Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-1 WITH ANSWERS

 SESSION ENDING EXAMINATION (2026)
 SAMPLE PAPER-1 

Portion

Part -1 

Ch - 5 Number Play

Ch - 6 We distribute, yet things multiply

Ch - 7 Proprtional Reasoning - 1

Part -2 

Ch - 1 Fractions in Disguise

CH2 PART 2 THE BAUDHĀYANA-PYTHAGORAS THEOREM

Ch - 3 Proportional Reasoning - 2

Ch - 7 Area

 Class: VIII                                                                                                       Subject: Mathematics 

 Time: 2 ½ Hrs.                                                                                              Max Marks: 60 

 General Instructions:

•  All questions are compulsory. 
•  The question paper consists of 30 questions divided into five sections A, B, C ,D and E. 
•  Section A contains 13MCQ questions and 2 assertion and reasoning questions of one mark each.
• Section B contains 5 short answer questions of 2 marks each. 
•  Section C contains 5 short answer questions of 3 marks each. 
•  Section D contains 3 long answer questions of 5 marks each. 
• Section E 2 case based questions of each4 marks.

Section A – MCQ & Assertion-Reason

1. The digital root of 63855 is
   a) 6 b) 9 c) 3 d) 12

2. If a number is divisible by 4 and 8 it must be divisible by
   a) 8 b) 12 c) 18 d) 24

3. Distributive property of (a+b)² can be expressed as
   a) (a+b)×(a+b) b) (a+b)×(a−b) c) a+b,a+b d) none

4. A Square of any odd number is always
   a) even b) multiple of 4 c) one more than multiple of 8 d) a multiple of 8

5. Which ratio is proportional to 96 and 144
   a) 2:5 b) 2:3 c) 3:2 d) 3:3

6. If 72 liters of milk sufficient for 288 people, milk required for 450 people
   a) 96 b) 108 c) 112.5 d) 120

7. 25% of 160 =
   a) 80 b) 80 c) 40 d) 42

8. Esha scored 42 marks out of 50 on English test, Score as a percentage
   a) 84% b) 90% c) 100% d) 52%

9. Is √2 value less than or greater than 1
   a) <1 b) >1 c) =1 d) none

10. If the hypotenuse of an isosceles right triangle is √72, the other two sides
    a) 6,6 b) 6,7 c) 8,9 d) 12,6

11. Find the area of a rhombus whose diagonals are 20 cm and 15 cm.
    a) 150 cm² b) 300 cm² c) 900 cm² d) 1500 cm²

12. Area of each triangle in the rectangle of length 7 cm and breadth 4 cm
    a) 14 cm² b) 15 cm² c) 20 cm² d) none

13. Area of the parallelogram obtained by
    a) base × height b) 1 × b c) 2(l+b) d) ½ × b × h

Assertion-Reason:
14. Assertion: (a+b)² − (a−b)² = 4a
Reason: On expansion, square terms cancel
15. Assertion: Area of trapezium = ½ × height × sum of parallel sides
Reason: Parallel sides of trapezium 12 cm and 16 cm and height 5 cm then area = 70 cm²

Section B (2 marks each)
16. Write 2 multiples of 36 between 45,000 and 47,000.
17. Draw the Venn diagram which captures the relationship between the multiples of 4,8 and 32.
18. Expand (a+b)(a+b) OR Expand (3+u)(v−3).
19. Nandini has 25 marbles of which 15 are white. What percentage of her marbles are white?
20. Find the diagonal of a square with side length 5 cm.

Section C (3 marks each)
21. The sum of four consecutive numbers is 34. What are these numbers?
OR The digital root of an 8-digit number is 5. What will be the digital root of number + 10?
22. Find the HCF of 72 and 96 OR Divide ₹4500 into two parts in the ratio 2:3.
23. Find the value and draw bar models: i) 7% of 10 kg ii) 62% of 360.
24. A right-angled triangle has short side 8 cm and hypotenuse 17 cm. Find the third side using Pythagoras theorem.
25. Find area of quadrilateral ABCD given AC=22 cm, BM=3 cm, DN=3 cm, BM ⟂ AC, DN ⟂ AC.

Section D (Long Answer – 4 marks each)
26. Compute using suitable identities: i) 397 × 403 ii) (2x−1)²
27. One acre of land costs ₹15,00,000. What is the cost of 2,400 sq ft of same land?
28. If (a,b,c) is a Pythagorean triple, then (ka,kb,kc) is also a triple for positive integer k. Verify with example.

Section E (Case-Based – 4 marks each)
29. Gangaram opened a book exhibition stall He aims to achieve a daily sales of atleast RS 5000 The sales on the first 2 days were Rs 2000 and Rs3500 

 i) What percentage of his target did he achieve?on day 1 and day2 (1m) 

 ii) In the next two days i.e day 3 and day4 ,he made Rs 5000 and 6000 respectively what percentage of his target are these values? ( 1m) 

 iii) What is the short of his target on day1 (2m) 

 Or 

 iv)what percentage of the target was achieved on day 4?

