ICSE Class 10 Maths Prelim Question Paper 2026: Practice Important Questions for High Score

Particulars

Details

Examination Name

ICSE Class 10 Mathematics Prelim Examination 2026

Conducting Body

Council for the Indian School Certificate Examinations (CISCE)

Subject

Mathematics

Exam Level

Class 10 (Secondary)

Exam Mode

Offline (Pen and Paper)

Total Marks

100 Marks

External Examination

80 Marks

Internal Assessment

20 Marks

Question Paper Type

Prelim/Practice Question Paper

Official Exam Date

Monday, 2 March 2026

Exam Timing

11:00 AM

Official Website

cisceboard.org 

Question Number

Questions

Marks

Section A

(Attempt all questions from this Section)

1

Choose one correct answer to the questions from the given options:

Do not copy the questions, write the answers only

(i) The solution of the given inequality 2x – 5 ≤ 5x + 4 < 11, where x ∈ I

(a) {1,2,3,……} 

(b) {–3, –2, –1, 0, 1} 

(c) {–3, –2, –1} 

(d) {0,1,2,3,4}

(ii) The volume of a conical tent is 462 m³ and the area of the base is 154 m². The height of the conical tent is __________

(a) 9.5 cm 

(b) 9 cm 

(c) 12 cm 

(d) 3 cm

(iii) If the straight lines are 3x – 5y = 7 and 4x + ay + 9 = 0 are perpendicular to one another, then the value of a is __________

(a) 4 

(b) 3/5 

(c) 5/3 

(d) 12/5

(iv) Assertion – Mr Sharma has a Recurring Deposit with a monthly deposit of ₹500 for 4 years at 10% p.a. The amount received at maturity is ₹4900.

Reason – The amount at the time of maturity is P + I
(a) Both Assertion and Reason are true
(b) Both Assertion and Reason are false
(c) Assertion is true and Reason is false
(d) Assertion is false and Reason is true

(v) A man invests ₹9600 on ₹100 shares at ₹80. If the company pays him 18% dividend, his total dividend is __________

(a) 120  

(b) 1200  

(c) 2160  

(d) 960

(vi) The quadratic equation 2x² – √5 x + 1 = 0 has __________

(a) Two distinct real roots

(b) two equal real roots

(c) no real roots

(d) more than two real roots

(vii) If 2b 8;9 a+b2b 8 ; 9 a + b2b 8;9 a+b = 6 8;9 86 8 ; 9 86 8;9 8 then the value of a is __________

(a) 5 

(b) 11 

(c) 8 

(d) 9

(viii) (v) 3a + 2b : 5a + 3b = 18 : 29. ∴ a : b = __________

(a) 3 : 4 

(b) 4 : 3 

(c) 1 : 4 

(d) 4 : 1

(ix) The median class for the given distribution is:

(a) 0–10 

(b) 10–20 

(c) 20–30 

(d) 30–40

(x) If the angle of depression of an object from a 75 m high tower is 30°, then the distance of the object from the tower is __________

(a) 25√3 m 

(b) 50√3 m 

(c) 75√3 m 

(d) 150 m

(xi) The CGST paid by a customer to the shopkeeper for an article which is priced ₹1200 is ₹36. The rate of GST charged is __________

(a) 12%  

(b) 6%  

(c) 3%  

(d) 9%

(xii) If the probability of an event is p, then the probability of its complementary event will be __________

(a) p – 1 

(b) p 

(c) 1 – p 

(d) 1 – 1/p

(xiii)

In the above figure, RPQ is a tangent to the circle at point P. AB is a chord parallel RPQ.

Assertion (A): ∠APR = ∠BPQ
Reason (R): ∠APR and ∠BPQ are angles in alternate segments.

(a) Assertion (A) is true, Reason (R) is false
(b) Assertion (A) is false, Reason (R) is true
(c) Both Assertion (A) and Reason (R) are true
(d) Both Assertion (A) and Reason (R) are false

(xiv) A model of a ship is made to a scale of 1 : 250. The area of the deck of the ship is __________ if the area of the deck of the model is 2.4 m².

(a) 15 km² 

(b) 0.15 km² 

(c) 600 m² 

(d) 6 km²

(xv) The value of k if x–2 is a factor of x³ + 2x² – kx + 10 is __________

(a) –9  

(b) 10  

(c) –13  

(d) 13

(15)

2

(i) Show that P (3, m – 5) is a point of trisection of the line segment joining the points A (4, –2) and B (1, 4). Hence, find the value of m. 

(ii) Use graph paper to answer the given questions:
(a) Plot the points A (4, 6) and B (1, 2)
(b) A¹ is the image of A when reflected in the X axis.
(c) B¹ is the image of B when B is reflected in the line AA¹.
(d) Give the geometrical name for the figure ABA¹B¹.
(e) Find the area of the figure ABA¹B¹. 

