ICSE Maths 2020

ICSE Class 10 Maths 2020 — all 35 questions from the paper

The complete question list from the ICSE Class 10 Mathematics 2020 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 2020 paper

1. Q1.The sum of the roots of the equation 4x² − 8x + 3 = 0 is:A) 2B) −2C) 3/4D) −3/4
2. Q2.Mr. Roy deposits ₹500 per month for 2 years at 7% p.a. in a recurring deposit. His total deposit is:A) ₹12,000B) ₹14,000C) ₹10,000D) ₹6,000
3. Q3.Two coins are tossed simultaneously. The probability of getting at most one head is:A) 1/4B) 1/2C) 3/4D) 1
4. Q4.The inclination of the line y = √3 x + 5 is:A) 30°B) 45°C) 60°D) 90°
5. Q5.If A = [[3, 0], [0, 3]], then A is called a:A) Unit matrixB) Scalar matrixC) Null matrixD) Column matrix
6. Q6.In the figure, O is the centre of the circle. ∠AOB = 100°. The value of ∠ADB (where D is on the major arc) is:A) 50°B) 100°C) 130°D) 200°
7. Q7.When x³ − 2x² + kx + 5 is divided by (x − 1), the remainder is 7. The value of k is:A) 3B) 5C) −3D) −5
8. Q8.The market value of a ₹100 share paying 8% dividend is ₹80. The rate of return on investment is:A) 8%B) 10%C) 6.4%D) 12.5%
9. Q9.If tan θ = 3/4, and θ is acute, then cos θ is:A) 3/5B) 4/5C) 4/3D) 5/4
10. Q10.A solid right circular cone has base radius 7 cm and slant height 25 cm. Its curved surface area is:A) 550 cm²B) 275 cm²C) 440 cm²D) 1100 cm²
11. Q11.The third proportional to 4 and 8 is:A) 16B) 12C) 32D) 6
12. Q12.If −5 ≤ 2x − 3 < 7, x ∈ R, then:A) −1 ≤ x < 5B) −4 ≤ x < 2C) −1 < x ≤ 5D) −4 < x ≤ 2
13. Q13.A retailer buys goods for ₹4,000 and sells them for ₹5,000. If CGST rate is 9%, the SGST collected from the buyer is:A) ₹450B) ₹360C) ₹900D) ₹90
14. Q14.For the data 2, 5, 5, 7, 8, the range is:A) 6B) 5C) 3D) 10
15. Q15.The product of the roots of 5x² − 4x + 2 = 0 is:A) 4/5B) 2/5C) −4/5D) −2/5
16. Q16.Solve: 6x² + 11x − 10 = 0. The roots are:A) x = 2/3 and x = −5/2B) x = −2/3 and x = 5/2C) x = 5/3 and x = −2D) x = 2 and x = −5/3
17. Q17.The 5th term of an AP is 20 and the 8th term is 32. The first term is:A) 4B) 8C) 6D) 2
18. Q18.If P = [[2, 3], [5, −1]] and Q = [[1, −2], [−3, 4]], find PQ. The element at position (2,1) of PQ is:A) 8B) −8C) 2D) −2
19. Q19.Find the equation of the line through (−2, 3) with slope 4.A) 4x − y + 11 = 0B) 4x + y − 11 = 0C) 4x − y − 11 = 0D) x − 4y + 11 = 0
20. Q20.If a/b = b/c, prove that (a² + b²)/b² = (a + c)/c. This property is a consequence of:A) Continued proportionB) InvertendoC) AlternendoD) Direct proportion
21. Q21.A dealer buys a washing machine for ₹15,000 from a manufacturer. He marks it up by 20% and sells it to a consumer. If GST is 12%, the amount paid by the consumer is:A) ₹20,160B) ₹18,000C) ₹19,200D) ₹16,800
22. Q22.Find the mean of the following distribution:
    
    Class: 0-10, 10-20, 20-30, 30-40, 40-50
    Frequency: 8, 12, 10, 11, 9
    
    The mean is:A) 24B) 25C) 26D) 23
23. Q23.A right circular cylinder has radius 3.5 cm and height 14 cm. It is melted to form small cones of radius 1.75 cm and height 3 cm. The number of cones formed is:A) 16B) 18C) 20D) 24
24. Q24.If 7 sin²θ + 3 cos²θ = 4, find tan θ.A) 1/√3B) √3C) 1D) 1/2
25. Q25.Numbers 1 to 20 are written on cards. A card is drawn at random. The probability that the number is divisible by 3 or 5 is:A) 9/20B) 7/20C) 2/5D) 1/2
26. Q26.If cos θ/(1 − sin θ) + cos θ/(1 + sin θ) = 4, find θ (0° < θ < 90°).A) 30°B) 45°C) 60°D) 0°
27. Q27.Find the image of the point (4, −3) when reflected in the line y = 0.A) (4, 3)B) (−4, −3)C) (−4, 3)D) (4, −3)
28. Q28.Mr. Patel invests ₹16,000 in buying shares of face value ₹10 at a premium of ₹6. The company pays 15% dividend. His annual income is:A) ₹1,500B) ₹2,400C) ₹1,200D) ₹1,000
29. Q29.Aman has a recurring deposit of ₹1,500 per month at 8% for 6 months. The maturity value is:A) ₹9,210B) ₹9,420C) ₹9,000D) ₹9,150
30. Q30.Given: 2x + 1 > 5, and 3x − 1 < 11, x ∈ R. The solution set is:A) 2 < x < 4B) 2 ≤ x ≤ 4C) x > 2 and x < 4D) x ≥ 2 and x ≤ 4
31. Q31.Construct a △PQR with PQ = 7 cm, QR = 8 cm, and ∠PQR = 75°. Draw the circumscribed circle. The construction requires finding the:A) Circumcentre (intersection of perpendicular bisectors)B) Incentre (intersection of angle bisectors)C) Centroid (intersection of medians)D) Orthocentre (intersection of altitudes)
32. Q32.From the top of a building 60 m high, the angles of depression of the top and bottom of a lamp post are 30° and 60° respectively. The height of the lamp post is:A) 20 mB) 40 mC) 30 mD) 45 m
33. Q33.Two tangents PA and PB are drawn to a circle with centre O from an external point P. If ∠APB = 50°, then ∠AOB is:A) 130°B) 100°C) 50°D) 80°
34. Q34.A hollow sphere of internal radius 2 cm and external radius 4 cm is melted into a cone of base diameter 8 cm. The height of the cone is:A) 14 cmB) 7 cmC) 10.5 cmD) 3.5 cm
35. Q35.Using the factor theorem, show that (x − 3) is a factor of x³ − 7x + 6. The other factors are:A) (x − 1)(x + 2)B) (x + 1)(x − 2)C) (x − 1)(x − 2)D) (x + 1)(x + 2)

Worked solutions from the ICSE 2020 paper

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