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ICSE Class X Board Examination

ICSE Mathematics — Board Examination 2024

Board2024Subject code 511
Open source paper at oswaal360.com (opens in a new tab)
Board
ICSE Class X Board Examination
Class
Class 10
Subject
Mathematics
Year
2024
Total marks
Not verified
Duration
Not verified

Verification and rights

Follows the published ICSE syllabus structure and links back to the source, but has not been reconciled line by line against a Council document.

Imported board paper from Oswaal Books (reproduction of CISCE board paper) on 2026-08-29.

Questions in this paper

  1. 1((i))15] Distance (in m) 60 90 y Choose the correct answers to the questions from the given options. Time (in s) 2 x 5 (Do not copy the questions, write the correct answers The values of x and y are: only.) (a) x = 4, y = 150 (b) x = 3, y = 100
    For an Intra-state sale, the CGST paid by a dealer to (c) x = 4, y = 100 (d) x = 3, y = 150
    the Central government is ` 120. If the marked price (viii) The 7th term of the given Arithmetic Progression
    of the article is ` 2000, the rate of GST is: (A.P.):
  2. 1((ii))15] Distance (in m) 60 90 y Choose the correct answers to the questions from the given options. Time (in s) 2 x 5 (Do not copy the questions, write the correct answers The values of x and y are: only.) (a) x = 4, y = 150 (b) x = 3, y = 100
    What must be subtracted from the polynomial x3 +
    x2 – 2x +1, so that the result is exactly divisible by 1  1 
    (x – 3)? (a)   6  (b)   7 
    a  a 
    (a) – 31 (b) – 30
    1  1 7 
    (c) 30 (d) 31 (c)   8  (d)   7 
  3. 1((iii))15] Distance (in m) 60 90 y Choose the correct answers to the questions from the given options. Time (in s) 2 x 5 (Do not copy the questions, write the correct answers The values of x and y are: only.) (a) x = 4, y = 150 (b) x = 3, y = 100
    The roots of the quadratic equation px2 – qx + r = 0 a  a 
    are real and equal if: (ix) The sum invested to purchase 15 shares of a company
  4. 1((iv))15] Distance (in m) 60 90 y Choose the correct answers to the questions from the given options. Time (in s) 2 x 5 (Do not copy the questions, write the correct answers The values of x and y are: only.) (a) x = 4, y = 150 (b) x = 3, y = 100
    If matrix A =   and A2 =  , (c) ` 1350 (d) ` 900
    0 2  0 4  then the
  5. 1((x))15] Distance (in m) 60 90 y Choose the correct answers to the questions from the given options. Time (in s) 2 x 5 (Do not copy the questions, write the correct answers The values of x and y are: only.) (a) x = 4, y = 150 (b) x = 3, y = 100
    The circumcentre of a triangle is the point which is:
    value of x is: (a) at equal distance from the three sides of the
    (a) 2 (b) 4 triangle.
    (c) 8 (d) 10 (b) at equal distance from the three vertices of the
    triangle.
  6. 1((v))15] Distance (in m) 60 90 y Choose the correct answers to the questions from the given options. Time (in s) 2 x 5 (Do not copy the questions, write the correct answers The values of x and y are: only.) (a) x = 4, y = 150 (b) x = 3, y = 100
    The median of the following observations arranged
    in ascending order is 64. Find the value of x: (c) the point of intersection of the three medians.
    27, 31, 46, 52, x, x + 4, 71, 79, 85, 90 (d) the point of intersection of the three altitudes of
  7. 1((vi))15] Distance (in m) 60 90 y Choose the correct answers to the questions from the given options. Time (in s) 2 x 5 (Do not copy the questions, write the correct answers The values of x and y are: only.) (a) x = 4, y = 150 (b) x = 3, y = 100
    Points A (x, y), B (3, –2) and C (4, –5) are collinear. The Statement 2: cosec2 q + cot2 q = 1
    value of y in terms of x is: Which of the following is valid?
    (a) 3x – 11 (b) 11 – 3x (a) only 1 (b) only 2
    (c) both 1 and 2 (d) neither 1 nor 2
    (c) 3x – 7 (d) 7 – 3x
  8. 1((xii))15] Distance (in m) 60 90 y Choose the correct answers to the questions from the given options. Time (in s) 2 x 5 (Do not copy the questions, write the correct answers The values of x and y are: only.) (a) x = 4, y = 150 (b) x = 3, y = 100
    In the given diagram, PS and PT are the tangents to (iii) 15, 30, 60, 120... are in G.P. (Geometric Progression).
    the circle. SQ || PT (a) Find the nth term of this G.P. in terms of n.
    and ∠SPT = 80°. The (b) How many terms of the above G.P. will give the
    value of ∠QST is: sum 945?
    (a) 140° Question 3
    (b) 90° (i) Factorize: sin3q + cos3q
    (c) 80° Hence, prove the following identity:
    (d) 50° sin 3 cos3
     sincos 1    4 marks
  9. 1((xiii))15] Distance (in m) 60 90 y Choose the correct answers to the questions from the given options. Time (in s) 2 x 5 (Do not copy the questions, write the correct answers The values of x and y are: only.) (a) x = 4, y = 150 (b) x = 3, y = 100
