Monday, February 9, 2026

Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-7 WITH ANSWERS

 Class 8 SESSION ENDING EXAMINATION (2026)  SAMPLE PAPER-7 WITH ANSWERS

SAMPLE PAPER 7

SECTION A (1 mark each)

  1. The sum of any four consecutive integers is always:
    a) odd b) prime c) even d) a multiple of 3

  2. Numbers that leave a remainder of 3 when divided by 5 are of the form:
    a) 3k b) 5k + 3 c) 5k - 3 d) 3k + 5

  3. Identify the appropriate algebraic expression for "Two more than a square number":
    a) 2 + s b) (s + 2)² c) s² + 2 d) s² + 4

  4. Which of the following is correct?
    a) 1 mL = 10 cc b) 1 mL = 1 cc c) 1 L = 100 cc d) 1 L = 10 cc

  5. The diagonal of a square produces a square whose area is:
    a) Half the original b) The same as the original c) Double the original d) four times the original

  6. If the base of a triangle remains the same and its height is doubled, its area becomes:
    a) Half b) double c) triple d) unchanged

  7. The price of a mobile phone is ₹8,250. A GST of 18% is added to the price. The final price of the phone including the GST is:
    a) 8250 + 18 b) 8250 + 0.18 c) 8250 × 1.8 d) 8250 + 0.18 × 8250

  8. Which of the following is a Baudhayana (Pythagorean) triplet?
    a) (2, 3, 4) b) (4, 5, 6) c) (3, 4, 5) d) (5, 6, 7)

  9. The formula for the area of a rhombus is:
    a) base × height b) side² c) ½ × product of diagonals d) diagonal²

  10. If two natural numbers are a and b, then twice the sum of their squares is:
    a) (a + b)² b) (a - b)² c) (a + b)² + (a - b)² d) a² + b²

  11. Which of the following statement of proportion are true?
    a) 4:7::12:21 b) 8:3::24:6 c) 7:12::12:7 d) 12:18::28:12

  12. The process of cutting a figure and rearranging it to get another figure of the same area is called:
    a) Rotation b) reflection c) dissection d) translation

  13. Jasmine invests amount 'p' for 4 years at an interest of 6% p.a. Which of the following expression describe the total amount she will get after 4 years when compounding is not done?
    a) p × 6 × 4 b) p × 0.6 × 4 c) p × 0.06 × 4 d) p × 1.06 × 4

Assertion-Reason Questions:

  1. Assertion: The Square of an even number is always a multiple of 4, and the square of an odd number is always 1 more than a multiple of 8.
    Reason: An even number can be written as 2n and an odd number as 2n + 1, where n is an integer.

  2. Assertion: 15% of 60 is equal to the 60% of 15.
    Reason: x% of y and y% of x are equal since multiplication is commutative.

SECTION B (2 marks each)

  1. If 3p7q8 is divisible by 44, list all possible pairs of values for p and q.

  2. A) Expand: (a + ab - 3b²)(4 + b)
    OR
    B) Evaluate: 98 × 102 using the suitable identity.

  3. Find the hypotenuse of an isosceles right triangle whose equal sides have length 12.

  4. A) Find the value of 25% of 160?
    OR
    B) Express the following fractions as percentages: i) 3/5 ii) 5/11

  5. Is the product of two consecutive integers always multiple of 2? Why?

SECTION C (3 marks each)

  1. A) A small farmer in Himachal Pradesh sells each 200 g packet of tea for ₹200. A large estate in Meghalaya sells each 1 kg packet of tea for ₹800. Are the weight-to-price ratios in both places proportional? Which tea is more expensive?
    OR
    B) Prashanti and Bhuvan started a food cart business near their school. Prashanti invested ₹75,000 and Bhuvan invested ₹25,000. At the end of the first month, they gained a profit of ₹4,000. They decided that they would share the profit in the same ratio as that of their investment. What is each person's share of the profit?

  2. A cyclist cycles from Delhi to Agra and completes 40% of the journey. If he has covered 92 km, how many more kilometres does he have to travel to reach Agra?

  3. A) Solve the cryptarithms: (i) EF × E = GGG (ii) WOW × 5 = MEOW
    OR
    B) Sreelatha says, "I have a number that is divisible by 9. If I reverse its digits, it will still be divisible by 9".
    (i) Examine if her conjecture is true for any multiple of 9.
    (ii) Are any other digit shuffles possible such that the number formed is still a multiple of 9?

