Sample Paper · Class 10 · ICSE · 2026

Class 10 ICSE Maths Sample Paper 2026 with Solutions

Practice with 30 questions covering all 17 chapters. Detailed solutions included.

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Paper Structure

SectionQuestionsMarks
Section A: Objective (MCQ)1010
Section B: Short Answer1020
Section C: Long Answer624
Section D: Case Study416
Total3070

Sample Questions (Preview)

Showing 10 representative questions from the paper across multiple topics and difficulty levels.

1Commercial Mathematics (Banking & GST)Easy
A shopkeeper buys an article for Rs 500 and sells it for Rs 600. What is his profit percentage?
A.10%
B.15%
C.20%
D.25%
Show Solution+

Answer: 20%

Step 1: Find the profit: [Profit = SP - CP = 600 - 500 = Rs 100]

Step 2: Calculate profit percentage: [Profit % = (100 / 500) x 100 = 20%]

2Commercial Mathematics (Banking & GST)Medium
A manufacturer in Mumbai sells goods worth Rs 50000 to a dealer in Mumbai. The dealer then sells it to a consumer for Rs 65000. If GST is 12%, what is the tax (GST) paid by the dealer to the government?
A.Rs 1800
B.Rs 6000
C.Rs 7800
D.Rs 1200
Show Solution+

Answer: Rs 1800

Step 1: Input tax (GST paid on purchase): [= 12% of 50000 = Rs 6000]

Step 2: Output tax (GST collected on sale): [= 12% of 65000 = Rs 7800]

Step 3: Tax paid to government: [= Output tax - Input tax = 7800 - 6000 = Rs 1800]

3Commercial Mathematics (Banking & GST)Hard
A manufacturer sells goods to a wholesaler for Rs 40000. The wholesaler sells to a retailer at a profit of 20%, and the retailer sells to a consumer at a profit of 10% on his cost. If GST is 12%, find the price paid by the consumer (including GST).
A.Rs 52800
B.Rs 59136
C.Rs 55440
D.Rs 60000
Show Solution+

Answer: Rs 59136

Step 1: Wholesaler's SP: [= 40000 + 20% of 40000 = Rs 48000]

Step 2: Retailer's SP: [= 48000 + 10% of 48000 = Rs 52800]

Step 3: GST on consumer's purchase: [= 12% of 52800 = Rs 6336]

Step 4: Price paid by consumer: [= 52800 + 6336 = Rs 59136]

4Statistics (Mean, Median & Mode)Easy
The mean of the first five natural numbers is:
A.22
B.33
C.2.52.5
D.3.53.5
Show Solution+

Answer: $3$

Step 1: Sum: [1+2+3+4+5 = 15]

Step 2: Mean: [\bar{x} = \frac{15}{5} = 3]

5Statistics (Mean, Median & Mode)Medium
Using the assumed mean method with A=25A = 25, find the mean of:

| Class | 0−100-10 | 10−2010-20 | 20−3020-30 | 30−4030-40 | 40−5040-50 |
|---|---|---|---|---|---|
| fif_i | 66 | 1010 | 1212 | 88 | 44 |
A.2222
B.2323
C.2424
D.2525
Show Solution+

Answer: $23$

Step 1: Class marks: [x_i = 5, 15, 25, 35, 45]

Step 2: Deviations: [d_i = -20, -10, 0, 10, 20]

Step 3: Products: [f_i d_i = -120, -100, 0, 80, 80]

Step 4: Sum: [\sum f_i d_i = -120-100+0+80+80 = -60]

Step 5: Total: [\sum f_i = 40]

Step 6: Mean: [\bar{x} = 25 + \frac{-60}{40} = 25 - 1.5 = 23.5]

6Statistics (Mean, Median & Mode)Hard
The mean of the following distribution is 57.657.6 and the total frequency is 5050. Find f1f_1 and f2f_2.

| Class | 0−200-20 | 20−4020-40 | 40−6040-60 | 60−8060-80 | 80−10080-100 |
|---|---|---|---|---|---|
| ff | 77 | f1f_1 | 1212 | f2f_2 | 88 |
A.f1=8,f2=15f_1 = 8, f_2 = 15
B.f1=10,f2=13f_1 = 10, f_2 = 13
C.f1=6,f2=17f_1 = 6, f_2 = 17
D.f1=9,f2=14f_1 = 9, f_2 = 14
Show Solution+

