ICSE Maths 2022

ICSE Class 10 Maths 2022 — all 35 questions from the paper

The complete question list from the ICSE Class 10 Mathematics 2022 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 2022 paper

1. Q1.The nature of roots of the quadratic equation 2x² − 3x + 1 = 0 is:A) Two distinct real rootsB) Two equal real rootsC) No real rootsD) Cannot be determined
2. Q2.Priya deposits ₹200 per month for 3 years in a bank's recurring deposit scheme at 10% p.a. The total deposit amount is:A) ₹6,000B) ₹7,200C) ₹7,800D) ₹8,400
3. Q3.A die is thrown once. The probability of getting a number greater than 4 is:A) 1/3B) 2/3C) 1/6D) 1/2
4. Q4.The y-intercept of the line 2x − 3y + 6 = 0 is:A) 2B) −2C) 3D) −3
5. Q5.If A = [[1, 2], [3, 4]], the order of the matrix is:A) 2 × 2B) 2 × 1C) 1 × 2D) 4 × 1
6. Q6.If two chords of a circle intersect internally, then the product of their segments are:A) EqualB) UnequalC) Proportional to radiiD) Zero
7. Q7.If 2x³ + ax² − 11x + b leaves remainder 0 when divided by (x − 2) and remainder −42 when divided by (x + 3), find a.A) 3B) −3C) 5D) −5
8. Q8.A man invests ₹20,000 in ₹100 shares of a company at ₹125. The company pays a dividend of 10%. His return percentage on investment is:A) 8%B) 10%C) 12.5%D) 6%
9. Q9.The value of sin 60° cos 30° + cos 60° sin 30° is:A) 0B) 1C) 1/2D) √3/2
10. Q10.The curved surface area of a cylinder with radius 7 cm and height 10 cm is:A) 440 cm²B) 220 cm²C) 880 cm²D) 308 cm²
11. Q11.If x/2 = y/3 = z/5, then (x + y + z)/z equals:A) 2B) 10/5C) 5D) 10
12. Q12.Solve: 3x + 5 < 4x − 2, x ∈ R. The solution is:A) x > 7B) x < 7C) x > 3D) x < 3
13. Q13.A manufacturer sells goods to a dealer for ₹6,000. The dealer sells them to a retailer for ₹8,000. If GST is 15%, the GST paid by the dealer to the government is:A) ₹300B) ₹900C) ₹1,200D) ₹200
14. Q14.The median of the data 5, 7, 9, 11, 15, 17, 20 is:A) 9B) 11C) 15D) 12
15. Q15.The distance of the point (3, 4) from the origin is:A) 5B) 7C) 1D) 25
16. Q16.Solve: x² + 7x − 18 = 0. The roots are:A) x = 2 and x = −9B) x = −2 and x = 9C) x = 3 and x = −6D) x = 6 and x = −3
17. Q17.How many terms of the AP 24, 20, 16, ... must be taken so that the sum is 72?A) 4B) 6C) 8D) 3
18. Q18.If M = [[2, 1], [0, −3]], find M². The element in the first row, second column of M² is:A) −1B) 1C) −2D) 5
19. Q19.Find the centroid of the triangle with vertices A(1, 2), B(3, −4), and C(5, 6).A) (3, 4/3)B) (3, 2)C) (9, 4)D) (3, 0)
20. Q20.If a/b = c/d = 3/4, find the value of (3a + 4c)/(3b + 4d).A) 3/4B) 4/3C) 9/16D) 12/16
21. Q21.A manufacturer buys raw materials worth ₹7,500 (before GST) and sells the finished goods for ₹12,000 (before GST). If the rate of GST is 18%, the tax liability of the manufacturer is:A) ₹810B) ₹2,160C) ₹1,350D) ₹3,510
22. Q22.Using a histogram, estimate the mode of the following distribution:
    
    Class: 10-20, 20-30, 30-40, 40-50, 50-60
    Frequency: 4, 8, 14, 8, 6
    
    The modal class is:A) 10-20B) 20-30C) 30-40D) 40-50
23. Q23.A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder of height 32 cm. The radius of the cylinder is:A) 3 cmB) 4 cmC) 6 cmD) 2 cm
24. Q24.Without using tables, evaluate: cos 70°/sin 20° + cos 57°/sin 33°.A) 1B) 2C) 0D) √2
25. Q25.A box contains 3 red, 5 black, and 2 white balls. A ball is drawn at random. What is the probability of drawing a black or white ball?A) 7/10B) 1/2C) 3/10D) 2/5
26. Q26.Prove: (cosec θ − sin θ)(sec θ − cos θ) = 1/(tan θ + cot θ). The LHS simplifies to:A) sin θ cos θB) 1/(sin θ cos θ)C) tan θ cot θD) sin²θ cos²θ
27. Q27.The line segment joining P(5, −2) and Q(9, 6) has its perpendicular bisector. The equation of the perpendicular bisector is:A) x + 2y − 11 = 0B) 2x + y − 11 = 0C) x + 2y + 11 = 0D) x − 2y − 11 = 0
28. Q28.Mr. Sharma has 200 shares of face value ₹25. The company declares a dividend of 9%. Mr. Sharma's dividend income is:A) ₹450B) ₹500C) ₹360D) ₹225
29. Q29.Sonia deposits ₹750 per month for 2 years in a recurring deposit at 8% p.a. Her maturity value is:A) ₹19,500B) ₹19,200C) ₹20,100D) ₹18,750
30. Q30.Solve the inequation: −1 ≤ 3 + 4x < 23, x ∈ Z. The solution set is:A) {−1, 0, 1, 2, 3, 4}B) {0, 1, 2, 3, 4}C) {−1, 0, 1, 2, 3, 4, 5}D) {0, 1, 2, 3, 4, 5}
31. Q31.Construct a △ABC where AB = 6.5 cm, BC = 5.5 cm, AC = 5 cm. Draw the incircle of the triangle. The construction requires drawing:A) Angle bisectors of all three anglesB) Perpendicular bisectors of all three sidesC) Altitudes from all three verticesD) Medians from all three vertices
32. Q32.The angles of elevation of the top of a tower from two points at distances 4 m and 9 m from the base (on the same side) are complementary. The height of the tower is:A) 6 mB) 36 mC) 13 mD) √13 m
33. Q33.In the given figure, PA and PB are tangents to the circle from external point P. If PA = 12 cm and ∠APB = 60°, the length of AB is:A) 12 cmB) 6 cmC) 12√3 cmD) 6√3 cm
34. Q34.A bucket is in the shape of a frustum of a cone with top radius 14 cm, bottom radius 7 cm, and height 30 cm. The volume of the bucket is:A) 10,780 cm³B) 15,400 cm³C) 7,546 cm³D) 12,320 cm³
35. Q35.If x − 2 is a factor of f(x) = x³ − kx² − 4x + 4k, find k. Then factorize f(x) completely.A) k = 1, f(x) = (x − 2)(x + 2)(x − 1)B) k = 2, f(x) = (x − 2)²(x + 2)C) k = −1, f(x) = (x − 2)(x + 2)(x + 1)D) k = 3, f(x) = (x − 2)(x − 3)(x + 2)

Worked solutions from the ICSE 2022 paper

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