30. Farmer’s field shapes – areas of quadrilaterals.

In a Village a farmer having the field in the form of following shapes the farmer son studied civil engineering .one day his father asked him to survey the areas of the fields the area of the following shapes will be ?

i)find the area of quadrilateral shape of field i) shown in figure? 1m 

 ii)what is the are a field ii) in figure? 1m 

 iii)what is the difference between area of fig iii) and iv) 2m 

 or

 iv)what is the area of fig iii) in meter square 

ANSWER KEY SAMPLE Paper 1 – Section A – All MCQs with Explanations

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Q1: The digital root of 63855 is
a) 6 b) 9 c) 3 d) 12
✅ Answer: b) 9
Explanation: Digital root = sum of digits until single digit:
6+3+8+5+5 = 27 → 2+7 = 9.

Q2: If a number is divisible by 4 and 8 it must be divisible by
a) 8 b) 12 c) 18 d) 24
✅ Answer: a) 8
Explanation: If divisible by 8, it’s automatically divisible by 4 (since 8 is multiple of 4), so LCM(4,8) = 8.

Q3: Distributive property of (a+b)² can be expressed as
a) (a+b) × (a+b) b) (a+b) × (a-b) c) a+b,a+b d) none
✅ Answer: a) (a+b) × (a+b)
Explanation: (a+b)² = (a+b)(a+b), which is distributive expansion.

Q4: Square of any odd number is always
a) even b) multiple of 4 c) one more than multiple of 8 d) multiple of 8
✅ Answer: c) one more than multiple of 8
Explanation: Odd number = 2n+1; square = 4n²+4n+1 = 4n(n+1)+1, and n(n+1) is even, so 4 × even + 1 = multiple of 8 + 1.

Q5: Which ratio is proportional to 96 and 144
a) 2:5 b) 2:3 c) 3:2 d) 3:3
✅ Answer: b) 2:3
Explanation: Simplify 96:144 = divide by 48 → 2:3.

Q6: If 72 litres of milk sufficient for 288 people, milk required for 450 people
a) 96 b) 108 c) 112.5 d) 120
✅ Answer: c) 112.5
Explanation: Milk per person = 72/288 = 0.25 litres. For 450 people: 0.25 × 450 = 112.5 litres.

Q7: 25% of 160 =
a) 80 b) 80 c) 40 d) 42
✅ Answer: c) 40
Explanation: 25% = 1/4, so (1/4) × 160 = 40.

Q8: Esha scored 42 marks out of 50, score as a percentage
a) 84% b) 90% c) 100% d) 52%
✅ Answer: a) 84%
Explanation: (42/50) × 100 = 84%.

Q9: Is √2 value less than or greater than 1
a) <1 b) >1 c) =1 d) none
✅ Answer: b) >1
Explanation: √2 ≈ 1.414 > 1.

Q10: If hypotenuse of an isosceles right triangle is √72, the other two sides
a) 6,6 b) 6,7 c) 8,9 d) 12,6
✅ Answer: a) 6,6
Explanation: In isosceles right triangle, hypotenuse = side × √2.
side × √2 = √72 = √(36×2) = 6√2 → side = 6.

Q11: Area of rhombus whose diagonals are 20 cm and 15 cm
a) 150 cm² b) 300 cm² c) 900 cm² d) 1500 cm²
✅ Answer: a) 150 cm²
Explanation: Area = ½ × d1 × d2 = ½ × 20 × 15 = 150 cm².

Q12: Area of each triangle in rectangle of length 7 cm and breadth 4 cm
a) 14 cm² b) 15 cm² c) 20 cm² d) none
✅ Answer: a) 14 cm²
Explanation: Rectangle area = 7×4 = 28 cm². Diagonal divides into two equal triangles: each area = 28/2 = 14 cm².

Q13: Area of parallelogram obtained by
a) base × height b) 1 × b c) 2(l+b) d) ½ × b × h
✅ Answer: a) base × height
Explanation: Standard formula: Area of parallelogram = base × corresponding height.

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Assertion-Reason Questions

Q14:
Assertion: (a+b)² − (a−b)² = 4a
Reason: On expansion, square terms cancel.
✅ Answer: (d) A is false but R is true
Explanation: LHS = a²+2ab+b² − (a²−2ab+b²) = 4ab, not 4a. So A false. R is true: squares cancel, but not completely correct as stated.

Q15:
Assertion: Area of trapezium = ½ × height × (sum of parallel sides)
Reason: Parallel sides 12 cm and 16 cm, height 5 cm ⇒ area = 70 cm².
✅ Answer: (b) Both A and R are true but R is not the correct explanation of A
Explanation: Formula is correct, example is correct, but the example does not explain why formula is true generally.

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Model Paper 1 – Section B & C – All Questions with Explanations

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Section B (5 × 2 marks)

Q16: Write 2 multiples of 36 between 45,000 and 47,000.
✅ Answer: 45,036 and 45,072 (or any multiples: divide 45,000 by 36 ≈ 1250, so 36×1251=45,036 and 36×1252=45,072).