Answer: $f_1 = 8, f_2 = 15$

Step 1: From total: [7 + f_1 + 12 + f_2 + 8 = 50 \implies f_1 + f_2 = 23 \quad \cdots(1)]

Step 2: Class marks: [10, 30, 50, 70, 90]

Step 3: Sum: [\sum f_i x_i = 70 + 30f_1 + 600 + 70f_2 + 720 = 1390 + 30f_1 + 70f_2]

Step 4: Mean = 57.6: [\frac{1390 + 30f_1 + 70f_2}{50} = 57.6]

Step 5: So: [30f_1 + 70f_2 = 1490 \implies 3f_1 + 7f_2 = 149 \quad \cdots(2)]

Step 6: From (1): $f_1 = 23 - f_2$. Substituting: [3(23-f_2) + 7f_2 = 149 \implies 69 + 4f_2 = 149 \implies f_2 = 20]

7ProbabilityEasy
A fair coin is tossed once. The probability of getting a head is:
A.00
B.12\frac{1}{2}
C.11
D.14\frac{1}{4}
Show Solution+

Answer: $\frac{1}{2}$

Step 1: Sample space: [S = \{H, T\},\; n(S) = 2]

Step 2: Favourable outcomes: [\{H\},\; n(E) = 1]

Step 3: P(H): [= \frac{1}{2}]

8ProbabilityMedium
A card is drawn from a deck of 5252 cards. What is the probability that it is a heart or a king?
A.413\frac{4}{13}
B.1652\frac{16}{52}
C.1752\frac{17}{52}
D.1552\frac{15}{52}
Show Solution+

Answer: $\frac{4}{13}$

Step 1: Hearts = 13, Kings = 4, King of Hearts = 1

Step 2: P(Heart or King): [= \frac{13 + 4 - 1}{52} = \frac{16}{52} = \frac{4}{13}]

9ProbabilityHard
A bag contains 55 white and 77 black balls. Two balls are drawn one after the other without replacement. What is the probability that the first is white and the second is black?
A.35132\frac{35}{132}
B.35144\frac{35}{144}
C.512\frac{5}{12}
D.722\frac{7}{22}
Show Solution+

Answer: $\frac{35}{132}$

Step 1: P(1st white): [= \frac{5}{12}]

Step 2: P(2nd black | 1st white): [= \frac{7}{11}]

Step 3: P: [= \frac{5}{12} \times \frac{7}{11} = \frac{35}{132}]

10MatricesEasy
What is the order of the matrix A=(354−2)A = \begin{pmatrix} 3 & 5 \\ 4 & -2 \end{pmatrix}?
A.1×21 \times 2
B.2×12 \times 1
C.2×22 \times 2
D.4×14 \times 1
Show Solution+

Answer: $2 \times 2$

Step 1: Count rows: 2 rows (horizontal lines of numbers).

Step 2: Count columns: 2 columns (vertical lines of numbers).

Step 3: Order = rows x columns [= 2 \times 2]

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Exam Tips for Class 10 ICSE Maths

  • 1Read the entire paper first and plan your time. Allocate roughly 1 minute per mark.
  • 2Attempt Section A (MCQs) first to secure easy marks and build confidence.
  • 3Show all working steps in Sections B, C, and D even if you know the final answer.
  • 4Draw neat diagrams for geometry questions and label all measurements clearly.
  • 5Leave 10 minutes at the end to review your answers and check for silly mistakes.

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Frequently Asked Questions

Is this Class 10 ICSE sample paper based on the latest syllabus?+
Yes, this sample paper follows the ICSE Class 10 Mathematics syllabus for the 2025-26 academic session and covers all prescribed chapters.
How many questions are in the Class 10 ICSE maths paper?+
The sample paper has 30 questions across 4 sections for a total of 70-80 marks, matching the actual ICSE exam pattern for Class 10.
Can I download this sample paper as PDF?+
You can practice the questions on this page with instant solutions. For a printable PDF, use SparkEd's worksheet generator to create custom worksheets for any topic.
How should I prepare for the Class 10 ICSE maths exam?+
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Are solutions provided for all questions?+
Yes, every question in this sample paper comes with a detailed step-by-step solution. Click "Show Solution" under each question to view the working.

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