Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-11 WITH ANSWERS

 Class 8 SESSION ENDING EXAMINATION (2026)  SAMPLE PAPER-11 WITH ANSWERS

SAMPLE PAPER 11

SECTION A

1. What is the digital root of the number 489710?
   a) 1 b) 2 c) 9 d) 11

2. A number is divisible by 9 if and only if:
   A) Its units digit is 0 or 9 B) It is an even number C) The sum of its digits is divisible by 9 D) It is also divisible by 11

3. What is the correct expansion of the identity (a+m)(b+n)?
   a) ab + mn b) ab + mb + an + mn c) ab + an + m d) am + bn + ab

4. According to Brahmagupta, what is the term for "multiplication by parts" using the distributive property?
   a) Ista-gunana b) Khanda-gunanam c) Ganita Prakash d) Brahmashputasiddhanta

5. What is the simplest form of the ratio 60:40?
   a) 20:1 b) 3:2 c) 1.5:1 d) 6:4

6. Two ratios a:b and c:d are proportional (indicated by the '::' symbol) if and only if:
   a) a + d = b + c b) ad = bc c) a = c and b = d d) Their terms are even numbers

7. Which of the following is the decimal equivalent of 40%?
   a) 4.0 b) 0.04 c) 0.4 d) 0.44

8. The simplest form of 36/48 is:
   a) 6/8 b) ¾ c) 3.099 d) 3.909

9. Which of the following sets of numbers is a Baudhāyana-Pythagoras triple?
   a) (1, 2, 3) b) (5, 12, 13) c) (2, 3, 4) d) (7, 8, 10)

10. The number √2 has which of the following properties?
    a) It is a terminating decimal b) It can be expressed as a fraction m/n where m and n are positive integers
    c) It lies between 1.414 and 1.415 but cannot be a terminating decimal d) It is equal to 1.5

11. A parallelogram has a base of 10 cm and a corresponding height of 6 cm. What is its area?
    a) 16 cm² b) 32 cm² c) 60 cm² d) 30 cm²

12. The standard unit of area is:
    a) metre b) square metre c) centimetre d) kilogram

13. A rhombus has diagonals measuring 10 cm and 24 cm. What is the area of this rhombus?
    a) 240 cm² b) 120 cm² c) 68 cm² d) 34 cm²

Assertion-Reason:

14. Assertion: (x+3)(x+5) = x² + 8x + 15
    Reason: Each term of the first bracket is multiplied with each term of the second bracket.

15. Assertion: The fraction 15/20 is simply 3/4 in disguise.
    Reason: Equivalent fractions are formed by multiplying or dividing the numerator and the denominator of a given fraction by the same non-zero number.

SECTION B (2 marks each)

16. If a number is divisible by 12, explain why it must also be divisible by 3 and 4.

17. Calculate the digital root for the number 320185.

18. Using the distributive property, explain the step-by-step process for multiplying 94×11 in a single line.
    OR
    Show how the product ab changes when both a and b are increased by 1. Write the final expanded expression.

19. Express 50% of a quantity 8 as a multiplication of its unit fraction and simplify the result.
    OR
    In a school, 15 of the 80 students come to school by walking. What percentage of the students come by walking?

20. The length of the two equal sides of an isosceles right triangle is 3 cm. Find the length of the hypotenuse.

SECTION C (3 marks each)

21. The sum of four consecutive numbers is 34. What are these numbers?
    OR
    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.

22. A car travels 90 km in 150 minutes. Show the conversion of 4 hours into minutes. Calculate the final distance covered in 4 hours using the corrected proportion.
    OR
    For the mid-day meal in a school with 120 students, the cook usually makes 15 kg of rice. On a rainy day, only 80 students came to school. How many kilograms of rice should the cook make so that the food is not wasted?

23. Fill in the blanks:
    (i) 3 is ___ % of 300 (ii) ___ is 40% of 4 (iii) 40 is 80% of ___

24. In one corner of the garden, there is a triangular flower bed. Its base is 6 m and its corresponding height is 4 m. If the school decided to double the base of this triangle to 12 m, while keeping the height the same, how would the area change?
    OR
    Give a method to obtain a rectangle whose area is twice that of a given triangle. What are the different methods that you can think of?