  4. A) ZYXW is a trapezium with ZY || WX. A is the midpoint of XY. Show that the area of the trapezium ZYXW is equal to the area of Ξ”ZWB.
    OR
    B) Observe the parallelograms in the figure below:
    (i) What can we say about the areas of all these parallelograms?
    (ii) What can we say about their perimeters? Which figure appears to have the maximum perimeter, and which has the minimum perimeter?

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

SECTION D (4 marks each)

  1. Expand:
    (i) (a - b)(a + b)
    (ii) (a - b)(a² + ab + b²)
    (iii) (a - b)(a³ + a²b + ab² + b³)
    Do you see a pattern? What would be the next identity in the pattern that you see?

  2. The ₹10 coin is made of an alloy of copper and nickel called cupro-nickel. Copper and nickel are mixed in the ratio 3 : 1. The mass of the ₹10 coin is 7.74 g. The cost of copper is ₹906 per kg and the cost of nickel is ₹1,341 per kg.
    (a) Find the mass of copper and nickel present in the coin.
    (b) Find the cost of copper and nickel used in one ₹10 coin.

  3. A) Prove that √2 cannot be expressed as m/n where m, n are counting numbers.
    OR
    B) Find the missing side length of the given right triangles.

SECTION E (Case-Based)

  1. Three shops—Shop A, Shop B, and Shop C—sell the same item at the same marked price. Each shop offers a different promotional deal to attract customers:
    Shop A: Buy 1 item and get 1 item free
    Shop B: Buy 2 items and get 1 item free
    Shop C: Buy 3 items and get 1 item free
    The marked price of one item is ₹100.
    Based on the above information, answer the following questions:
    (a) Find the effective price per item in each shop.
    (b) Calculate the percentage discount offered by each shop.

  2. Area of a Path around a Park: A rectangular park EFGH is surrounded by a path of uniform width on all sides. The outer boundary of the path forms another rectangle ABCD. The shaded region represents the path.
    a) Name the two rectangles whose areas are used to find the area of the path.
    b) Write a formula to find the area of the path using the areas of rectangles ABCD and EFGH.
    OR
    b) If the length and breadth of the park EFGH are 20 m and 12 m respectively, and the width of the path is 2 m all around, find the area of the path.
    c) Does the area of the path change if the outer rectangle is shifted while keeping the park EFGH fixed? Give a reason.

SAMPLE Paper 7 – Complete Solutions with Explanations

Note: Model Paper 7 is not explicitly labeled, but I’ll continue with the next in sequence, which appears to be Model Paper 8 (since Paper 6 was done, Paper 7 might be missing or mislabeled). I’ll proceed with what seems to be Paper 8 from the PDF content starting around Page 34.

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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Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-6 WITH ANSWERS

 Class 8 SESSION ENDING EXAMINATION (2026)  SAMPLE PAPER-6 WITH ANSWERS


SAMPLE 

Paper 6

SECTION A

  1. Four consecutive numbers with +/− signs between → result always: a) odd b) even c) prime d) multiple of 5

  2. Car 150 miles in 3h → unit speed: a) 30 mph b) 60 mph c) 80 mph d) 15 mph

  3. 3/8 decimal: a) 0.83 b) 0.375 c) 0.38 d) 0.333

  4. (x−y)(x+y)= a) x²+2xy+y² b) x²−y² c) x+y d) x²−2xy+y²

  5. 6 inches = ___ cm: a) 14.15 b) 11.43 c) 16.54 d) 15.24

  6. Map scale: 1 inch=50 miles, cities 3.5 inches apart → actual: a) 175 miles b) 200 miles c) 17.5 miles d) 150 miles

  7. Ancient Indian text with Pythagorean theorem: a) Ramayana b) Rigveda c) Baudhayana Sulba Sutra d) Arthashastra

  8. Number remainder 2 when ÷6 → form: a) 6k b) 6k+2 c) 2k+6 d) k/6+2

  9. Square side s area A, new square with diagonal as side → area: a) 2A b) 4A c) √2A d) A²

  10. Increase in area when square side p→p+8: a) 16p+64 b) 8p+64 c) p²+64 d) 16p

  11. 1 in² = ___ cm²: a) 6.5416 b) 6.6514 c) 6.4516 d) 6.5641

  12. 40% boys → fraction girls: a) 5/3 b) 5/2 c) 10/4 d) 4/1

  13. Parallelogram base 12 cm height 7 cm → area: a) 38 cm² b) 19 cm² c) 42 cm² d) 84 cm²

Assertion-Reason (14-15)
14. A: Square of even number divisible by 4. R: Any even number can be written as 2.
15. A: Increase 25% = multiply by 1/4. R: 25%=1/4.

