ICSE Class 10 Question Paper 2026 Mathematics

ICSE | Class 10

Mathematics
Question Paper 2026

Council for the Indian School Certificate Examinations (CISCE)

Free Syllabus · Sample Papers · Previous Year Papers · Solutions & more


· ICSE · ISC · CBSE · State Boards

MATHEMATICS

Maximum Marks: 80

Time allowed: Three hours

1. Answers to this Paper must be written on the paper provided separately.

2. You will not be allowed to write during first 15 minutes.

3. This time is to be spent in reading the question paper.

4. The time given at the head of this Paper is the time allowed for writing the answers.

5. Attempt all questions from Section A and any four questions from Section B.

6. All working, including rough work, must be clearly shown, and must be done on the
same sheet as the rest of the answer.

7. Omission of essential working will result in loss of marks.

8. The intended marks for questions or parts of questions are given in brackets [ ]

9. Mathematical tables and graph papers are to be provided by the school.

Instruction for the Supervising Examiner

Kindly read aloud the Instructions given above to all the candidates present in the
Examination Hall.

This paper consists of 16 printed pages.
T26 511 Turn Over
© Copyright reserved.

ICSE Class 10 · Question Paper 2026 · Mathematics Page 1 of 16

SECTION A (40 Marks)

(Attempt all questions from this Section.)

Question 1
Choose the correct answers to the questions from the given options. [15]
(Do not copy the questions, write the correct answers only.)
(i) (𝑥𝑥 + 3), 1, (3𝑥𝑥 − 7) and −5 are in proportion. The value of 𝑥𝑥 is:

(a) –1

(b) 1

(c) –5

(d) 5

(ii) The marked price of a refrigerator is ₹ 12,000 and GST paid by the customer
is ₹ 2,160. The rate of GST is:

(a) 5%

(b) 12%

(c) 18%

(d) 28%

(iii) Rakhi’s mobile number has the following integers:
1, 6, 9, 8, 9, 1, 7, 8, 9
The mode of the above given data is:

(a) 1

(b) 6

(c) 8

(d) 9

T26 511 2

ICSE Class 10 · Question Paper 2026 · Mathematics Page 2 of 16

(iv) A and B opened a recurring deposit account in a bank which is paying simple
interest at 9% per annum. A deposited ₹ 1,500 for one year and B deposited
₹ 1,200 for 15 months. The amount invested by:

(a) A is ₹ 27 more than B

(b) A is ₹ 300 more than B

(c) A is ₹ 300 less than B

(d) Both A and B are same (₹ 18,000)

(v) Find the equation of a line whose y-intercept is 6 and is parallel to x-axis.

(a) y=6

(b) x=6

(c) x+y=6

(d) y–x=6

(vi) Asha buys ₹ 20 shares of a company which pays 9% dividend at such a price
that she gets a return of 12% on her investment. At what price did she buy
each share?

(a) ₹ 20

(b) ₹ 15

(c) ₹ 25

(d) ₹ 18

T26 511 3 Turn Over

ICSE Class 10 · Question Paper 2026 · Mathematics Page 3 of 16

(vii) The total surface area of a solid sphere (S1) and a solid hemisphere (S2), as
shown in the diagram, are equal. The ratio of radii R and r is:

S1 S2
(a) 1:1

(b) 2:1

(c) √3 ∶ 2

(d) 2 ∶ √3

(viii) In the given diagram, O is the centre of the circle and ABCD is a cyclic
quadrilateral. If ∠CDE = 65o, then the value of x is:

(a) 32.5o

(b) 65o

(c) 115o

(d) 130o

T26 511 4

ICSE Class 10 · Question Paper 2026 · Mathematics Page 4 of 16

(ix) The nature of roots of quadratic equation 𝟑𝟑𝒙𝒙𝟐𝟐 − 𝟔𝟔𝟔𝟔 − 𝟑𝟑 = 𝟎𝟎 are:

(a) real and equal

(b) real, distinct and rational

(c) real, distinct and irrational

(d) no real roots

(x) Assertion (A): If a die is rolled, the probability of getting a number greater
𝟏𝟏
than 6 is .
𝟔𝟔

Reason (R): There are six possible outcomes when rolling a die,
{1, 2, 3, 4, 5, 6}.