25. A total of ₹4,500 needs to be divided into two parts in the ratio 2:3. Determine the exact value of each of the two parts.

SECTION D (4 marks each)

26. Kishanlal recently opened a garment shop. He aims to achieve a daily sales of at least ₹5000. The sales on the first 2 days were ₹2000 and ₹3500. What percentage of his target did he achieve?

27. Verify if the triple (8, 15, 17) satisfies the Baudhāyana-Pythagoras theorem. Show all your calculations for a², b², and c².
    OR
    Find the side length of a rhombus whose diagonals are of length 24 units and 70 units.

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

SECTION E (Case-Based - 4 marks each)

29. The School Library Project: The students of Class 8 found that the library has a total of 800 books. Upon categorization: (i) 40% of the books are Storybooks (ii) 1/4 of the total books are Science and Mathematics books (iii) The remaining books are Biography and General Knowledge.
    (a) How many Storybooks are there in the library?
    (b) Find the total number of Science and Mathematics books, and express this amount as a percentage of the total books in the library.
    (c) If 20% of the Biography and General Knowledge books are donated to a local primary school, how many books 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 1 m?
    (c) How much area increased?

SAMPLE Paper 11 – Complete Solutions with Explanations

(Assuming the next paper in sequence is Paper 11, though it may be labeled differently in the PDF. I’ll proceed with the remaining content.)

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Section A – MCQs with Explanations

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Q1: Digital root of 489710?
a) 1 b) 2 c) 9 d) 11
✅ Answer: c) 9
Explanation: 4+8+9+7+1+0=29 → 2+9=11 → 1+1=2. Wait, recalc:
Sum=4+8=12, +9=21, +7=28, +1=29, +0=29 → 2+9=11 → 1+1=2. So digital root=2.
But option b) is 2, c) is 9.
Check: 489710 ÷ 9 remainder? Sum=29, 29÷9=3 remainder 2 → digital root=2. ✅ Answer: b) 2.

Q2: Number divisible by 9 if and only if:
A) Units digit 0 or 9 B) Even number C) Sum of digits divisible by 9 D) Divisible by 11
✅ Answer: C) Sum of digits divisible by 9.

Q3: Expand (a+m)(b+n):
a) ab+mn b) ab+mb+an+mn c) ab+an+m d) am+bn+ab
✅ Answer: b) ab+mb+an+mn

Q4: “Multiplication by parts” using distributive property is called in Brahmagupta’s work:
a) Ista-gunana b) Khanda-gunanam c) Ganita Prakash d) Brahmashputasiddhanta
✅ Answer: b) Khanda-gunanam.

Q5: Simplest form of 60:40:
a) 20:1 b) 3:2 c) 1.5:1 d) 6:4
✅ Answer: b) 3:2
Explanation: Divide by 20 → 3:2.

Q6: Two ratios a:b and c:d proportional (::) if:
a) a+d=b+c b) ad=bc c) a=c and b=d d) Terms are even
✅ Answer: b) ad=bc

Q7: Decimal equivalent of 40%:
a) 4.0 b) 0.04 c) 0.4 d) 0.44
✅ Answer: c) 0.4

Q8: Simplest form of 36/48:
a) 6/8 b) ¾ c) 3.099 d) 3.909
✅ Answer: b) ¾

Q9: Pythagorean triple:
a) (1,2,3) b) (5,12,13) c) (2,3,4) d) (7,8,10)
✅ Answer: b) (5,12,13)

Q10: √2 has property:
a) Terminating decimal b) Expressible as m/n with m,n positive integers c) Between 1.414 and 1.415, non-terminating d) Equal to 1.5
✅ Answer: c)

Q11: Parallelogram base 10 cm, height 6 cm → area:
a) 16 cm² b) 32 cm² c) 60 cm² d) 30 cm²
✅ Answer: c) 60 cm²
Explanation: 10×6=60.

Q12: Standard unit of area:
a) metre b) square metre c) centimetre d) kilogram
✅ Answer: b) square metre

Q13: Rhombus diagonals 10 cm and 24 cm → area:
a) 240 cm² b) 120 cm² c) 68 cm² d) 34 cm²
✅ Answer: b) 120 cm²
Explanation: ½×10×24=120.