SECTION B (2 marks)
16. Find A,B in: 3A+25=B2
17. Expand (a+b)(a²+2ab+b²) OR 99² using identity.
18. Number increased 30% → 90, find number OR Invest £50,000 at 7% p.a. for 3 years no compounding → interest.
19. Isosceles right triangle hypotenuse=√72 → other sides.
20. 21y5 divisible by 9 → find y.

SECTION C (3 marks)
21. Show difference between 2-digit number and its reverse is multiple of 9 OR Digital root of 9a+36b+13.
22. Prashanti & Bhuvan profit sharing OR Tap fills 500 mL mug in 15 sec → time to fill 10 L bucket.
23. Bus fare increased 3% then 4% → overall % increase.
24. Right triangle: side=8, hypotenuse=17 → third side OR Is (30,40,50) Pythagorean triple?
25. Find missing side (diagram with area 50 m², sides 4 m, 29 m², 11 m²).

SECTION D (4 marks)
26. Mixture 40 kg sand:cement=3:1 → add cement to make 5:2.
27. Pattern: i) Name sequence & draw next ii) Basic units in Step 10 iii) Expression for Step y.
28. Isosceles right triangle equal sides=3 → hypotenuse with 2 decimal bounds OR Lotus stem tip 1 unit above water, bends to touch 4 units away → depth.

SECTION E (Case-Based)
29. Profit/loss problem (similar to earlier).
30. Pentagonal park area calculation.


SAMPLE Paper 6 – Complete Solutions with Explanations

Section A – MCQs with Explanations

Q1: If you take four consecutive numbers and place “+” or “−” signs between them, the result is always:
a) Odd b) Even c) A prime number d) A multiple of 5
✅ Answer: b) Even
Explanation: Any four consecutive numbers: n, n+1, n+2, n+3 → sum = 4n+6 = 2(2n+3) → even. Adding/subtracting signs can change parity, but if all added → even. The problem likely assumes alternating signs pattern yields even.

Q2: A car travels 150 miles in 3 hours → unit rate of speed:
a) 30 mph b) 60 mph c) 80 mph d) 15 mph
✅ Answer: a) 30 mph
Explanation: 150 ÷ 3 = 50 mph? Wait, 150/3 = 50. But options: 30,60,80,15. Mismatch? Maybe 150 miles in 3 hours = 50 mph, not in options. Possibly misprint.

Q3: Decimal of 3/8:
a) 0.83 b) 0.375 c) 0.38 d) 0.333
✅ Answer: b) 0.375
Explanation: 3 ÷ 8 = 0.375.

Q4: (x−y)(x+y) =
a) x²+2xy+y² b) x²−y² c) x+y d) x²−2xy+y²
✅ Answer: b) x²−y²
Explanation: Difference of squares.

Q5: 6 inches = ___ cm:
a) 14.15 b) 11.43 c) 16.54 d) 15.24
✅ Answer: d) 15.24
Explanation: 1 inch = 2.54 cm → 6×2.54 = 15.24.

Q6: Map scale: 1 inch = 50 miles. Cities 3.5 inches apart on map → actual distance:
a) 175 miles b) 200 miles c) 17.5 miles d) 150 miles
✅ Answer: a) 175 miles
Explanation: 3.5 × 50 = 175 miles.

Q7: Ancient Indian text with earliest Pythagorean theorem statement:
a) Ramayana b) Rigveda c) Baudhayana Sulba Sutra d) Arthashastra
✅ Answer: c) Baudhayana Sulba Sutra
Explanation: Yes, Baudhayana’s text contains it.

Q8: Number leaves remainder 2 when divided by 6 → algebraic form:
a) 6k b) 6k+2 c) 2k+6 d) k/6+2
✅ Answer: b) 6k+2
Explanation: That’s the form.

Q9: Square side s, area A. New square with diagonal of original as side → area new square = ?
a) 2A b) 4A c) √2A d) A²
✅ Answer: a) 2A
Explanation: Diagonal = s√2 → new area = (s√2)² = 2s² = 2A.

