Class 8 SESSION ENDING EXAMINATION (2026) SAMPLE PAPER-7 WITH ANSWERS
SAMPLE PAPER 7
SECTION A (1 mark each)
The sum of any four consecutive integers is always:
a) odd b) prime c) even d) a multiple of 3Numbers that leave a remainder of 3 when divided by 5 are of the form:
a) 3k b) 5k + 3 c) 5k - 3 d) 3k + 5Identify the appropriate algebraic expression for "Two more than a square number":
a) 2 + s b) (s + 2)² c) s² + 2 d) s² + 4Which of the following is correct?
a) 1 mL = 10 cc b) 1 mL = 1 cc c) 1 L = 100 cc d) 1 L = 10 ccThe 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 originalIf the base of a triangle remains the same and its height is doubled, its area becomes:
a) Half b) double c) triple d) unchangedThe 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 × 8250Which of the following is a Baudhayana (Pythagorean) triplet?
a) (2, 3, 4) b) (4, 5, 6) c) (3, 4, 5) d) (5, 6, 7)The formula for the area of a rhombus is:
a) base × height b) side² c) ½ × product of diagonals d) diagonal²If 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 + b²Which 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::28:12The 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) translationJasmine 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:
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.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)
If 3p7q8 is divisible by 44, list all possible pairs of values for p and q.
A) Expand: (a + ab - 3b²)(4 + b)
OR
B) Evaluate: 98 × 102 using the suitable identity.Find the hypotenuse of an isosceles right triangle whose equal sides have length 12.
A) Find the value of 25% of 160?
OR
B) Express the following fractions as percentages: i) 3/5 ii) 5/11Is the product of two consecutive integers always multiple of 2? Why?
SECTION C (3 marks each)
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?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?
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?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 ΞZWB.
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?Find the side length of a rhombus whose diagonals are of length 24 units and 70 units.
SECTION D (4 marks each)
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?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.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)
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.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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