ICSE Class 10 Question Paper 2024 Mathematics

ICSE
QUESTION
PAPER
2024

U DY MA
S TE
E
R
S

IA
IC

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MATHEMATICS

Maximum Marks: 80

Time allowed: Two and half hours

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

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

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

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

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

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

Omission of essential working will result in loss of marks.

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

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

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) For an Intra-state sale, the CGST paid by a dealer to the Central government is
` 120. If the marked price of the article is ` 2000, the rate of GST is:

(a) 6%

(b) 10%

(c) 12%

(d) 16.67%

This paper consists of 12 printed pages.
T24 511 Turn Over
© Copyright reserved.

(ii) What must be subtracted from the polynomial x3 + x2 – 2x + 1, so that the result is
exactly divisible by (x – 3)?

(a) – 31

(b) – 30

(c) 30

(d) 31

(iii) The roots of the quadratic equation px2 – qx + r = 0 are real and equal if:

(a) p2 = 4qr

(b) q2 = 4pr

(c) – q2 = 4pr

(d) p2 > 4qr

(iv) 2 2 4 𝑥𝑥
If matrix 𝐴𝐴 = � � and 𝐴𝐴2 = � �, then the value of x is:
0 2 0 4
(a) 2

(b) 4

(c) 8

(d) 10

(v) The median of the following observations arranged in ascending order is 64.
Find the value of x:
27, 31, 46, 52, x, x + 4, 71, 79, 85, 90
(a) 60

(b) 61

(c) 62

(d) 66

(vi) Points A (x, y), B (3, -2) and C (4, -5) are collinear. The value of y in terms of x is∶

(a) 3x – 11

(b) 11 - 3x

(c) 3x – 7

(d) 7 – 3x
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(vii) The given table shows the distance covered and the time taken by a train moving
at a uniform speed along a straight track.

Distance (in m) 60 90 y
Time (in sec) 2 x 5

The values of x and y are:

(a) x = 4, y = 150

(b) x = 3, y = 100

(c) x = 4, y = 100

(d) x = 3, y = 150

(viii) The 7th term of the given Arithmetic Progression (A.P.):
1 1 1
, � + 1� , � + 2� … is:
𝑎𝑎 𝑎𝑎 𝑎𝑎
1
(a) � + 6�
𝑎𝑎
1
(b) � + 7�
𝑎𝑎
1
(c) � + 8�
𝑎𝑎
1
(d) � + 77 �
𝑎𝑎
(ix) The sum invested to purchase 15 shares of a company of nominal value ` 75 available
at a discount of 20% is:

(a) ` 60

(b) ` 90

(c) ` 1350

(d) ` 900

(x) The circumcentre of a triangle is the point which is∶

(a) at equal distance from the three sides of the triangle.

(b) at equal distance from the three vertices of the triangle.

(c) the point of intersection of the three medians.

(d) the point of intersection of the three altitudes of the triangle.
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(xi) Statement 1: sin2 𝜃𝜃 + cos2 𝜃𝜃 = 1
Statement 2: cosec 2 𝜃𝜃 + cot 2 𝜃𝜃 = 1
Which of the following is valid?

(a) only 1

(b) only 2

(c) both 1 and 2

(d) neither 1 nor 2

(xii) In the given diagram, PS and PT are the tangents to the circle. SQ || PT and
∠SPT = 80°. The value of ∠QST is:

(a) 140°

(b) 90°

(c) 80°

(d) 50°

(xiii) Assertion (A): A die is thrown once and the probability of getting an even
𝟐𝟐
number is .
𝟑𝟑
Reason (R): The sample space for even numbers on a die is {2, 4, 6}

(a) A is true, R is false.

(b) A is false, R is true.

(c) Both A and R are true.

(d) Both A and R and false.

(xiv) A rectangular sheet of paper of size 11 cm x 7 cm is first rotated about the side
11 cm and then about the side 7 cm to form a cylinder, as shown in the diagram.
The ratio of their curved surface areas is:

(a) 1∶1

(b) 7 ∶ 11

(c) 11 ∶ 7
11𝜋𝜋 7𝜋𝜋
(d) ∶
7 11

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(xv) In the given diagram, ∆ABC ∼ ∆PQR. If AD and PS are bisectors of ∠BAC and
∠QPR respectively then:

(a) ∆ABC ∼ ∆PQS

(b) ∆ABD ∼ ∆PQS

(c) ∆ABD ∼ ∆PSR

(d) ∆ABC ∼ ∆PSR

Question 2

(i) 𝑥𝑥 0 4 0 4 0 [4]
𝐴𝐴 = � � , 𝐵𝐵 = � � 𝑎𝑎𝑎𝑎𝑎𝑎 𝐶𝐶 = � �
1 1 𝑦𝑦 1 𝑥𝑥 1
Find the values of x and y, if AB = C.