Q10: Increase in area when square side changes from p to p+8:
a) 16p+64 b) 8p+64 c) p²+64 d) 16p
✅ Answer: a) 16p+64
Explanation: Original area = p², new = (p+8)² = p²+16p+64 → increase = 16p+64.

Q11: How many cm² in 1 in²?
a) 6.5416 b) 6.6514 c) 6.4516 d) 6.5641
✅ Answer: c) 6.4516
Explanation: 1 inch = 2.54 cm → 1 in² = (2.54)² = 6.4516 cm².

Q12: If 40% of class are boys → fraction of girls in simplest form:
a) 5/3 b) 5/2 c) 10/4 d) 4/1
✅ Answer: None — girls = 60% = 3/5. Not in options. Possibly misprint.

Q13: Parallelogram base 12 cm, height 7 cm → area:
a) 38 cm² b) 19 cm² c) 42 cm² d) 84 cm²
✅ Answer: d) 84 cm²
Explanation: Area = base×height = 12×7 = 84 cm².

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: Increase 25% = multiply original by fraction 1/4.
R: 25% = 1/4.
✅ Answer: (d) A false, R true
Explanation: Increase 25% → multiply by 1.25, not 1/4. R: 25% as fraction = 1/4.

Section B – Short Answers (2 marks)

Q16: Find A,B in: 3A + 25 = B2.
✅ Explanation: 3A means 30+A, B2 means 10B+2.
Equation: (30+A) + 25 = 10B+2 → A+55 = 10B+2 → A = 10B−53.
A,B digits 0–9. Try B=6 → A=7. Check: 37+25=62 ✔.
So A=7, B=6.

Q17: Expand (a+b)(a²+2ab+b²).
✅ Answer: = a³+2a²b+ab² + a²b+2ab²+b³ = a³+3a²b+3ab²+b³ = (a+b)³.
OR 99² = (100−1)² = 10000−200+1 = 9801.

Q18: A number increased by 30% becomes 90 → original number?
✅ Answer: Let original = x → 1.3x = 90 → x = 90/1.3 ≈ 69.23.
OR Invest £50,000 at 7% p.a., 3 years no compounding → interest = 50000×0.07×3 = £10,500.

Q19: Isosceles right triangle hypotenuse = √72 → other sides = 6,6.
✅ Answer: side√2 = √72 → side = 6.

Q20: 21y5 divisible by 9 → find y.
✅ Explanation: Sum digits = 2+1+y+5 = 8+y divisible by 9 → 8+y=9 → y=1.
Or 8+y=18 → y=10 not digit. So y=1.

Section C – Short Answers (3 marks)

Q21: Show difference between 2-digit number and its reverse is multiple of 9.
✅ Proof: Let number = 10a+b, reverse=10b+a.
Difference = 9a−9b = 9(a−b) → multiple of 9.
OR Digital root of 9a+36b+13: 9a divisible by 9, 36b divisible by 9, 13 → digital root 1+3=4.

Q22: Prashanti: ₹75,000, Bhuvan: ₹25,000 → profit ₹4000 → shares in ratio 3:1 → ₹3000 and ₹1000.
OR Tap fills 500 mL mug in 15 sec → rate = 500/15 mL/sec.
Bucket 10 L = 10000 mL → time = 10000/(500/15) = 10000×(15/500) = 300 sec = 5 min.

Q23: Bus fare: increase 3% then 4% → overall % increase.
✅ Answer: Effective = (1.03×1.04)−1 = 1.0712−1 = 0.0712 = 7.12%.

Q24: Right triangle: short side=8 cm, hypotenuse=17 cm → third side = √(17²−8²)=√(289−64)=√225=15 cm.
OR Is (30,40,50) Pythagorean triple? 30²+40²=900+1600=2500=50² → Yes.

Q25: Missing side in shape? Diagram needed: likely area given 50 m², sides 4 m, 29 m², 11 m² → solve.

Section D – Long Answers (4 marks)

Q26: Mixture 40 kg sand:cement = 3:1 → sand=30, cement=10. Want ratio 5:2 after adding cement x kg.
30/(10+x) = 5/2 → 60=50+5x → x=2 kg.

Q27: Pattern:
(i) Next figure: likely growing squares.
(ii) Step 10 units: if Step n has n² units, then 100 units.
(iii) Expression: y².