(a) (A) is true and (R) is false.

(b) (A) is false and (R) is true.

(c) Both (A) and (R) are true and (R) is the correct explanation of (A).

(d) Both (A) and (R) are true but (R) is not the correct explanation of (A).

(xi) If the areas of two similar triangles are in the ratio 9 : 64, then the ratio of
their corresponding altitudes is:

(a) 3:8

(b) 2:1

(c) 9 : 64

(d) 8:3

T26 511 5 Turn Over

ICSE Class 10 · Question Paper 2026 · Mathematics Page 5 of 16

(xii) What must be added to 𝑥𝑥 3 + 7𝑥𝑥 2 + 3𝑥𝑥 + 2 so that the result is completely
divisible by (𝑥𝑥 + 2)?

(a) – 40

(b) –16

(c) 16

(d) 40

(xiii) In the given diagram, ΔAOB is a right-angled triangle and C is the mid-point
of AB. The coordinates of the point which is equidistant from the three
vertices of ΔAOB is:

(a) (𝑥𝑥, 𝑦𝑦)

(b) (𝑦𝑦, 𝑥𝑥)
𝑥𝑥 𝑦𝑦
(c) � , �
2 2
2𝑥𝑥 2𝑦𝑦
(d) � , �
3 3

T26 511 6

ICSE Class 10 · Question Paper 2026 · Mathematics Page 6 of 16

(xiv) 2 3
Given matrix 𝐴𝐴 = � � and matrix 𝐵𝐵 = [2 − 4]. Product AB is a matrix
1 2
of order:

(a) 2×2

(b) 2×1

(c) 1×2

(d) product AB is not possible

(xv) Assertion (A): The 9th term of a Geometric Progression (G.P.)
6, –12, 24, – 48… is a positive term.

Reason (R): The value of (–2)8 is always positive.

(a) (A) is true and (R) is false.

(b) (A) is false and (R) is true.

(c) Both (A) and (R) are true and (R) is the correct explanation of (A).

(d) Both (A) and (R) are true but (R) is not the correct explanation of (A).

Question 2

(i) The fourth and seventh terms of an Arithmetic Progression (A.P.), are 60 [4]
and 114 respectively. Find the:

(a) first term and common difference.

(b) sum of its first 10 terms.

(ii) 3 1 −1 𝑎𝑎 𝑏𝑏 7 [4]
Given, 𝐴𝐴 = � � and 𝐵𝐵 = � � and product 𝐴𝐴𝐴𝐴 = � �.
5 3 3 −5 4 5
Find the values of ‘a’ and ‘b’.

T26 511 7 Turn Over

ICSE Class 10 · Question Paper 2026 · Mathematics Page 7 of 16

(iii) In the given diagram, O is the centre of the circle and the tangent DE touches [4]
the circle at B. If, ∠ADB = 32o. Find the values of x and y.

Question 3
(i) The polynomial 𝑘𝑘𝑥𝑥 3 + 3𝑥𝑥 2 − 11𝑥𝑥 − 6 when divided by (𝑥𝑥 + 1), leaves a [4]
remainder of 6.

(a) Find the value of k.

(b) Using the value of k factorise completely the polynomial
𝑘𝑘𝑥𝑥 3 + 3𝑥𝑥 2 − 11𝑥𝑥 − 6

(ii) An eye drop bottle is prepared consisting of a hemisphere, a cylinder and a [4]
conical cap, as shown in the given diagram. Height of the cylindrical and
conical parts are each, equal to the diameter (7 cm). Find the:

(a) minimum height of the cylindrical box required
to pack this bottle.