(ii) A solid metallic cylinder is cut into two identical halves along its height (as shown [4]
in the diagram). The diameter of the cylinder is 7 cm and the height is 10 cm. Find:
(a) The total surface area (both the halves).
(b) The total cost of painting the two halves at the rate of ` 30 per cm2
𝟐𝟐𝟐𝟐
�𝑼𝑼𝑼𝑼𝑼𝑼 𝝅𝝅 = 𝟕𝟕 �

(iii) 15, 30, 60, 120… are in G.P. (Geometric Progression). [4]

(a) Find the nth term of this G.P. in terms of n.

(b) How many terms of the above G.P. will give the sum 945?

Question 3

(i) Factorize: 𝑠𝑠𝑠𝑠𝑠𝑠3 𝜃𝜃 + 𝑐𝑐𝑐𝑐𝑐𝑐 3 𝜃𝜃 [4]
Hence, prove the following identity:
𝑠𝑠𝑠𝑠𝑠𝑠3 𝜃𝜃 + cos 3 𝜃𝜃
+ sin 𝜃𝜃𝜃𝜃𝜃𝜃𝜃𝜃𝜃𝜃 = 1
sin 𝜃𝜃 + cos 𝜃𝜃

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(ii) In the given diagram, O is the centre of the circle. PR and PT are two tangents [4]
drawn from the external point P and touching the circle at Q and S respectively.
MN is a diameter of the circle. Given ∠PQM = 42o and ∠PSM = 25o.

Find:

(a) ∠OQM

(b) ∠QNS

(c) ∠QOS

(d) ∠QMS

(iii) Use graph sheet for this question. Take 2 cm = 1 unit along the axes. [5]

(a) Plot A(0, 3), B(2, 1) and C(4, -1).

(b) Reflect point B and C in y-axis and name their images as B' and C'
respectively. Plot and write coordinates of the points B' and C'.

(c) Reflect point A in the line BB' and name its images as A'.

(d) Plot and write coordinates of point A'.

(e) Join the points ABA'B' and give the geometrical name of the closed figure so
formed.

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

Question 4
(i) Suresh has a recurring deposit account in a bank. He deposits ` 2000 per month and the [3]
bank pays interest at the rate of 8% per annum. If he gets ` 1040 as interest at the time of
maturity, find in years total time for which the account was held.

(ii) The following table gives the duration of movies in minutes. [3]
Duration
100 – 110 110 – 120 120 – 130 130 – 140 140 – 150 150 – 160
(in minutes)
No. of
5 10 17 8 6 4
movies
Using step – deviation method, find the mean duration of the movies.
T24 511 6

(iii) (𝑎𝑎 + 𝑏𝑏)3 64 [4]
𝐼𝐼𝐼𝐼 =
(𝑎𝑎 − 𝑏𝑏)3 27
𝑎𝑎 + 𝑏𝑏
(a) Find
𝑎𝑎 − 𝑏𝑏
(b) Hence using properties of proportion, find a : b.

Question 5

(i) The given graph with a histogram represents the number of plants of different heights [5]
grown in a school campus. Study the graph carefully and answer the following questions:

(a) Make a frequency table with respect to the class boundaries and their corresponding
frequencies.

(b) State the modal class.

(c) Identify and note down the mode of the distribution.

(d) Find the number of plants whose height range is between 80 cm to 90 cm.
T24 511 7 Turn Over

(ii) The angle of elevation of the top of a 100 m high tree from two points A and B on the [5]
opposite side of the tree are 52o and 45o respectively. Find the distance AB, to the nearest
metre.

Question 6

(i) Solve the following quadratic equation for x and give your answer correct to three [3]
significant figures: 𝟐𝟐𝒙𝒙𝟐𝟐 – 𝟏𝟏𝟏𝟏𝟏𝟏 + 𝟓𝟓 = 𝟎𝟎
(Use mathematical tables if necessary)

(ii) The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 – n). [3]
Find∶

(a) its first term and common difference

(b) sum of its first 25 terms

(iii) In the given diagram ∆ADB and ∆ACB are two right angled triangles with [4]
∠ADB = ∠BCA = 90o. If AB = 10 cm, AD = 6 cm, BC = 2.4 cm and DP = 4.5 cm

(a) Prove that ∆APD ∼ ∆BPC

(b) Find the length of BD and PB

(c) Hence, find the length of PA

(d) Find area ∆APD : area ∆BPC
T24 511 8

Question 7

(i) In the given diagram, an isosceles ∆ABC is inscribed in a circle with centre O. [3]
PQ is a tangent to the circle at C. OM is perpendicular to chord AC and ∠COM = 65°.

