# ICSE Class 10 Mathematics Previous Year Question Paper 2019

Mathematics is one of the crucial and most scoring subjects in ICSE Class 10. TopperLearning presents study materials for ICSE Class 10 Mathematics which will enable students to score well in the board examination. The syllabus includes certain challenging concepts like Value Added Tax, Ratio and Proportion, Quadric Equations among others which require effective study materials. Our study materials for ICSE Class 10 consist of video lessons, question banks, sample papers, revision notes and past year papers which improve the quality of learning.

**Q 1.**

(a) Solve the following inequation and write down the solution set:

11x - 4 < 15x + 4 <13x + 14, x ∈ W

Represent the solution on a real number line.

(b) A man invests Rs. 4500 in shares of a company which is paying 7.5% dividend. If Rs. 100 shares are available at a discount of 10%.

Find:

(i) Number of shares he purchases.

(ii) His annual income.

(c) In class of 40 students, marks obtained by the students a class test (out of 10) are given below,

Marks |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Number of students |
1 | 2 | 3 | 3 | 6 | 10 | 5 | 4 | 3 | 3 |

Calculate the following for the given distribution:

(i) Median

(ii) Mode

**Q 2.**

(a) Using the factor theorem, show that (x - 2) is a factor of x^{3} + x^{2} – x^{4} – 4, Hence factorise the polynomial completely.

(b) Prove that:

(cosec θ - sin θ)(sec θ – cos θ) (tan θ + cot θ) =1

(c) In an Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively, Find the:

(i) first term

(ii) common difference

(iii) sum of the first 20 terms

**Q 3.**

(a) Simplify

(b) M and N are two points on the X axis and Y axis respectively.

P(3, 2) divides the line segment MN in the ratio 2 : 3.

Find:

(i) the coordinates of M and N

(ii) slope of the line MN.

(c) A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder of height 32cm. Find the

(i) radius of the cylinder

(ii) curved surface area of the cylinder

**Take Π = 3.1**

**Q 4.**

(a) The following numbers, K + 3, K + 2, 3K - 7 and 2K – 3 are in proportion. Find K.

(b) Solve for x the quadratic equation x^{2} – 4x – 8 = 0.

Give your answer correct to three significant figures.

(c) Use ruler and compass only for answering this question.

Draw a circle of radius 4 cm. Mark the centre as O. Mark a point P outside the circle at a distance of 7 cm from the centre, Construct two tangents to the circle from the external point P.

Measure and write down the length of any one tangent.

**Q 5.**

(a) There are 25 discs numbered 1 to 25. They are put in a closed box and shaken thoroughly. A disc is drawn at random from the box.

Find the probability that the number on the disc is:

(i) an odd number

(ii) divisible by 2 and 3 both.

(iii) a number less than 16.

(b) Rekha opened a recurring deposit account for 20 months. The rate of interest is 9% per annum and Rekha receives Rs. 441 as interest at the time of maturity.

Find the amount Rekha deposited each month.

(c) Use a graph sheet for this question.

Take 1 cm = 1 unit along both x and y axis.

(i) Plot the following points:

A(0,5), B(3,0), C(1,0), and D(1,-5)

(ii) Reflect the points B, C, and D on the y axis and name them as B’, C’ and D’ respectively.

(iii) Write down the coordinates of B’, C’ and D’.

(iv) Join the points A, B, C, D, D’, C’, B’, A in order and give a name to the closed figure ABCDD’C’B’.

**Q 6.**

(a) In the given figure ∠PQR = ∠PST = 90^{o}, PQ = 5 cm and PS = 2 cm.

(i) Prove that △PQR = △PST

(ii) Find Area of △PQR: Area of quadrilateral SRQT.

(b) The first and last term of a Geometrical Progression (G.P.) are 3 and 96 respectively. If the common ratio is 2, find:

(i) **‘n’** the number of terms of the G.P.

(ii) Sum of the **n** terms.

(c) A hemispherical and a conical hole is scooped out of a solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:

The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm.

Give your answer correct to the nearest whole number Take

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