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Assertion-Reason

Q14:
A: (x+3)(x+5)=x²+8x+15
R: Each term of first bracket multiplied with each term of second.
✅ Answer: (a) Both true, R explains A

Q15:
A: 15/20 = ¾
R: Equivalent fractions from multiplying/dividing numerator and denominator by same nonzero number.
✅ Answer: (a) Both true, R explains A
Explanation: 15/20 ÷ 5/5 = ¾.

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Section B – Short Answers (2 marks)

Q16: If a number divisible by 12, why must it be divisible by 3 and 4?
✅ Explanation: 12=3×4, and 3 and 4 are coprime → divisibility by 12 implies by both 3 and 4.

Q17: Digital root of 320185:
Sum=3+2+0+1+8+5=19 → 1+9=10 → 1+0=1.

Q18: Using distributive property: 94×11 = 94×(10+1)=940+94=1034.
OR ab when a,b increased by 1: (a+1)(b+1)=ab+a+b+1.

Q19: 50% of 8 = 0.5×8=4.
OR 15 of 80 students walk → %=(15/80)×100=18.75%.

Q20: Isosceles right triangle equal sides=3 cm → hypotenuse=3√2 cm.

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Section C – Short Answers (3 marks)

Q21: Sum of four consecutive numbers=34 → numbers=7,8,9,10.
OR 31z5 divisible by 9 → sum=3+1+z+5=9+z divisible by 9 → z=0 or 9 → two answers possible.

Q22: Car travels 90 km in 150 min → speed=90/150=0.6 km/min. In 4h=240 min → distance=0.6×240=144 km.
OR Midday meal: 120 students→15 kg rice, 80 students→ (15/120)×80=10 kg.

Q23: Fill blanks:
(i) 3 is 1% of 300.
(ii) 1.6 is 40% of 4.
(iii) 40 is 80% of 50.

Q24: Triangle base 6 m, height 4 m → area=12 m². If base doubled to 12 m, height same → area=24 m² (doubles).
OR Rectangle with area twice triangle: Use triangle as half of rectangle with same base and height → double triangle area = base×height rectangle.

Q25: ₹4500 divided in ratio 2:3 → parts = (2/5)×4500=1800 and (3/5)×4500=2700.

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Section D – Long Answers (4 marks)

Q26: Kishanlal target ₹5000/day. Day1=₹2000 (40%), Day2=₹3500 (70%).
Achieved 40% and 70%.

Q27: Verify (8,15,17) Pythagorean: 8²+15²=64+225=289=17² ✔.
OR Side of rhombus diagonals 24 and 70 → side=√(12²+35²)=37 units.

Q28: Area of shaded region in rectangle → need diagram.

Section E – Case-Based Questions (4 marks each)

Q29. The School Library Project

Context:
Total books = 800

• 40% are Storybooks.

• 1/4 are Science and Mathematics books.

• The rest are Biography and General Knowledge.

Questions:

(a) How many Storybooks?
✅ Answer:
40% of 800 = $0.40\times 800=320$
So, 320 Storybooks.

(b) Total number of Science and Mathematics books, and as a percentage of total.
✅ Answer:
1/4 of 800 = $\frac{1}{4}\times 800=200$ books.
Percentage = $\frac{200}{800}\times 100=25\mathrm{\%}$.

(c) If 20% of Biography and General Knowledge books are donated, how many books are donated?
✅ Answer:
Remaining books = 800 − (320 + 200) = 280 (Biography + GK).
20% of 280 = $0.20\times 280=56$ books donated.

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Q30. Rectangular Garden Dimensions

Context:
Original garden:

• Length = $x+8$ meters

• Breadth = $x-2$ meters
  Both length and breadth increased by 1 meter.

Questions:

(a) Area of original garden:
✅ Answer:

$$\text{Area}=(x+8)(x-2)=x^2+6x-16{\text{m}}^2$$

(b) Area after increasing both dimensions by 1 m:
✅ Answer:
New length = $x+9$
New breadth = $x-1$

$$\text{New area}=(x+9)(x-1)=x^2+8x-9{\text{m}}^2$$

(c) Increase in area:
✅ Answer:

$$\text{Increase}=(x^2+8x-9)-(x^2+6x-16)=2x+7{\text{m}}^2$$