ICSE Maths 2019

ICSE Class 10 Maths 2019 — all 35 questions from the paper

The complete question list from the ICSE Class 10 Mathematics 2019 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 2019 paper

1. Q1.If the equation (k − 2)x² − (k − 4)x − 2 = 0 has equal roots, the value of k is:A) 6B) 0C) −6D) 2
2. Q2.Meena has a cumulative deposit account. She deposits ₹640 per month for 4.5 years. If the rate is 12% p.a., her interest earned is:A) ₹8,208B) ₹7,200C) ₹9,360D) ₹6,480
3. Q3.From a pack of 52 cards, a card is drawn at random. The probability that the card is neither a king nor a queen is:A) 11/13B) 2/13C) 4/13D) 48/52
4. Q4.A line passes through (0, 3) and (−3, 0). Its equation is:A) x − y + 3 = 0B) x + y − 3 = 0C) x − y − 3 = 0D) x + y + 3 = 0
5. Q5.If B = [[0, −1], [1, 0]], then B² equals:A) [[−1, 0], [0, −1]]B) [[1, 0], [0, 1]]C) [[0, 1], [−1, 0]]D) [[0, −1], [1, 0]]
6. Q6.The exterior angle of a cyclic quadrilateral is equal to:A) The interior opposite angleB) The adjacent interior angleC) Half the opposite angleD) Twice the opposite angle
7. Q7.If (x − 3) and (x + 4) are both factors of x³ + ax² + bx + 24, then a + b equals:A) −2B) 2C) −10D) 10
8. Q8.Ravi invests ₹6,400 in ₹80 shares at a discount of ₹16. The number of shares he owns is:A) 80B) 100C) 50D) 64
9. Q9.If cos A = 4/5, then the value of 2 cos A − 3 tan A is:A) −17/20B) 17/20C) −7/4D) 7/4
10. Q10.The lateral surface area of a cylinder with diameter 14 cm and height 20 cm is:A) 880 cm²B) 440 cm²C) 1,760 cm²D) 308 cm²
11. Q11.The fourth proportional to 2, 4, and 5 is:A) 8B) 10C) 20D) 2.5
12. Q12.The solution set of 3x − 2 > 7, x ∈ N, is:A) {4, 5, 6, ...}B) {3, 4, 5, ...}C) {1, 2, 3}D) {3}
13. Q13.A shopkeeper buys goods worth ₹6,000 from a wholesaler and sells them to a consumer for ₹8,000. If SGST is 6%, the amount of SGST paid by the consumer is:A) ₹480B) ₹360C) ₹120D) ₹960
14. Q14.The mean of 8, 11, 6, 14, x, 13 is 11. The value of x is:A) 12B) 14C) 10D) 16
15. Q15.If a line has x-intercept 4 and y-intercept −3, its equation is:A) 3x − 4y − 12 = 0B) 3x − 4y + 12 = 0C) 4x − 3y − 12 = 0D) 4x + 3y − 12 = 0
16. Q16.Solve for x: x² − 5x + 6 = 0 by factorization. The roots are:A) x = 2 and x = 3B) x = −2 and x = −3C) x = 1 and x = 6D) x = −1 and x = −6
17. Q17.The 10th term of the AP 2, 7, 12, 17, ... is:A) 47B) 52C) 42D) 57
18. Q18.If A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 3]], find AB. The element at position (1,1) is:A) 4B) 2C) 6D) 8
19. Q19.The midpoint of the line segment joining A(−4, 2) and B(8, −6) is:A) (2, −2)B) (4, −4)C) (6, 4)D) (−2, 2)
20. Q20.If x/(b+c−a) = y/(c+a−b) = z/(a+b−c), show that (b−c)x + (c−a)y + (a−b)z = 0. This follows from:A) Property of equal ratiosB) Componendo-DividendoC) AlternendoD) Cross multiplication
21. Q21.Goods worth ₹10,000 are purchased from another state. IGST is 28%. The total amount paid including tax is:A) ₹12,800B) ₹11,400C) ₹13,600D) ₹10,280
22. Q22.Draw an ogive for the following distribution and estimate the median:
    
    Class: 0-10, 10-20, 20-30, 30-40, 40-50
    Frequency: 5, 10, 20, 10, 5
    
    The median is approximately:A) 25B) 20C) 30D) 22.5
23. Q23.A cylindrical can has base radius 14 cm and height 20 cm. How many litres of milk can it hold? (1 litre = 1000 cm³)A) 12.32 litresB) 17.60 litresC) 8.80 litresD) 6.16 litres
24. Q24.Without using tables, evaluate: (sin 35° cos 55° + cos 35° sin 55°)/(cosec²10° − tan²80°).A) 1B) 0C) 1/2D) 2
25. Q25.A bag contains 12 balls of which some are red. If 6 more red balls are added, the probability of drawing a red ball doubles. The number of red balls originally was:A) 3B) 4C) 5D) 6
26. Q26.Prove: (1 − cos²θ) sec²θ = tan²θ. What is (1 − cos²θ)?A) sin²θB) cos²θC) tan²θD) cot²θ
27. Q27.The line 3x + y − 9 = 0 meets the axes at A and B. Find the coordinates of A (x-intercept).A) (3, 0)B) (0, 9)C) (9, 0)D) (0, 3)
28. Q28.A man invests ₹9,600 in ₹100 shares at ₹80. If the company pays 15% dividend, his annual income from the shares is:A) ₹1,800B) ₹1,440C) ₹1,200D) ₹2,400
29. Q29.Mr. Jacob deposits ₹900 per month for 20 months at 9% p.a. in a recurring deposit. His interest earned is:A) ₹1,417.50B) ₹1,350C) ₹1,500D) ₹1,260
30. Q30.Solve the inequation: (2x − 1)/3 ≥ (3x − 2)/4 − (2 − x)/5. If x ∈ W (whole numbers) and x ≤ 8, the solution set is:A) {0, 1, 2, 3, 4, 5, 6, 7, 8}B) {1, 2, 3, 4, 5, 6, 7, 8}C) {0, 1, 2}D) {0, 1, 2, 3}
31. Q31.Construct a △ABC with BC = 6 cm, ∠B = 45°, and AB = 5 cm. Then construct a tangent to the circumscribed circle from a point P outside the circle. The angle in the semicircle used in this construction is:A) 90°B) 45°C) 60°D) 180°
32. Q32.A man standing on a cliff 125 m above the sea level observes a ship at an angle of depression of 30°. The distance of the ship from the base of the cliff is:A) 125√3 mB) 125/√3 mC) 250 mD) 62.5√3 m
33. Q33.In the figure, AB is a diameter and ∠BCD = 130°. Find ∠DBA.A) 40°B) 50°C) 60°D) 130°
34. Q34.A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius is 5 cm, height of cylinder is 13 cm, and total height is 30 cm. The total surface area of the toy is:A) 770 cm²B) 825.7 cm²C) 616 cm²D) 714 cm²
35. Q35.Factorize completely: x³ + x² − 4x − 4.A) (x + 1)(x + 2)(x − 2)B) (x − 1)(x + 2)(x − 2)C) (x + 1)(x − 2)²D) (x + 1)²(x − 4)

Worked solutions from the ICSE 2019 paper

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