(b) volume of the liquid medicine (shaded part) in
the bottle. Give your answer to the nearest
𝟐𝟐𝟐𝟐
whole number. (Use 𝝅𝝅 = )
𝟕𝟕

T26 511 8

ICSE Class 10 · Question Paper 2026 · Mathematics Page 8 of 16

(iii) Use ruler and compass for the following construction: [5]

(a) construct an equilateral triangle ABC of side 5 cm.

(b) construct the circumcircle of ΔABC.

(c) construct the locus of points which are equidistant from AB and BC.
Mark the point where the circumcircle and locus meet, as D.

(d) give the geometrical name of quadrilateral ABCD.

SECTION B (40 Marks)
(Attempt any four questions from this Section.)

Question 4
(i) Prove that: [3]
(𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 − 𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄)(𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄 − 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔) = 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔

(ii) The cost price of a TV set is ₹ 20,000. The shopkeeper marked it for ₹ 24,000. [3]
He sells it to a customer at a discount of 10% on the marked price. If the sale
is intra-state and the rate of GST is 12%, find the:

(a) discounted price of the TV set.

(b) amount paid by the customer to clear the bill.

(iii) In the given diagram, DE ∥ BC and AD : DB = 2 : 3. [4]

(a) Prove that: ΔADE ~ ΔABC and
hence find DE : BC

(b) Prove: ΔDFE ~ ΔCFB

(c) Given, area of ΔDFE = 16 square
units, find the area of ΔCFB.

T26 511 9 Turn Over

ICSE Class 10 · Question Paper 2026 · Mathematics Page 9 of 16

Question 5

(i) The histogram drawn on the graph represents the number of students of [3]
different heights (in cm).

Scale: x-axis, 2 cm = 10 cm of height
y-axis, 2 cm = 2 students

Using the graph, answer the following:

(a) the number of students whose height is 150 cm and above.

(b) the modal height.

(c) the total number of students.

T26 511 10

ICSE Class 10 · Question Paper 2026 · Mathematics Page 10 of 16

(ii) A(–10, –2) and B(2, 10) are two end points of a line segment. If AB intersects [3]
the x-axis at P, find the:

(a) ratio in which ‘P’ divides AB.

(b) coordinates of point P.

(iii) Solve the quadratic equation (𝒙𝒙 − 𝟐𝟐)𝟐𝟐 − 𝟓𝟓𝟓𝟓 − 𝟑𝟑 = 𝟎𝟎 and give your answer [4]
correct to 3 significant figures.
(Use Mathematical Tables for this question if necessary.)

Question 6
(i) Kabir bought 120 shares of a company with nominal value ₹ 100, available [3]
at a premium of ₹ 25. Find:

(a) the money invested by Kabir in buying these shares.

(b) the rate of dividend, if he received ₹ 1,080 as dividend from these shares
after one year.

(c) his rate of return.

(ii) Find the mean of the following frequency distribution using step-deviation [3]
method.
Take assumed mean = 28

Class
0–8 8 – 16 16 – 24 24 – 32 32 – 40 40 – 48
Interval

Frequency 10 20 14 16 18 22

(iii) 𝟑𝟑 [4]
The difference of two natural numbers is 5 and sum of their reciprocals is .
𝟏𝟏𝟏𝟏

Find the two numbers.

T26 511 11 Turn Over

ICSE Class 10 · Question Paper 2026 · Mathematics Page 11 of 16

Question 7
(i) A flagpole is erected at the top of a building. The angle of elevation of the top [5]
and foot of the flagpole from a point 100 m away, on the same level as that
of the foot of the building, are 33o and 31o respectively. Find the height of the
flagpole. Give your answer correct to the nearest metre.
(Use Mathematical Tables for this question.)

(ii) Using a graph paper, draw an ogive for the following distribution which [5]
shows a record of weight in kilograms of 100 students.