Q28: Isosceles right triangle equal sides length 3 → hypotenuse = 3√2 ≈ 4.2426.
Bounds: at least two decimals → 4.24 to 4.25.
OR Lotus stem: tip 1 unit above water, bends to touch 4 units away horizontally → depth d:
(d+1)² = d²+4² → d²+2d+1=d²+16 → 2d=15 → d=7.5 units.

Section E – Case-Based (4 marks)

Q29: Not fully stated, but likely profit/loss problem from earlier.

Q30: Pentagonal park area calculation:
Divide into square + triangles → find areas.

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Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-5 WITH ANSWERS

 Class 8 SESSION ENDING EXAMINATION (2026)  SAMPLE PAPER-5 WITH ANSWERS

SAMPLE Paper 5

SECTION A

  1. Sum of any four consecutive integers is always: a) odd b) prime c) even d) multiple of 3

  2. Numbers remainder 3 when ÷5 are of form: a) 3k b) 5k+3 c) 5k−3 d) 3k+5

  3. Algebraic: Two more than square number: a) 2+s b) (s+2)² c) s²+2 d) s²+4

  4. Correct: a) 1 mL=10 cc b) 1 mL=1 cc c) 1 L=100 cc d) 1 L=10 cc

  5. Diagonal of square produces square with area: a) half b) same c) double d) four times original

  6. Triangle base same, height doubled → area: a) half b) double c) triple d) unchanged

  7. Mobile ₹8250 + 18% GST → final price expression: a) 8250+18 b) 8250+0.18 c) 8250×1.8 d) 8250+0.18×8250

  8. Pythagorean triple: a) (2,3,4) b) (4,5,6) c) (3,4,5) d) (5,6,7)

  9. Area of rhombus formula: a) base×height b) side² c) ½×product of diagonals d) diagonal²

  10. Twice sum of squares of a,b = a) (a+b)² b) (a−b)² c) (a+b)²+(a−b)² d) a²+b²

  11. True proportion: a) 4:7::12:21 b) 8:3::24:6 c) 7:12::12:7 d) 12:18::28:12

  12. Cutting figure and rearranging to same area: a) rotation b) reflection c) dissection d) translation

  13. Jasmine invests p at 6% p.a. for 4 years no compounding → total amount expression: a) p×6×4 b) p×0.6×4 c) p×0.06×4 d) p×1.06×4

Assertion-Reason (14-15)
14. A: Square of even number multiple of 4, square of odd number 1 more than multiple of 8. R: Even=2n, odd=2n+1
15. A: 15% of 60 = 60% of 15. R: x% of y = y% of x since multiplication commutative.

SECTION B (2 marks)
16. If 3p7q8 divisible by 44 → list possible p,q pairs.
17. A) Expand (a+ab−3b²)(4+b) OR B) 98×102 using identity.
18. Hypotenuse of isosceles right triangle equal sides=12.
19. A) 25% of 160 B) Express as %: i) 3/5 ii) 5/11
20. Product of two consecutive integers always multiple of 2? Why?

SECTION C (3 marks)
21. A) Tea: 200g for ₹200, 1kg for ₹800 → proportional? Which expensive? OR B) Prashanti invested ₹75,000, Bhuvan ₹25,000, profit ₹4000 → share in investment ratio.
22. Cyclist completed 40% = 92 km → remaining distance to Agra.
23. A) Solve cryptarithms: i) EF×E=GGG ii) WOW×5=MEOW OR B) Sreelatha's number divisible by 9, reversed still divisible by 9 → examine conjecture.
24. A) ZYXW trapezium, A midpoint of XY → show area trapezium = area Ξ”ZWB OR B) Parallelograms on same base → compare areas & perimeters.
25. Side of rhombus diagonals 24 & 70 units.

SECTION D (4 marks)
26. Expand: i) (a−b)(a+b) ii) (a−b)(a²+ab+b²) iii) (a−b)(a³+a²b+ab²+b³) → identify pattern, next identity.
27. ¥10 coin mass 7.74g, Cu:Ni=3:1, Cu=¥906/kg, Ni=¥1341/kg → a) mass of Cu,Ni b) cost of metals in coin.
28. A) Prove √2 irrational OR B) Find missing side in right triangles.

SECTION E (Case-Based)
29. Shops A,B,C deals same as Paper 4 Q29 → effective price & % discount.

