ICSE Maths 2023

ICSE Class 10 Maths 2023 — all 35 questions from the paper

The complete question list from the ICSE Class 10 Mathematics 2023 board examination is below. Every question can be attempted in the timed interactive test above, with visual step-by-step solutions and AI coaching after each answer. Three fully worked solutions from this paper follow the question list.

Questions from the 2023 paper

1. Q1.If one root of the equation x² + px + 12 = 0 is 4, then the value of p is:A) −7B) 7C) −4D) 4
2. Q2.Anu deposits ₹1,000 per month in a recurring deposit for 9 months at 6% p.a. The interest she earns is:A) ₹225B) ₹200C) ₹250D) ₹270
3. Q3.A card is drawn from a well-shuffled deck of 52 cards. The probability of getting a red face card is:A) 6/52B) 3/26C) 3/13D) 1/13
4. Q4.The point (3, −4) lies in which quadrant?A) First quadrantB) Second quadrantC) Third quadrantD) Fourth quadrant
5. Q5.If A is a 2×2 matrix such that A × [[1], [−1]] = [[3], [−1]], and A × [[0], [1]] = [[2], [5]], then A is:A) [[5, 2], [4, 5]]B) [[3, 2], [−1, 5]]C) [[1, 2], [−1, 5]]D) [[5, 2], [−1, 5]]
6. Q6.The angle subtended by a semicircle at any point on the circle is:A) 45°B) 60°C) 90°D) 180°
7. Q7.If (x + 2) is a factor of x³ + ax² + 4bx + 12 and a = 3, then b is:A) −1B) 1C) 2D) −2
8. Q8.Rohit invests ₹10,000 in ₹50 shares at a premium of ₹10. The number of shares he buys is:A) 100B) 200C) 167D) 250
9. Q9.If sec θ = 13/5, then the value of tan θ is:A) 12/5B) 5/12C) 12/13D) 5/13
10. Q10.The volume of a right circular cone with radius 7 cm and height 12 cm is:A) 616 cm³B) 308 cm³C) 1,848 cm³D) 924 cm³
11. Q11.If a : b = 3 : 5, then (2a + 3b) : (3a + 2b) is:A) 21:19B) 19:21C) 3:5D) 5:3
12. Q12.The solution set of 2x − 3 > x − 5, x ∈ N (natural numbers), when x < 4 is:A) {1, 2, 3}B) {0, 1, 2, 3}C) {1, 2, 3, 4}D) {−1, 0, 1, 2, 3}
13. Q13.A dealer in Kolkata buys goods worth ₹5,000 from a dealer in Mumbai. If IGST is 18%, the amount paid by the Kolkata dealer is:A) ₹5,900B) ₹5,450C) ₹5,500D) ₹6,000
14. Q14.The mode of the data: 3, 5, 7, 5, 9, 5, 3, 7, 5 is:A) 3B) 5C) 7D) 9
15. Q15.Two circles touch externally. If their radii are 5 cm and 3 cm, the distance between their centres is:A) 2 cmB) 8 cmC) 4 cmD) 15 cm
16. Q16.Solve: x² − 4x − 8 = 0 using the quadratic formula. The roots correct to 2 decimal places are:A) x = 5.46 and x = −1.46B) x = 4.83 and x = −0.83C) x = 6.00 and x = −2.00D) x = 5.00 and x = −1.00
17. Q17.The 4th term of a GP is 24 and the 7th term is 192. The common ratio is:A) 2B) 3C) 4D) 1/2
18. Q18.If A = [[2, −1], [3, 4]] and B = [[0, 3], [−1, 2]], find 2A − B.A) [[4, −5], [7, 6]]B) [[4, 1], [5, 6]]C) [[2, −4], [4, 2]]D) [[4, −5], [5, 10]]
19. Q19.Find the reflection of the point (3, −5) in the x-axis.A) (3, 5)B) (−3, 5)C) (−3, −5)D) (3, −5)
20. Q20.If (a² + b²)/(a² − b²) = 13/5, using componendo-dividendo, a/b equals:A) 3/2B) 2/3C) 9/4D) 4/9
21. Q21.A shopkeeper buys an article from a wholesaler for ₹2,000 and sells it to a consumer for ₹3,000. If SGST is 6%, the total tax (CGST + SGST) collected by the shopkeeper from the consumer is:A) ₹360B) ₹180C) ₹240D) ₹120
22. Q22.The mean of the following distribution is 50. Find the missing frequency f.
    
    Class: 0-20, 20-40, 40-60, 60-80, 80-100
    Frequency: 17, f, 32, f, 19
    
    The value of f is:A) 28B) 26C) 24D) 30
23. Q23.A solid sphere of radius 3 cm is melted and reformed into a solid right circular cone of height 4 cm. The radius of the cone is:A) 3 cmB) 4.5 cmC) 6 cmD) 9 cm
24. Q24.If sin(A + B) = 1 and cos(A − B) = √3/2, where 0° ≤ A + B ≤ 90°, find A and B.A) A = 60°, B = 30°B) A = 45°, B = 45°C) A = 75°, B = 15°D) A = 30°, B = 60°
25. Q25.A bag contains 4 white, 6 red, and 5 blue balls. Two balls are drawn at random. The probability that both are red is:A) 1/7B) 3/7C) 6/15D) 2/7
26. Q26.Prove that: (1 + cos θ)/sin θ + sin θ/(1 + cos θ) = 2 cosec θ. The LHS simplifies to:A) 2 cosec θB) 2 sec θC) cosec θ + cot θD) 2(1 + cos θ)/sin θ
27. Q27.The line 2x + y = 8 meets the x-axis at A and y-axis at B. Find the area of △AOB where O is the origin.A) 16 sq unitsB) 8 sq unitsC) 32 sq unitsD) 12 sq units
28. Q28.A man invests ₹22,500 in ₹50 shares available at 10% discount. If the dividend paid is 12%, his annual income is:A) ₹3,000B) ₹2,700C) ₹2,500D) ₹3,600
29. Q29.Ravi deposits ₹1,200 per month for 15 months in a recurring deposit at 5% p.a. His maturity amount is:A) ₹18,600B) ₹18,900C) ₹19,200D) ₹18,000
30. Q30.Solve the inequation −2 ≤ (1/2) − (2x/3) ≤ 1(5/6), x ∈ N. The solution set is:A) {1, 2}B) {1, 2, 3}C) {0, 1, 2}D) {1}
31. Q31.Construct a regular hexagon of side 4 cm. The circumradius of the hexagon is:A) 4 cmB) 8 cmC) 4√3 cmD) 2√3 cm
32. Q32.From the top of a cliff 80 m high, the angle of depression of a boat is 30°. The distance of the boat from the base of the cliff is:A) 80√3 mB) 80/√3 mC) 40√3 mD) 160 m
33. Q33.A chord of length 16 cm is at a distance of 6 cm from the centre of a circle. The radius of the circle is:A) 10 cmB) 8 cmC) 12 cmD) √292 cm
34. Q34.A wooden toy is in the shape of a cone mounted on a hemisphere. The radius is 3.5 cm and total height of the toy is 17.5 cm. The total surface area of the toy is:A) 214.5 cm²B) 228.65 cm²C) 192.5 cm²D) 245 cm²
35. Q35.Using the remainder theorem, find the remainder when x³ − 3x² + 4x − 7 is divided by (x − 2).A) −3B) 1C) 3D) −1

Worked solutions from the ICSE 2023 paper

Start the test above to see visual step-by-step solutions for all 35 questions — free, with AI coaching when you get stuck.