ICSE Maths 2018

ICSE Class 10 Maths 2018 — all 35 questions from the paper

The complete question list from the ICSE Class 10 Mathematics 2018 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 2018 paper

1. Q1.The roots of the equation x² + 2x − 15 = 0 are:A) x = 3 and x = −5B) x = −3 and x = 5C) x = 3 and x = 5D) x = −3 and x = −5
2. Q2.Ramesh deposits ₹300 per month for 2 years in a recurring deposit at 12% p.a. The interest he earns is:A) ₹900B) ₹720C) ₹600D) ₹1,080
3. Q3.From a bag containing 20 balls numbered 1 to 20, a ball is drawn. The probability that the number is a prime number is:A) 2/5B) 3/10C) 7/20D) 9/20
4. Q4.The distance between the points (2, 3) and (5, 7) is:A) 5B) 7C) 25D) √7
5. Q5.A matrix A has order 3 × 2. Matrix B has order 2 × 4. The order of AB is:A) 3 × 4B) 2 × 2C) 3 × 2D) 2 × 4
6. Q6.A tangent to a circle is perpendicular to the radius at the point of contact. If the radius is 5 cm and the tangent length from a point to the circle is 12 cm, the distance from the point to the centre is:A) 13 cmB) 17 cmC) 7 cmD) √119 cm
7. Q7.The remainder when 2x³ − 3x² + 7x − 8 is divided by (x − 1) is:A) −2B) 2C) −8D) 0
8. Q8.A man invests ₹4,500 in ₹10 shares at ₹15. If the dividend rate is 12%, his rate of return is:A) 8%B) 10%C) 12%D) 6%
9. Q9.If sin A = 1/2, then the value of 3 cos A − 4 cos³A is:A) 0B) 1C) −1D) 1/2
10. Q10.The volume of a sphere of diameter 42 cm is:A) 38,808 cm³B) 19,404 cm³C) 77,616 cm³D) 9,702 cm³
11. Q11.If a : b = 5 : 3, find (5a + 8b) : (6a − 7b).A) 49:9B) 7:3C) 49:3D) 7:1
12. Q12.If 5x − 3 ≤ 5 + 3x ≤ 4x + 2, x ∈ R, the solution set is:A) x ≤ 4 and x ≥ 3, i.e., 3 ≤ x ≤ 4B) x ≤ 3C) x ≥ 4D) No solution
13. Q13.A manufacturer sells a TV for ₹13,000 to a dealer. The dealer sells it to a consumer for ₹15,000. If SGST = CGST = 6%, the GST paid by the dealer to the government is:A) ₹240B) ₹120C) ₹360D) ₹180
14. Q14.The mean of the data 6, 8, 9, x, 13 is 9. The value of x is:A) 9B) 10C) 8D) 11
15. Q15.If the lines 2x + 3y = 5 and kx − 6y = 7 are parallel, then k equals:A) −4B) 4C) −3D) 3
16. Q16.Solve: 2x² − 5x − 3 = 0. The roots are:A) x = 3 and x = −1/2B) x = −3 and x = 1/2C) x = 3/2 and x = −1D) x = 5 and x = −3/2
17. Q17.Find the sum of the first 15 terms of the AP: 5, 11, 17, 23, ...A) 705B) 660C) 735D) 780
18. Q18.If A = [[4, −2], [6, −3]], find A². What type of matrix is A²?A) Null matrix (all zeros)B) Identity matrixC) Scalar matrixD) Diagonal matrix
19. Q19.Find the equation of the line perpendicular to 3x + y = 8 and passing through the midpoint of the line joining (1, 1) and (5, 3).A) x − 3y + 3 = 0B) x − 3y − 3 = 0C) 3x − y − 3 = 0D) x + 3y − 9 = 0
20. Q20.If a : b = c : d, show that (ma + nc)/(mb + nd) = a/b. This is called:A) Addendo propertyB) Componendo-DividendoC) InvertendoD) Property of equal ratios
21. Q21.A dealer buys an article for ₹7,500. He sells it to a consumer within the same state for ₹8,500. If GST is 8%, the amount of tax (SGST + CGST) the consumer pays is:A) ₹680B) ₹600C) ₹340D) ₹80
22. Q22.The following table gives marks of students in an exam:
    
    Marks: 30-35, 35-40, 40-45, 45-50, 50-55, 55-60
    Frequency: 14, 16, 18, 23, 18, 11
    
    The modal class is:A) 40-45B) 45-50C) 35-40D) 50-55
23. Q23.A metallic sphere of radius 10.5 cm is melted and recast into small cones of radius 3.5 cm and height 3 cm. The number of cones obtained is:A) 126B) 63C) 252D) 84
24. Q24.Prove that: tan²θ/(1 + tan²θ) + cot²θ/(1 + cot²θ) = 1. The expression tan²θ/(1 + tan²θ) equals:A) sin²θB) cos²θC) tan²θD) 1
25. Q25.A box contains 90 discs numbered 1 to 90. A disc is drawn at random. The probability that it bears a two-digit number divisible by 5 is:A) 17/90B) 1/5C) 4/15D) 9/45
26. Q26.If 4 sin θ − 3 cos θ = 0, find the value of (4 sin²θ − 3 cos²θ + 2)/(4 sin²θ + 3 cos²θ − 2).A) 1B) 2C) 29/23D) 17/13
27. Q27.The line 4x − 3y + 12 = 0 meets the x-axis at A. Find the equation of the line through A and perpendicular to the given line.A) 3x + 4y + 9 = 0B) 3x + 4y − 9 = 0C) 4x + 3y + 9 = 0D) 3x − 4y + 9 = 0
28. Q28.A man holds 300 shares of ₹25 each in a company paying 7.5% dividend. He sells the shares at ₹27.50 each and invests the proceeds in ₹50 shares at ₹33 paying 10% dividend. The change in his annual income is:A) Increase of ₹187.50B) Decrease of ₹187.50C) Increase of ₹250D) Decrease of ₹250
29. Q29.Vikram deposits ₹500 per month for 10 months at 10% p.a. His maturity value is:A) ₹5,229.17B) ₹5,250C) ₹5,000D) ₹5,500
30. Q30.Solve: 2x − 5 ≤ 5x + 4 < 11, x ∈ Z. The solution set is:A) {−3, −2, −1, 0, 1}B) {−2, −1, 0, 1}C) {−3, −2, −1, 0}D) {−3, −2, −1, 0, 1, 2}
31. Q31.Using ruler and compass, construct △ABC where AB = 5 cm, BC = 6 cm, AC = 7 cm. Then draw the incircle. The number of angle bisectors needed is:A) 2B) 3C) 1D) 0
32. Q32.Two poles of heights 6 m and 11 m stand on a plane ground. The distance between their feet is 12 m. The distance between their tops is:A) 13 mB) 14 mC) 11 mD) 12 m
33. Q33.In a circle with centre O, AB is a chord and ∠AOB = 80°. The ∠ACB where C is on the major arc is:A) 40°B) 80°C) 160°D) 100°
34. Q34.Water flows through a cylindrical pipe of diameter 7 cm at 5 m/s. In how many minutes will it fill a tank of dimensions 11 m × 7 m × 5 m?A) 200 minB) 100 minC) 150 minD) 250 min
35. Q35.Factorize: 2x³ − x² − 13x − 6.A) (x − 3)(2x + 1)(x + 2)B) (x + 3)(2x − 1)(x + 2)C) (x − 3)(2x − 1)(x − 2)D) (x + 3)(2x + 1)(x − 2)

Worked solutions from the ICSE 2018 paper

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