SEE Mathematics Sample Paper (Class VIII)

SECTION-A (15 Questions)

Q1. Sum of two consecutive even numbers:

(a) Always an odd number
(b) Always an even number
(c) Never be an even number
(d) Never be an odd number

Q2. Which of the following numbers is divisible by 11?

(a) 4686
(b) 5678
(c) 3742
(d) 5416

Q3. The digital root of a number is 8. What is the digital root of the number plus 12?

(a) 2
(b) 3
(c) 7
(d) 9

Q4. Which of the sum of digits will always be divisible by 3?

(a) 5+9+3
(b) 4+7+8
(c) 3+6+9
(d) 2+5+7

Q5. 735 × 101 = ?

(a) 74245
(b) 74345
(c) 74235
(d) 74525

Q6. If a : b :: c : d then

(a) a/b : c/d
(b) c/a : a/b
(c) ad = bc
(d) All are true

Q7. In the proportion 14:21 :: 6:x, the value of x is?

(a) 13
(b) 4
(c) 9
(d) None of these

Q8. The altitude of triangle whose base is 6cm and area is 12 cm².

(a) 5 cm
(b) 3 cm
(c) 4 cm
(d) 6 cm

Q9. The area of rhombus whose diagonals are 10 cm and 16 cm.

(a) 80 cm²
(b) 90 cm²
(c) 75 cm²
(d) 100 cm²

Q10. 3 inches = ? centimeters.

(a) 7.21 cm
(b) 7.4 cm
(c) 7.52 cm
(d) 7.62 cm

Q11. Express 21/75 fraction as percentage.

(a) 30%
(b) 28%
(c) 40%
(d) 42%

Q12. If a shopkeeper offers a 25% discount on all shoes. If original price of a shoe is Rs.500, how much will Arnav have to pay?

(a) Rs.350
(b) Rs.375
(c) Rs.425
(d) Rs.450

Q13. If 5 cm on a map represents 60 km on the ground, then 15 cm represents:

(a) 150 km
(b) 160 km
(c) 170 km
(d) 180 km

Q14. If 8 workers complete a work in 6 days, how many days will 12 workers take to complete the same work?

(a) 5 days
(b) 4 days
(c) 3 days
(d) 6 days

Q15. The ratio of 8 books to 20 books is:

(a) 2:5
(b) 5:2
(c) 4:5
(d) 5:4

SECTION-B (5 Questions)

Q16. The price of gold per gram is Rs.12000. A GST of 12% is added to the price. Find the final price of the gold for 4 grams including GST.

Q17. Red, Blue and Yellow paints are mixed in the ratio 3:4:5. Find the quantity of each colour required to make 96 litres of paint.

Q18. To make soft idlis, you need to mix rice and urad Dal in the ratio 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?

Q19. Expand the product:

(a) (3 + u)(v - 3)
(b) 2/3(15 + 6a)

Q20. I hold some pebbles not too many when I group them in 3's one stays with me. Try pairing them up it simply will not 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 hundred would be far too bold, can you tell me the number of pebbles I hold?

SECTION-C (4 Questions)

Q21. The value of a machine decreases by 8% every year. If its present value is Rs.60000, what will be its value after 2 years?

Q22. 12 water tankers can supply water to a village for 15 days. If 4 tankers stop working, for how many days will the remaining tankers supply water?

Q23. Using identity (a + b)(a - b):

(a) Expand the identity
(b) Express 86 × 74 using above identity
(c) Find the final value of 86 × 74

Using the identity (a + b)², find the area of a square with a side length of 65 m.

Q24. A truck travels 360 km in 6 hours.

(a) Find speed of truck.
(b) Find distance travelled by truck in 11 hours.

A tractor can plough the same area of a field 4 times faster than a pair of oxen. A farmer wants to plough his 20-acre field. A pair of oxen takes 6 hours to plough an acre of land. How much time would it take if the farmer used a pair of oxen to plough the field? How much time would it take him if he decides to use a tractor instead?

SECTION-D (3 Questions)

Q25. A rectangular bedroom has a length of (x + 8) feet and a breadth of (x - 2) feet. Find its area. If both the length and breadth are increased by 1 foot, find the increase in the area of the room.