Weight (in kg) Number of students
35 – 40 4
40 – 45 6
45 – 50 10
50 – 55 24
55 – 60 26
60 – 65 17
65 – 70 8
70 – 75 5
Use your ogive to estimate the following:

(a) the median weight of the students.

(b) percentage of students whose weight is 60 kg or more.

(c) the weight above which 20% of the students lie.

T26 511 12

ICSE Class 10 · Question Paper 2026 · Mathematics Page 12 of 16

Question 8
(i) Rohit and Vinay both opened a recurring deposit account in a bank for 2 years [3]
at 8% simple interest. Vinay deposited ₹ 300 per month. On maturity, Rohit’s
interest was ₹ 800 more than Vinay’s interest. Find the:

(a) interest earned by Vinay.

(b) sum deposited by Rohit every month.

(ii) The fourth term of a Geometric Progression (G.P.) is 16 and its seventh term [3]
is 128. Find its:

(a) common ratio

(b) first term

(iii) Use graph sheet for this question. Take 2 cm = 1 unit along both x and y axis. [4]
Graphically represent parallelogram OABC, where O(0, 0), A(2, 3), B(5, 3)
and C(3, 0).

Reflect OABC:

(a) on the x-axis and name its image as ODEC.

(b) through the origin and name its image as OIJH.

(c) on the y-axis and name its image as OFGH.

Question 9
(i) Solve the following inequation, write the solution set and represent it on the [3]
real number line.

𝟐𝟐𝟐𝟐 − 𝟑𝟑 𝒙𝒙
−𝟏𝟏 < − ≤ 𝟏𝟏, 𝒙𝒙 ∈ 𝑹𝑹
𝟑𝟑 𝟓𝟓

T26 511 13 Turn Over

ICSE Class 10 · Question Paper 2026 · Mathematics Page 13 of 16

(ii) Use the following graph and answer the given questions: [3]

(a) Write the co-ordinates of points A, B and C.

(b) Find the equation of a line passing through the mid-point of AC and
parallel to AB.

T26 511 14

ICSE Class 10 · Question Paper 2026 · Mathematics Page 14 of 16

(iii) A solid wooden toy is prepared by joining a cone, a cylinder and a sphere, as [4]
shown in the given diagram. The radius of each of the three solids is 7 cm
and heights of each of the cone and the cylinder is 24 cm. Find:

(a) the total surface area of the given solid.

(b) the cost of painting the total surface at the rate of ₹ 0.50 per cm2.
𝟐𝟐𝟐𝟐
(Use 𝝅𝝅 = )
𝟕𝟕

Question 10
(i) 5𝑎𝑎𝑎𝑎 [3]
𝐼𝐼𝐼𝐼 𝑥𝑥 = , 𝒂𝒂 ≠ 𝒃𝒃,
𝑎𝑎 − 𝑏𝑏
𝒙𝒙
(a) Find:
𝒂𝒂
𝒙𝒙 + 𝒂𝒂
(b) Using properties of proportion, find:
𝒙𝒙 − 𝒂𝒂

T26 511 15 Turn Over

ICSE Class 10 · Question Paper 2026 · Mathematics Page 15 of 16

(ii) A survey was conducted on 300 families having 2 children each. The results [3]
obtained are given below.

Number of girl child 2 1 0 Total
Number of families 95 165 40 300

If one family is selected at random, find the probability that it will have:

(a) one girl child
(b) one or more girl child
(c) no boy child

(iii) In the given figure ‘O’ is the centre of the circle. PQ is a tangent to the circle [4]
at B and AB = AC. If ∠𝑪𝑪𝑪𝑪𝑪𝑪 = 𝟒𝟒𝟒𝟒°, find the unknown angles 𝒙𝒙, 𝒚𝒚, 𝒛𝒛 𝑎𝑎𝑎𝑎𝑎𝑎 𝒘𝒘.

T26 511 16

ICSE Class 10 · Question Paper 2026 · Mathematics Page 16 of 16