    Assertion (A): A die is thrown once and the prob- sin cos
    2 (ii) In the given diagram, O is the centre of the circle.
    ability of getting an even number is .
    3 PR and PT are R
    Reason (R): The sample space for even numbers on two tangents
    a die is {2, 4, 6}. drawn from Q
  10. 1((xiv))15] Distance (in m) 60 90 y Choose the correct answers to the questions from the given options. Time (in s) 2 x 5 (Do not copy the questions, write the correct answers The values of x and y are: only.) (a) x = 4, y = 150 (b) x = 3, y = 100
    A rectangular sheet of paper of size 11 cm × 7 cm S respectively. M
    is first rotated about the side 11 cm and then about MN is a 25°
    P T
    the side 7 cm to form a cylinder, as shown in the dia- diameter of the S
    gram. The ratio of their curved surface areas is: circle. Given ∠PQM = 42° and ∠PSM = 25°.
    Find:    4 marks
  11. 1((iii) [cont.])15] Distance (in m) 60 90 y Choose the correct answers to the questions from the given options. Time (in s) 2 x 5 (Do not copy the questions, write the correct answers The values of x and y are: only.) (a) x = 4, y = 150 (b) x = 3, y = 100
    Use graph sheet for this question. Take 2 cm = 1 unit
    along the a
    11 cm 11 cm (a) Plot A(0, 3), B(2, 1) and C(4, –1).
    (a) 1:1 (b) 7:11 (b) Reflect point B and C in y-axis and name their
    11p 7 p images as B’ and C’ respectively. Plot and write
    (c) 11:7 (d) : coordinates of the points B’ and C’.
    7 11
    (c) Reflect point A in the line BB’ and name its    5 marks
  12. 1((xv))15] Distance (in m) 60 90 y Choose the correct answers to the questions from the given options. Time (in s) 2 x 5 (Do not copy the questions, write the correct answers The values of x and y are: only.) (a) x = 4, y = 150 (b) x = 3, y = 100
    In the given diagram, DABC ~ DPQR. If AD and PS images as A’.
    are bisectors of ∠BAC and ∠QPR respectively then: (d) Plot and write coordinates of point A’.
    A
    P (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.)
  13. 2((i))time for which the account was held. [3] x 0  4 0  4 0 
    A   ,B    and C    (ii) The following table gives the duration of movies in
    1 1  y 1  x 1 
    minutes.
    Find the values of x and y, if AB = C. Duration
    No. of movies    4 marks
  14. 2((ii))time for which the account was held. [3] x 0  4 0  4 0 
    A solid metallic cylinder is cut into two identical (in minutes)
    halves along its height (as shown in the diagram). 100 - 110 5
    The diameter of the cylinder is 7 cm and the height 110 - 120 10
    is 10 cm. Find: 120 - 130 17
    (a) the total surface area (both the halves). 130 - 140 8
    (b) the total cost of painting the two halves at the 140 - 150 6
     22 
    rate of 30 per cm2 Use p   150 - 160 4
     7 
    Using step - deviation method, find the mean
    duration of the movies.
    ( a  b )3 64
  15. 5((i))(a) Prove that DAPD ~ DBPC
    The given graph with a histogram represents the (b) Find the length of BD and PB
    number of plants of different heights in a school (c) Hence, find the length of PA
    campus. Study the graph carefully and answer the
    following questions: (d) Find area DAPD: area DBPC
  16. 7((i))In the given diagram, an isosceles DABC is inscribed
    in a circle with centre O. PQ is a tangent to the circle
    at C. OM is perpendicular to chord AC and ∠COM
    = 65°.
    Find:
    A
    P
    65° M
    O 65°
    B C
    (a) Make a frequency table with respect to the class
    boundaries and their corresponding frequencies.
    Q
    (b) State the modal class.
    (c) Identify and note down the mode of the (a) ∠ABC (b) ∠BAC
    distribution. (c) ∠BCQ
    (d) Find the number of plants whose height range is (ii) Solve the following in equation, write down the
    between 80 cm to 90 cm. solution set and represent it on the real number line.    3 marks
  17. 7((ii))The angle of elevation of the top of a 100 m high tree 7x
    from two points A and B on the opposite side of the 3  x   2  8  2 x , x  I
    tree are 52° and 45° respectively. Find the distance 2
    AB, to the nearest metre. (iii) In the given diagram, ABC is a triangle, where
    B(4,–4) and C(– 4, –2). D is a point on AC.
    y
    6 A    3 marks
  18. 6((i))Solve the following quadratic equation for x and 2
    give your answer correct up to three significant 1
    figures: 2x2 – 10x + 5 = 0 D
    x
    (Use mathematical tables if necessary) _6 _5 _4 _3 _2 _1
    _1 1 2 3 4 5 6
  19. 6((ii))The nth term of an Arithmetic Progression (A.P.) is
    _2
    given by the relation Tn = 6(7 – n).
    C( _ 4 _ 2)
    Find: _3
    (a) its first term and common difference _4
    (b) sum of its first 25 terms B(4, _ 4)    3 marks
  20. 6((iii))In the given diagram DADB and DACB are two right _5
    angled triangles with ∠ADB = ∠BCA = 90°. If AB = _6
    10 cm, AD = 6 cm, BC= 2.4 cm and DP = 4.5 cm    4 marks