ICSE question bank

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444 questions

Class 10 · Mathematics
The marks of 200 students in a test were recorded as follows:
Marks % 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100
No. of
5 7 11 20 40 52 36 15 9 5
students
Using a graph sheet draw ogive for the given data and use it to find the:
(a) median.
(b) number of students who obtained more than 65% marks. Analysis &
(c) number of students who did not pass, if the pass percentage was 35. Evaluation]
5 marksDiagram based
Class 10 · Mathematics
Choose the correct answers to the questions from the given options. [15] (Do not copy the question, write the correct answers only.)
The sum of money required to buy 50, ₹ 40 shares at ₹ 38.50 is:
MCQ
Class 10 · Mathematics
1 1 1 0
Given matrix, X = � � a I = � �, prove that X 2 = 4X + 5I.
8 3 0 1
3 marksShort answer
Class 10 · Mathematics
While factorizing a given polynomial, using remainder & factor theorem,
a student finds that (2x + 1) is a factor of 2x3 + 7x2 + 2x – 3.
(a) Is the student’s solution correct stating that (2x + 1) is a factor of the
given polynomial?
(b) Give a valid reason for your answer.
4 marksLong answer
Class 10 · Mathematics
Use a graph sheet for this question. Take 1 cm = 1 unit along both the x and
y axis. Plot ABCDE, where A (4, 0), B (4, 2), C (2, 2), D (2,4) and E (0,4).
(a) Reflect the points A, B, C and D on the y-axis and name them as F, G,
H and I respectively.
(b) Join the points A, B, C, D, E, I, H, G and F in order. Reflect the figure
ABCDEIHGF on the x-axis and name it as AMNPQRSTF.
(c) Give the geometrical name of the closed figure AEFQ.
ICSE 2026 SPECIMEN
4 marksLong answer
Class 10 · Mathematics
Find the coordinates of the centroid P of the ∆ABC, whose vertices are
A(–1, 3), B(3, –1) and C(0, 0). Hence, find the equation of a line passing
3 marksShort answer
Class 10 · Mathematics
Ms. Kaur invested ₹ 8,000 in buying ₹100 shares of a company paying 6%
dividend at ₹ 80. After a year, she sold these shares at ₹75 each and invested
the proceeds including the dividend received during the first year in buying
₹ 20 shares, paying 15% dividend at ₹ 27 each. Find the:
(a) dividend received by her during the first year. Application &
(b) number of shares purchased by her using the total proceeds. Evaluation]
3 marksShort answer
Class 10 · Mathematics
Choose the correct answers to the questions from the given options. [15] (Do not copy the question, write the correct answers only.)
A mixture of paint is prepared by mixing 2 parts of red pigments with 5
parts of the base. Using the given information in the following table, find
the values of a, b & c to get the required mixture of paint.
Parts of red pigment 2 4 b 6
Parts of base 5 a 12.5 c
(a) a = 10, b = 10, c = 10
(b) a = 5, b = 2, c = 5
(c) a = 10, b = 5, c = 10
Short answer
Class 10 · Mathematics
The sum of the squares of three consecutive even numbers is 596. Find the
numbers.
3 marksShort answer
Class 10 · Mathematics
Choose the correct answers to the questions from the given options. [15] (Do not copy the question, write the correct answers only.)
(x - 2) and (x + 2) are the factors of x 3 + x 2 - 4x - 4. The third
factor of the given polynomial is:
MCQ
Class 10 · Mathematics
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first
8 terms is twice the sum of the first 5 terms. Find the common difference of
3 marksShort answer
Class 10 · Mathematics
In the given figure (not drawn to scale) chords AD and BC intersect at P,
where AB = 9 cm, PB = 3 cm and PD = 2 cm.
A
P C
B D
(a) Prove that ∆APB ~ ∆CPD.
(b) Find the length of CD.
3 marksShort answer
Class 10 · Mathematics
Choose the correct answers to the questions from the given options. [15] (Do not copy the question, write the correct answers only.)
Assertion (A): If s + t = a a s - t = b then ab =1
Reason (R): s 2 θ - t2 θ = 1
(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).
Assertion–reason
Class 10 · Mathematics
The following bill shows the GST rate and the marked price of articles:
Rajdhani Departmental Store
S. No. Item Marked Discount Rate of
Price GST
(a) Dry fruits (1 kg) ₹ 1200 ₹100 12%
(b) Packed Wheat flour (5kg) ₹ 286 Nil 5%
(c) Bakery products ₹ 500 10% 12%
Find the total amount to be paid (including GST) for the above bill.
4 marksLong answer
Class 10 · Mathematics
Choose the correct answers to the questions from the given options. [15] (Do not copy the question, write the correct answers only.)
Given that the sum of the squares of the first seven natural numbers is
140, then their mean is:
(a) 20
(b) 70
(c) 280
Short answer
Class 10 · Mathematics
A manufacturing company prepares spherical ball bearings, each of radius
7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box
can have a maximum of 2156 cm³ of ball bearings. Find the:
(a) maximum number of ball bearings that each box can have.
4 marksLong answer
Class 10 · Mathematics
Draw the necessary diagram for this question.
A man on the top of a lighthouse observes the angle of depression of two
ships on the opposite sides of the lighthouse as 30° and 50° respectively. If
the height of the lighthouse is 80m, find the distance between the two ships.
5 marksDiagram based
Class 10 · Mathematics
Prove the following trigonometry identity:
(sinθ + cosθ) (cosecθ – secθ) = cosecθ.secθ – 2 tanθ
4 marksLong answer
Class 10 · Mathematics
The roots of equation (q – r) x2 + (r – p) x + (p - q) = 0 are equal.
4 marksLong answer
Class 10 · Mathematics
Choose the correct answers to the questions from the given options. [15] (Do not copy the question, write the correct answers only.)
A solid sphere is cut into two identical hemispheres.
Assertion (A): The total volume of two hemispheres is equal to the volume
of the original sphere.
Reason (R): The total surface area of two hemispheres together is equal
to the surface area of the original sphere.
MCQ