Q26. The parallel sides of a trapezium are in the ratio 3:5. Its height is 12 cm and its area is 192 cm².

(a) Find the length of the parallel sides.
(b) If 4 cm is added to each parallel side, find the new area.

Q27. Sarah wants to invest Rs.50,000 for a period of 2 years. She has two options from different banks.

Option 1: Offers simple interest at a rate of 10% per annum.
Option 2: Offers compound interest at a rate of 10% per annum, compounded annually.
(a) Calculate the total simple interest Sarah would earn from Option 1.
(b) Calculate the total compound interest Sarah would earn from Option 2.
(c) Calculate the difference between the interest earned in the two options.

A shopkeeper buys 100 kg of sugar at Rs 40 per kg. He sells 40 kg at 10% profit, 35 kg at 20% loss, and the remaining at 25% profit. Find his overall profit or loss percentage.

SECTION-E (CBQ) (2 Questions)

Q28. A triangle and a parallelogram are on the same base 18 cm and between the same parallels. The area of the parallelogram is 288 cm².

(a) Find the height of the parallelogram.
(b) Find the area of the triangle.
(c) Find the height of the triangle.
(d) What relation do you observe between their heights?

Q29. The percentage of ingredients in a 500g box of "Healthy Muesli" with 5 ingredients is given below:

Ingredient	Percentage
Wheat flakes	20%
Rolled oats	40%
Raisins	15%
Almonds	12.5%
Honey	12.5%

(a) What is the total weight of Almonds and Raisins in a 500g packet?
(b) If Rohan buys a larger "Family pack" of the same mix weighing 1kg, what would be the new weight of the honey?
(c) How many more grams of Raisins are there in a box compared to Rolled oats?
(d) If the label was torn and the percentage for Wheat Flakes was missing, how could you find it using the other percentages provided?

SEE MATHEMATICS BLUEPRINT (Class VIII)

Exam Details

Total Marks: 60
Time: 2½ Hours
Question Format: Multiple Choice, Short Answer, Long Answer, Case-Based

SECTION-WISE DISTRIBUTION

Section	Question Type	No. of Questions	Marks per Question	Total Marks
A	MCQ	15	1	15
B	Short Answer	5	2	10
C	Medium Answer	4	3	12
D	Long Answer	3	5	15
E	Case-Based	2	4	8
TOTAL		29		60

CHAPTER/TOPIC-WISE WEIGHTAGE

Topic	Questions	Marks	Weightage (%)
Number System & Operations	Q1, Q2, Q3, Q4, Q5	5	8.3%
Ratio & Proportion	Q6, Q7, Q13, Q14, Q15, Q17, Q18	7	11.7%
Mensuration (Area, Perimeter)	Q8, Q9, Q25, Q26, Q28	5	15%
Percentage, Profit & Loss, Discount	Q11, Q12, Q16, Q27	4	11.7%
Algebraic Expressions & Identities	Q19, Q23, Q25	3	10%
Time & Work	Q14, Q22, Q24	3	8.3%
Direct & Inverse Proportion	Q13, Q14, Q22	3	6.7%
Simple & Compound Interest	Q27	1	5%
Number Puzzles/Patterns	Q20	1	3.3%
Data Interpretation/Case Study	Q29	1	6.7%
Unit Conversion	Q10	1	1.7%
Miscellaneous (Speed, Map Scale)	Q13, Q24	2	5%
GST/Taxation	Q16	1	3.3%
Depreciation	Q21	1	3.3%

DIFFICULTY LEVEL ANALYSIS

Difficulty Level	Question Numbers	Total Marks	Percentage
Easy	Q1, Q2, Q5, Q6, Q7, Q8, Q9, Q10, Q11, Q12, Q14, Q15, Q18	13	21.7%
Medium	Q3, Q4, Q13, Q16, Q17, Q19, Q21, Q22, Q23, Q24, Q28(a,b)	11	30%
Hard	Q20, Q25, Q26, Q27, Q28(c,d), Q29	5	25%
HOTS/Application	Q20, Q27 (OR), Q29(d)	3	23.3%