Q17: Draw Venn diagram for multiples of 4, 5, and 32.
✅ Explanation:

• Multiples of 32 are subset of multiples of 4 (since 32 = 4×8).

• Multiples of 5 are separate, but LCM(4,5)=20 and LCM(32,5)=160 give overlaps.
  Draw three circles: “Multiples of 4” large, contains “Multiples of 32” inside, “Multiples of 5” overlaps both.

Q18: Expand (a+b)(a+b) OR (3+u)(v−3)
✅ Answer:

• (a+b)(a+b) = a² + 2ab + b²

• (3+u)(v−3) = 3v − 9 + uv − 3u = uv + 3v − 3u − 9.

Q19: Nandini has 25 marbles, 15 white. Percentage white?
✅ Answer: (15/25) × 100 = 60%.

Q20: Diagonal of square with side 5 cm.
✅ Answer: Diagonal = side × √2 = 5√2 cm ≈ 7.07 cm.

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Section C (5 × 3 marks)

Q21: Sum of four consecutive numbers is 34. Find them.
OR Digital root of an 8-digit number is 5. What will be digital root of number + 10?
✅ Answer:
Let numbers be n, n+1, n+2, n+3.
Sum = 4n+6 = 34 ⇒ 4n = 28 ⇒ n=7. Numbers: 7,8,9,10.
OR Digital root = sum of digits mod 9. If original digital root = 5, adding 10 increases sum of digits by 1+0=1, so new digital root = 6.

Q22: HCF of 72 and 96 OR Divide ₹4500 in ratio 2:3.
✅ Answer:
HCF: factors of 72=2³×3², 96=2⁵×3 ⇒ HCF=2³×3=24.
OR 2:3 ⇒ parts = (2/5)×4500 = 1800 and (3/5)×4500 = 2700.

Q23: Find value and draw bar models:
(i) 7% of 10 kg
(ii) 62% of 360
✅ Answer:
(i) 0.07 × 10 = 0.7 kg
(ii) 0.62 × 360 = 223.2
Bar model: For (i) 100% = 10 kg, 7% small bar.

Q24: Right triangle: short side 8 cm, hypotenuse 17 cm. Find third side.
✅ Answer: Using Pythagoras:
third side² = 17² − 8² = 289 − 64 = 225 ⇒ side = 15 cm.

Q25: Find area of quadrilateral ABCD: AC=22 cm, BM=3 cm, DN=3 cm, BM ⟂ AC, DN ⟂ AC.
✅ Answer: Quadrilateral ABCD is split into two triangles ABC and ADC with same base AC=22 cm, heights BM=3 and DN=3.
Area = ½ × AC × BM + ½ × AC × DN = ½×22×3 + ½×22×3 = 33 + 33 = 66 cm².

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Model Paper 1 – Section D & E – All Questions with Explanations

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Section D (Long Answer – 4 marks each)

Q26: Compute using suitable identities:
(i) 397 × 403 (ii) (2x − 1)²
✅ Answer:
(i) 397×403 = (400−3)(400+3) = 400² − 3² = 160000 − 9 = 159,991.
(ii) (2x − 1)² = (2x)² − 2(2x)(1) + 1 = 4x² − 4x + 1.

Q27: One acre = ₹15,00,000. Cost of 2,400 sq ft of same land?
✅ Answer: 1 acre = 43,560 sq ft.
Cost per sq ft = 15,00,000 / 43,560 ≈ ₹34.44.
For 2,400 sq ft: 34.44 × 2400 ≈ ₹82,656.

Q28: If (a,b,c) is Pythagorean triple, is (ka,kb,kc) also triple for positive integer k? Verify.
✅ Answer: Yes.
If a²+b²=c², then (ka)²+(kb)² = k²a²+k²b² = k²(a²+b²) = k²c² = (kc)².
Example: (3,4,5) ⇒ (6,8,10): 6²+8²=36+64=100=10².

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Section E (Case-Based – 4 marks each)

Q29: Gangaram book stall: daily target ₹5000.
Sales: Day1=₹2000, Day2=₹3500.
(i) Percentage of target on Day1 and Day2?
✅ Answer: Day1: (2000/5000)×100 = 40%. Day2: (3500/5000)×100 = 70%.

(ii) Day3=₹5000, Day4=₹6000, percentage of target?
✅ Answer: Day3: (5000/5000)×100 = 100%. Day4: (6000/5000)×100 = 120%.

(iii) Shortfall on Day1?
✅ Answer: Target ₹5000 − Sales ₹2000 = ₹3000 short.

(iv) Percentage achieved on Day4?
✅ Answer: Already in (ii): 120%.

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Q30: Farmer’s fields shapes:
(i) Area of quadrilateral shape in fig (i) – need diagram but usually trapezium.
(ii) Area of field (ii) – rectangle/triangle.
(iii) Difference between area of fig (iii) and (iv).
(iv) Area of fig (iii) in m².

• Quadrilateral area = divide into triangles.

• Rectangle area = l×b.

• Trapezium area = ½ × h × (a+b).

•