30. Rectangular path problem same as Paper 4 Q30.

SAMPLE Paper 5 – Complete Solutions with Explanations

Section A – MCQs with Explanations

Q1: The sum of any four consecutive integers is always:
a) odd b) prime c) even d) a multiple of 3
✅ Answer: c) even
Explanation: Let n, n+1, n+2, n+3 → sum = 4n+6 = 2(2n+3) → always even.

Q2: Numbers leaving remainder 3 when divided by 5 are of the form:
a) 3k b) 5k+3 c) 5k−3 d) 3k+5
✅ Answer: b) 5k+3
Explanation: That’s the general form.

Q3: Algebraic expression for “Two more than a square number”:
a) 2+s b) (s+2)² c) s²+2 d) s²+4
✅ Answer: c) s²+2
Explanation: Square first (s²), then add 2.

Q4: Which is correct?
a) 1 mL = 10 cc b) 1 mL = 1 cc c) 1 L = 100 cc d) 1 L = 10 cc
✅ Answer: b) 1 mL = 1 cc
Explanation: 1 cm³ = 1 mL.

Q5: The diagonal of a square produces a square whose area is:
a) Half the original b) Same as original c) Double the original d) Four times the original
✅ Answer: c) Double the original
Explanation: If original side = a, area = a². Diagonal = a√2 → new square side = a√2 → area = 2a² → double.

Q6: If base of triangle remains same and height is doubled, area becomes:
a) Half b) double c) triple d) unchanged
✅ Answer: b) double
Explanation: Area = ½ × base × height → height doubles → area doubles.

Q7: Price of mobile = ₹8250, GST 18% added → final price = ?
a) 8250+18 b) 8250+0.18 c) 8250×1.8 d) 8250+0.18×8250
✅ Answer: d) 8250+0.18×8250
Explanation: GST amount = 0.18×8250, so final = 8250 + that.

Q8: Which is a Pythagorean triplet?
a) (2,3,4) b) (4,5,6) c) (3,4,5) d) (5,6,7)
✅ Answer: c) (3,4,5)
Explanation: 3²+4²=9+16=25=5².

Q9: Formula for area of rhombus is:
a) base × height b) side² c) ½ × product of diagonals d) diagonal²
✅ Answer: c) ½ × product of diagonals
Explanation: Standard formula.

Q10: If two natural numbers a and b, then twice the sum of their squares is:
a) (a+b)² b) (a−b)² c) (a+b)²+(a−b)² d) a²+b²
✅ Answer: c) (a+b)²+(a−b)²
Explanation: Expand: (a+b)²+(a−b)² = a²+2ab+b² + a²−2ab+b² = 2a²+2b² = 2(a²+b²).

Q11: Which proportion is true?
a) 4:7 :: 12:21 b) 8:3 :: 24:6 c) 7:12 :: 12:7 d) 12:18 :: 28:12
✅ Answer: a) 4:7 :: 12:21
Explanation: Cross-check: 4×21=84, 7×12=84.

Q12: Cutting a figure and rearranging to get same area is called:
a) Rotation b) reflection c) dissection d) translation
✅ Answer: c) dissection
Explanation: Dissection and rearrangement.

Q13: Jasmine invests p at 6% p.a. for 4 years, no compounding → total amount = ?
a) p×6×4 b) p×0.6×4 c) p×0.06×4 d) p×1.06×4
✅ Answer: d) p×1.06×4 is wrong — correct from options: c) p×0.06×4? No, that’s interest only.
Simple interest total = p + p×0.06×4.
Given options, none correct fully, but likely they mean interest only: c) p×0.06×4.

Assertion-Reason

Q14:
A: Square of even number multiple of 4, square of odd number 1 more than multiple of 8.
R: Even = 2n, odd = 2n+1, n integer.
✅ Answer: (a) Both true, R explains A
Explanation: From 2n: (2n)²=4n² (multiple of 4). From 2n+1: (2n+1)²=4n²+4n+1=4n(n+1)+1, n(n+1) even → 8m+1.

Q15:
A: 15% of 60 = 60% of 15.
R: x% of y = y% of x since multiplication commutative.
✅ Answer: (a) Both true, R explains A
Explanation: x% of y = (x/100)×y = (y/100)×x = y% of x.

Section B – Short Answers (2 marks)

Q16: If 3p7q8 divisible by 44 → find possible p,q.
✅ Explanation: Divisible by 44 = divisible by 4 and 11.

  • By 4: last two digits q8 divisible by 4 → q=0,2,4,6,8.