Find:

(a) ∠ABC

(b) ∠BAC

(c) ∠BCQ

(ii) Solve the following inequation, write down the solution set and represent it on the real [3]
number line.
7𝑥𝑥
−3 + 𝑥𝑥 ≤ + 2 < 8 + 2𝑥𝑥, 𝑥𝑥 𝜖𝜖 𝐼𝐼
2

(iii) In the given diagram, ABC is a triangle, where B(4,– 4) and C(– 4, – 2). D is a point on [4]
AC.

(a) Write down the coordinates
of A and D.

(b) Find the coordinates of the
centroid of ∆ABC.

(c) If D divides AC in the ratio
k : 1, find the value of k.

(d) Find the equation of the line
BD.

T24 511 9 Turn Over

Question 8

(i) The polynomial 3x3 + 8x2 – 15x + k has (x – 1) as a factor. Find the value of k. Hence [3]
factorize the resulting polynomial completely.

(ii) The following letters A, D, M, N, O, S, U, Y of the English alphabet are written on separate [3]
cards and put in a box. The cards are well shuffled and one card is drawn at random. What
is the probability that the card drawn is a letter of the word,

(a) MONDAY?

(b) which does not appear in MONDAY?

(c) which appears both in SUNDAY and MONDAY?

(iii) Oil is stored in a spherical vessel occupying 3/4 of its full capacity. Radius of this spherical [4]
vessel is 28 cm. This oil is then poured into a cylindrical vessel with a radius of 21 cm.
Find the height of the oil in the cylindrical vessel (correct to the nearest cm).
𝟐𝟐𝟐𝟐
𝑻𝑻𝑻𝑻𝑻𝑻𝑻𝑻 𝝅𝝅 =
𝟕𝟕

Question 9

(i) The figure shows a circle of radius 9 cm with O as the centre. The diameter AB produced [3]
meets the tangent PQ at P. If PA = 24 cm, find the length of tangent PQ.

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(ii) Mr. Gupta invested ` 33000 in buying ` 100 shares of a company at 10% premium. The [3]
dividend declared by the company is 12%. Find:

(a) the number of shares purchased by him.

(b) his annual dividend.

(iii) A life insurance agent found the following data for distribution of ages of 100 policy [4]
holders:

Age in years Policy Holders Cumulative frequency
(frequency)
20 – 25 2 2
25 – 30 4 6
30 – 35 12 18
35 – 40 20 38
40 – 45 28 66
45 – 50 22 88
50 – 55 8 96
55 – 60 4 100

On a graph sheet draw an ogive using the given data. Take 2 cm = 5 years along one axis
and 2 cm = 10 policy holders along the other axis. Use your graph to find:

(a) The median age.

(b) Number of policy holders whose age is above 52 years.

Question 10
(i) Rohan bought the following eatables for his friends : [3]

Soham Sweet Mart : Bill
S. No. Item Price Quantity Rate of GST
1 Laddu ` 500 per kg 2 kg 5%
2 Pastries ` 100 per piece 12 pieces 18%

Calculate :
(a) Total GST paid.

(b) Total bill amount including GST.

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(ii) (a) If the lines kx – y + 4 = 0 and 2y = 6x + 7 are perpendicular to each other, find the [3]
value of k.

(b) Find the equation of a line parallel to 2y = 6x + 7 and passing through (–1, 1)

(iii) Use ruler and compass to answer this question. Construct ∠ABC = 90o, where [4]
AB = 6 cm, BC = 8 cm.

(a) Construct the locus of points equidistant from B and C.

(b) Construct the locus of points equidistant from A and B.

(c) Mark the point which satisfies both the conditions (a) and (b) as O. Construct the
locus of points keeping a fixed distance OA from the fixed point O.

(d) Construct the locus of points which are equidistant from BA and BC.

T24 511 12

CISCE STUDY MATERIAL

ICSE ISC

INFORMATION CLASS STUDY MATERIAL

1 Time Table 9 Specimen Paper
10 Specimen Paper
2 Result
11 Specimen Paper
3 Syllabus 12 Specimen Paper

OTHER RESOURCES
10 Question Paper
Maps of India, Maps of World
Writing Skill Formats 12 Question Paper
Periodic Table
9/10 Lab Manuals
BOOKS 11/12 Lab Manuals
ICSE Class 10 Prescribed Books
ISC Class 12 Prescribed Books
ISC Class 12 Project Work

ENTRANCE EXAMS

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