5: Percentages are fractions with denominator ___
a) 100 b) 10 c) 1 d) 50
✅ Answer: a) 100

Q6: Diagonal of square side 5 cm:
a) 25 cm b) 5√2 cm c) 2√5 cm d) 20 cm
✅ Answer: b) 5√2 cm

Q7: Pythagorean triple:
a) 3,4,6 b) 6,8,11 c) 5,12,14 d) 12,16,20
✅ Answer: d) 12,16,20
Explanation: 12²+16²=144+256=400=20².

Q8: Area of unshaded triangle in rectangle → need diagram.
Likely half of rectangle.

Q9: Match formulas:
i) Triangle area → ½×base×height
ii) Rhombus area → ½×product of diagonals
iii) Parallelogram area → base×height
iv) Trapezium area → ½×height×sum of parallel sides
✅ Answer: D) i-b, ii-a, iii-d, iv-c

Q10: Which ratio pair NOT proportional?
a) 18:27 & 4:6 (both 2:3) b) 25:40 & 5:8 (both 5:8) c) 21:35 & 3:5 (both 3:5) d) 16:24 & 5:7 (16:24=2:3, 5:7≠2:3)
✅ Answer: d) 16:24 & 5:7

Q11: Incorrect identity:
a) (a+b)² = a²+2ab+b² b) (a−b)² = a²−2ab+b² c) (a+b)(c−d) = ac+ad+bc+bd d) a²−b² = (a+b)(a−b)
✅ Answer: c) Should be ac−ad+bc−bd.

Q12: Distributive property example:
a) a+b=b+a b) a(b+c)=ab+ac c) (a+b)+c=a+(b+c) d) ab=ba
✅ Answer: b)

Q13: How many m² in 1 km²?
a) 1,000,000 b) 100,000 c) 10,000 d) 1000
✅ Answer: a) 1,000,000

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: Price increases 20% then decreases 20% → same as original.
R: Increase and decrease by same % cancel.
✅ Answer: (d) A false, R false
Explanation: They don’t cancel multiplicatively.

Section B – Short Answers (2 marks)

Q16: Four consecutive numbers sum to 94 → find them.
✅ Answer: Let numbers: n, n+1, n+2, n+3 → 4n+6=94 → 4n=88 → n=22 → numbers: 22,23,24,25.

Q17: Coach buys 24 kits, each: 2 shoes + 3 T-shirts. Distributes to 20 boys (1 shoe+1 T-shirt each). T-shirts left?
✅ Explanation: Total T-shirts = 24×3=72. Used = 20×1=20 → left=52.
But careful: Shoes per boy=1, T-shirts per boy=1. Yes, so T-shirts used=20 → left=72−20=52.

Q18: TV ₹21,000, depreciates 5% after 1 year → value = 21000×0.95=₹19,950.

Q19: Right triangle sides a=8 cm, b=12 cm → hypotenuse = √(8²+12²)=√(64+144)=√208=4√13 cm.

Q20: 3p7q8 divisible by 6 → find two pairs for p,q.
✅ Explanation: Divisible by 6 → divisible by 2 and 3.

  • By 2: last digit 8 even ✔

  • By 3: sum digits=3+p+7+q+8=18+p+q divisible by 3 → p+q divisible by 3.
    Pick p=1,q=2 (sum=3) → 31728.
    p=2,q=1 → 32718.

Section C – Short Answers (3 marks)

Q21: Divisibility test for 11 using place value:
Odd-position digits sum − Even-position digits sum = 0 or multiple of 11.
Example: 121: (1+1)−2=0 ✔ divisible.

Q22: Not fully stated, likely percentage calculations.

Q23: Area of shaded region in rectangle → need diagram.

Q24: Side of rhombus diagonals 24 and 70 → side=√(12²+35²)=√1369=37 units.

Q25: Simplify ratios:
a) 72:108 = 2:3 b) 20:30=2:3
c) Proportional? Yes, both 2:3.

Section D – Long Answers (4 marks)

Q26: Shopkeeper pens: (21+x) pens, each cost ₹(21−x) → total cost = (21+x)(21−x)=441−x².
If x=4 → total=441−16=425.

Q27: Scout camp:
(i) 6 buses for 150 students → 1 bus=25 students. If 75 more join → total=225 → buses=225/25=9.
(ii) 45 students → 20 min, 30 students → time inversely proportional → (45/30)×20=30 min.

Q28: Equilateral triangle side 6 units → height = 3√3 → area = ½×6×3√3=9√3 units².

Section E – Case-Based (4 marks)

Q29: Pentagonal park:
a) Square part area = side² (need dimensions).
b) Triangular part area = ½×base×height.
c) Easier method depends on division.

Q30: KV attendance table:
a) Primary (I–V) total strength = 777 → % of total 1537 = (777/1537)×100≈50.55%.
b) Total absent = Total strength − Total present = 1537−1351=186 → % absent = (186/1537)×100≈12.1%.
c) Class VIII: Boys present=74, total boys=82 → % boys present=90.24%. Girls present=65, total girls=76 → % girls present=85.53%. Difference ≈ 4.71%.

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Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-9 WITH ANSWERS

 Class 8 SESSION ENDING EXAMINATION (2026)  SAMPLE PAPER-9 WITH ANSWERS

SAMPLE

PAPER 9

SECTION A

  1. Which of the following Venn diagrams captures the relationship between the multiples of 4, 8 and 32?

  2. If 8 exactly divides two numbers separately it must exactly divide their sum:
    a) Always true b) sometimes true c) never true d) none

  3. By how much does the product increase in 23 × 27, if 23 is increased by 1?
    a) 1 b) 23 c) 27 d) 21

  4. The 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))²

  5. 120:15::80:?
    a) 5 b) 10 c) 15 d) 20

  6. 25°C is equal to:
    a) 70°F b) 75°F c) 77°F d) 79°F

  7. Compounding is an example of:
    a) linear growth b) exponential growth c) both d) none

  8. What 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)

  9. The longest side of a right angled triangle is called:
    a) diagonal b) hypotenuse c) height d) adjacent side

  10. What is the sum of the first n odd numbers?
    a) 2n b) 2 + n c) 2 - n d) n²

  11. How many m² is a km²?
    a) 1000000 m² b) 1000 m² c) 100 m² d) 1000 m²

  12. Find the area of the rhombus whose diagonals are 20 cm and 15 cm:
    a) 150 cm² b) 140 cm² c) 200 cm² d) 300 cm²

  13. How many cm² is 1 in²?
    a) 2.34² b) 2.44² c) 2.54² d) 2.64²

Assertion-Reason:

  1. 50% discount is not equal to 30% + 20%.
    x% + y% means compounding.

  2. (a+b)(a-b) = a² - b²
    dcab × (10 + 1) = (dcab × 10) + dcab

SECTION B (2 marks each)

  1. 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?"

  2. 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?

  3. Which is greater: (a-b)² or (b-a)²? Justify your answer.
    OR
    Express 100 as the difference of two squares.

  4. 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?

  5. Is √2 less than or greater than 2?

SECTION C (3 marks each)

  1. "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.

  2. 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?

  3. 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?

  4. What fraction of the total area of the rectangle is the area of the dark shaded region? (diagram)

SECTION D (4 marks each)

  1. 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.

  2. 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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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)

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

  2. 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)

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

  2. 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.

  3. 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.

  4. 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.

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

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

  1. 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?

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

  3. 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?

  4. 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.

  5. 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)

  1. 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.

  2. 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.

  3. 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)

  1. 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?

  2. 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

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.

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.

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.

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.

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.

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.

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