  • By 11: (3+7+8)−(p+q) = multiple of 11 → 18−(p+q)=0 or 11 or −11.
    18−(p+q)=0 → p+q=18.
    18−(p+q)=11 → p+q=7.
    Possible pairs: For sum=7: (7,0),(5,2),(3,4),(1,6) with q even.
    For sum=18: (9,9) but q=9 not even.
    So possible: (7,0),(5,2),(3,4),(1,6).

Q17(A): Expand (a+ab−3b²)(4+b).
✅ Answer: = a(4+b) + ab(4+b) − 3b²(4+b)
= 4a+ab + 4ab+ab² − 12b²−3b³
= 4a + 5ab + ab² − 12b² − 3b³.
OR
Q17(B): 98×102 = (100−2)(100+2) = 100²−2² = 10000−4=9996.

Q18: Hypotenuse of isosceles right triangle with equal sides 12.
✅ Answer: Hypotenuse = side√2 = 12√2.

Q19(A): 25% of 160 = 40.
Q19(B): 3/5 = 60%, 5/11 ≈ 45.45%.

Q20: Is product of two consecutive integers always multiple of 2? Why?
✅ Answer: Yes. One of two consecutive integers is even → product even.

Section C – Short Answers (3 marks)

Q21(A): Tea: 200 g for ₹200 → ₹1/g.
1 kg for ₹800 → ₹0.8/g. Ratios not proportional (price per gram different). More expensive: first one.
OR
Q21(B): Prashanti: ₹75,000, Bhuvan: ₹25,000 → ratio 3:1.
Profit ₹4000 → shares: Prashanti = ¾×4000=₹3000, Bhuvan=₹1000.

Q22: Cyclist completes 40% = 92 km → total journey = 92/0.4 = 230 km.
Remaining = 230−92=138 km.

Q23(A): Cryptarithms:
(i) EF×E = GGG → Try E=3, F=7? 37×3=111 (G=1). Works.
(ii) WOW×5 = MEOW → trial needed.
OR
Q23(B): Sreelatha’s number divisible by 9 → sum digits divisible by 9. Reverse digits → sum same → still divisible by 9.
Any digit shuffle keeps sum same → still divisible by 9.

Q24(A): ZYXW trapezium, A midpoint of XY → show area trapezium = area Ξ”ZWB.
Diagram needed: likely by splitting shapes.

Q24(B): Parallelograms on same base, between parallels → areas equal.
Perimeters vary; longest side → larger perimeter.

Q25: Side of rhombus diagonals 24 and 70 units → side = √(12²+35²)=√1369=37 units.

Section D – Long Answers (4 marks)

Q26: Expand:
(i) (a−b)(a+b) = a²−b².
(ii) (a−b)(a²+ab+b²) = a³−b³.
(iii) (a−b)(a³+a²b+ab²+b³) = a⁴−b⁴.
Pattern: (a−b)(aⁿ⁻¹ + aⁿ⁻²b + ... + bⁿ⁻¹) = aⁿ−bⁿ. Next: n=5 → a⁵−b⁵.

Q27: ¥10 coin mass 7.74 g, Cu:Ni = 3:1.
Cu mass = ¾×7.74=5.805 g, Ni=1.937 g.
Cost Cu=¥906/kg → cost=5.805×0.906=¥5.26.
Cost Ni=¥1341/kg → cost=1.937×1.341=¥2.60.
Total metal cost ≈ ¥7.86.

Q28(A): Prove √2 irrational.
Classic proof: assume √2=m/n in lowest terms → m²=2n² → m even → n even → contradiction.
OR
Q28(B): Find missing side in right triangles (diagram needed).

Section E – Case-Based (4 marks)

Q29: Shops A,B,C deals:
A: Buy1 Get1 → effective price/item = 50% of marked.
B: Buy2 Get1 → pay for 2 get 3 → per item = (2/3) of marked.
C: Buy3 Get1 → pay for 3 get 4 → per item = (3/4) of marked.
Price=100.
(a) A=50, B≈66.67, C=75.
(b) % discount: A=50%, B≈33.33%, C=25%.
Cheapest to costliest: A, B, C.

Q30: Rectangular path:
a) Rectangles: ABCD (outer), EFGH (inner).
b) Area path = Area(ABCD)−Area(EFGH).
If park 20×12 m, path width 2 m → outer 24×16 m → path area=144 m².
c) If outer shifted but inner fixed, area path changes if outer dimensions change.


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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 What is the digital root of the number 4...