COMPETENCY-BASED DISTRIBUTION

Competency	Question Numbers	Marks	Percentage
Knowledge/Remembering	Q1, Q2, Q5, Q6, Q8, Q9, Q10, Q11	8	13.3%
Understanding	Q3, Q4, Q7, Q12, Q13, Q14, Q15, Q18, Q19	9	15%
Application	Q16, Q17, Q21, Q22, Q23, Q24, Q27, Q28	8	26.7%
Analysis/Evaluation	Q20, Q25, Q26, Q29	4	25%
Creation/Synthesis	Q27(OR), Q29(d)	2	20%

BLUEPRINT SUMMARY

Total Questions: 29
Total Marks: 60
MCQs: 15 questions (25% of paper)
Case-Based Questions: 2 questions (13.3% of paper)
Application-Based Questions: ~40% of paper
Algebra & Mensuration: Highest weightage (~25%)
Competency Focus: Balanced mix of Knowledge, Understanding, Application, and Higher-Order Thinking

answers with explanations for all the questions in the sample paper, organized by section:

SECTION-A (15 × 1 = 15 Marks)

Q1. Sum of two consecutive even numbers:

Answer: (b) Always an even number
Explanation: Even numbers are multiples of 2. Sum of two even numbers is always even.

Q2. Which of the following numbers is divisible by 11?

Answer: (a) 4686
Explanation: Difference of sum of alternate digits: (4+8) - (6+6) = 12 - 12 = 0, divisible by 11.

Q3. The digital root of a number is 8. What is the digital root of the number plus 12?

Answer: (a) 2
Explanation: Digital root of 8 + 12 = 20 → 2+0 = 2.

Q4. Which of the sum of digits will always be divisible by 3?

Answer: (c) 3+6+9 = 18
Explanation: Sum = 18, divisible by 3.

Q5. 735 × 101 =

Answer: (c) 74235
Explanation: 735 × 100 = 73500, + 735 = 74235.

Q6. If a : b :: c : d then

Answer: (c) ad = bc
Explanation: In proportion, product of means = product of extremes.

Q7. In the proportion 14:21 :: 6:x, the value of x is?

Answer: (c) 9
Explanation: 14/21 = 6/x → 14x = 126 → x = 9.

Q8. The altitude of triangle whose base is 6cm and area is 12 cm².

Answer: (c) 4 cm
Explanation: Area = ½ × base × height → 12 = ½ × 6 × h → h = 4.

Q9. The area of rhombus whose diagonals are 10 cm and 16 cm.

Answer: (a) 80 cm²
Explanation: Area = ½ × d1 × d2 = ½ × 10 × 16 = 80.

Q10. 3 inches = centimeters.

Answer: (d) 7.62 cm
Explanation: 1 inch = 2.54 cm → 3 × 2.54 = 7.62.

Q11. Express 21/75 fraction as percentage.

Answer: (b) 28%
Explanation: (21/75) × 100 = 28%.

Q12. If a shopkeeper offers a 25% discount on all shoes. If original price of a shoe is Rs.500, how much will Arnav have to pay?

Answer: (b) Rs.375
Explanation: Discount = 25% of 500 = 125, Price after discount = 500 - 125 = 375.

Q13. If 5 cm on a map represents 60 km, then 15 cm represents:

Answer: (d) 180 km
Explanation: 5 cm = 60 km → 1 cm = 12 km → 15 cm = 180 km.

Q14. If 8 workers complete a work in 6 days, how many days will 12 workers take?

Answer: (b) 4 days
Explanation: M1D1 = M2D2 → 8×6 = 12×D → D = 4.

Q15. The ratio of 8 books to 20 books is:

Answer: (a) 2:5
Explanation: 8:20 = 2:5.

SECTION-B (5 × 2 = 10 Marks)

Q16. Price of gold per gram = Rs.12000, GST = 12%. Final price for 4 grams including GST:

Price for 4g = 4 × 12000 = 48000
GST = 12% of 48000 = 5760
Final price = 48000 + 5760 = Rs.53760

Q17. Red:Blue:Yellow = 3:4:5, total paint = 96 litres

Total parts = 3+4+5 = 12
Red = (3/12)×96 = 24 L
Blue = (4/12)×96 = 32 L
Yellow = (5/12)×96 = 40 L

Q18. Rice:Urad Dal = 2:1, total mixture = 6 cups

Total parts = 3
Rice = (2/3)×6 = 4 cups
Urad Dal = (1/3)×6 = 2 cups

Q19. Expand:

(a) (3 + u)(v - 3) = 3v - 9 + uv - 3u
(b) 2/3(15 + 6a) = 10 + 4a

Q20. Pebbles puzzle:

Let number = N
N mod 3 = 1, N mod 2 = 1, N mod 5 = 1, N mod 7 = 0
LCM of 3,2,5 = 30, so N = 30k + 1, divisible by 7
Try k = 1 → 31, k=2 → 61, k=3 → 91 (91 ÷ 7 = 13)
N = 91 pebbles (less than 100)

SECTION-C (4 × 3 = 12 Marks)

Q21. Machine value decreases by 8% every year. Present value = Rs.60000. Value after 2 years:

After 1st year = 60000 × (1 - 0.08) = 55200
After 2nd year = 55200 × 0.92 = Rs.50784

Q22. 12 tankers → 15 days. If 4 stop, remaining = 8 tankers:

12 × 15 = 8 × D → D = (12×15)/8 = 22.5 days

Q23. Identity (a + b)(a - b) = a² - b²

(a) Identity: (a + b)(a - b) = a² - b²
(b) 86 × 74 = (80 + 6)(80 - 6)
(c) = 80² - 6² = 6400 - 36 = 6364

OR
(a + b)² = a² + 2ab + b²

Side = 65 m → Area = 65² = 4225 m²

Q24. Truck travels 360 km in 6 hours:

(a) Speed = 360/6 = 60 km/h
(b) Distance in 11 hours = 60 × 11 = 660 km

Oxen ploughs 1 acre in 6 hours → 20 acres = 120 hours
Tractor is 4 times faster → Time = 120/4 = 30 hours

SECTION-D (3 × 5 = 15 Marks)

Q25. Length = (x + 8), Breadth = (x - 2)

Area = (x + 8)(x - 2) = x² + 6x - 16
New length = (x + 9), new breadth = (x - 1)
New area = (x + 9)(x - 1) = x² + 8x - 9
Increase = (x² + 8x - 9) - (x² + 6x - 16) = 2x + 7

Q26. Parallel sides ratio = 3:5, height = 12 cm, area = 192 cm²

(a) Let sides = 3k and 5k
Area = ½ × (3k + 5k) × 12 = 192
½ × 8k × 12 = 192 → 48k = 192 → k = 4
Sides = 12 cm and 20 cm
(b) New sides = 16 cm and 24 cm
New area = ½ × (16 + 24) × 12 = ½ × 40 × 12 = 240 cm²

Q27. Investment = Rs.50,000, 2 years, 10% rate

(a) Simple Interest = 50000 × 2 × 0.10 = Rs.10000
(b) Compound Interest = 50000 × (1.1)² - 50000 = 60500 - 50000 = Rs.10500
(c) Difference = 10500 - 10000 = Rs.500

Cost = 100 × 40 = 4000
40 kg at 10% profit → SP = 40 × 40 × 1.1 = 1760
35 kg at 20% loss → SP = 35 × 40 × 0.8 = 1120
Remaining 25 kg at 25% profit → SP = 25 × 40 × 1.25 = 1250
Total SP = 1760 + 1120 + 1250 = 4130
Profit = 4130 - 4000 = 130
Profit % = (130/4000) × 100 = 3.25%

SECTION-E (CBQ) (2 × 4 = 8 Marks)

Q28. Triangle and parallelogram on same base 18 cm, area of parallelogram = 288 cm²

(a) Height of parallelogram = Area/Base = 288/18 = 16 cm
(b) Area of triangle = ½ × base × height = ½ × 18 × 16 = 144 cm²
(c) Height of triangle = same as parallelogram = 16 cm
(d) Observation: Heights are equal (same base and between same parallels)

Q29. Muesli ingredients in 500g:

(a) Almonds = 12.5% of 500 = 62.5g, Raisins = 15% of 500 = 75g → Total = 137.5g
(b) Honey in 1kg = 12.5% of 1000 = 125g
(c) Rolled oats = 40% of 500 = 200g, Raisins = 75g → Difference = 200 - 75 = 125g more oats
(d) Missing Wheat Flakes % = 100 - (40 + 15 + 12.5 + 12.5) = 100 - 80 = 20%

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Wednesday, February 18, 2026