(iii) From a solid cylinder of height is 36 cm and radius 14 cm, a conical cavity of height 24 cm and radius 7 cm is drilled out. Find the volume and total surface area of the remaining solid.

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3

(i) If (x – 2) is a factor of 2x³ – x² – px – 2.
(a) Find the value of p
(b) Factorise the given expression completely. 

(ii) In the given figure, O is the centre of the circle. ∠DAE = 70°. Find, giving suitable reasons, the measure of:

(a) ∠BCD 

(b) ∠BOD 

(c) ∠OBD 

(d) ∠BAD 

(iii) The 4ᵗʰ term of an A.P. is 22 and the 15ᵗʰ term is 66. Find the first term and the common difference. Find the A.P. Hence find the sum of the series to 8 terms.

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(Section B)

(Attempt any four questions)

4

(i) Solve the given inequation and represent the solution set on the number line.
–3 + x ≤ 8x/3 + 2 ≤ 14/3 + 2x, where x ∈ I

(ii) A bag contains 5 white balls, 6 red balls and 9 green balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is:
(a) green ball
(b) a white or red ball
(c) Is neither a green ball nor a white ball 

(iii) Find the amount of bill for the following intra state transaction of goods/services: 

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5

(i) As observed from the top of a 100 meter high lighthouse, the angle of depression of two ships on opposite sides of it are 48° and 36° respectively. Find the distance between the 2 ships to the nearest metre. 

(ii) (a) Using the step deviation method, calculate the mean marks of the following distribution.
(b) State the modal class. 

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6

(i) The daily wage of 80 workers in a project are given below:

Use a graph paper to draw an ogive for the above distribution and estimate:

(a) The median wage of the workers

(b) The lower quartile wage of workers

(c) The number of workers who earn more than ₹625 daily

(ii) Five years ago, a woman’s age was the square of her son’s age. Ten years later her age will be twice that of her son’s age. Find:
(a) The age of the son five years ago
(b) The present age of the woman 

(iii) Shyam opened a recurring deposit account in a bank. He deposited ₹2500 per month for two years. At the time of maturity he got ₹67,500. Find:
(a) the total interest earned by Shyam
(b) the rate of interest per annum [3]

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7

(i) The first term of a G.P. is 1. The sum of its third and fifth terms is 90. Find the common ratio of the G.P. [3]

(ii) The coordinates of the vertex A of a square ABCD are (1, 2) and the equation of the diagonal BD is x + 2y = 10. Find the equation of the other diagonal and the coordinates of the point of intersection of the two diagonals. [3]

(iii) A mathematics aptitude test of 50 students was recorded as follows:

Draw a histogram for the above data using a graph paper and hence locate the mode.

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8

(i) Construct a ΔABC with BC = 5.8 cm, AB = 5.4 cm and ∠ABC = 120°. Construct its circumcircle. Measure and record its radius. 

(ii) Given that
(x³ + 3xy²) / (y³ + 3x²y) = 63 / 62.
Find the value of x / y. 

(iii) A vessel in the form of an inverted cone is filled with water to the brim. Its height is equal to 20 cm and diameter is 16.8 cm. Two equal solid cones are dropped in it so that they are fully submerged. As a result, 1/3 of the water in the original cone overflows. What is the volume of each of the solid cones submerged? 

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9

(i) Construct a triangle ABC in which ∠ABC = 75°, AB = 5 cm and BC = 6.4 cm. Draw perpendicular bisector of side BC and also the bisector of ∠ACB. If these points intersect each other at Point P, prove that P is equidistant from B and C; and also from AC and BC. 

(ii) Ravi invested rupees 8000 in 7%, ₹100 shares at ₹80. After a year he sold these shares at ₹75 each and invested the proceeds (including the dividend) in 18%, ₹25 shares at ₹41. Find:
(a) His dividend for the first year
(b) His annual income in the second year

 (c) The percentage increase in his return on his original investment.

(iii) Solve the given quadratic equation correct to two significant figures.
x – 18/x = 6, x ≠ 0

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10

(i) A = 4–2;6–34 –2 ; 6 –34–2;6–3,
B = 02;1–10 2 ; 1 –102;1–1 and
C = –23;–1–1–2 3 ; –1 –1–23;–1–1

Find A² – A + BC 

(ii) In the above figure, ABC and CEF are two triangles where BA is parallel to CE and AF : AC is equal to 5 : 8.
(a) Prove that ΔADF ~ ΔCEF.
(b) Find AD if CE = 6 cm.
(c) If DF is parallel to BC, find A(ΔADF) : A(ΔABC) 

(iii) Prove that

√((1 + sin A)/(1 – sin A)) – √((1 – sin A)/(1 + sin A)) = 2 tan A

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ICSE Class 10 Maths Exam Prelim Question Paper 2026 PDF

Subject Name

Percentage Marks - External Exams (%)

Percentage Marks - Internal Exams (%)

Maths

80%

20%