Subject

Mathematics

Class

ICSE Class 10

Pre Boards

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Sample Papers

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ICSE Class 10 Mathematics Solved Question Paper 2013

Short Answer Type

21.

Find x and y if $[\begin{matrix} x & 3 x \\ y & 4 y \end{matrix}] [\begin{matrix} 2 \\ 1 \end{matrix}] = [\begin{matrix} 5 \\ 12 \end{matrix}]$

22.

A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.

23.

Without solving the following quadratic equation, find the value of ‘p' for which the given equation has real and equal roots:

x² + (p – 3)x + p = 0.

24.

In the figure alongside, OAB is a quadrant of a circle. The radius OA = 3.5 cm and OD = 2 cm. Calculate the area of the shaded portion. (Take $π = \frac{22}{7}$ ).

25.
A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball, find the number of black balls in the box.

As given,

Number of white balls in the bag = 30

Let consider the number of black balls in the box be x.

$∴$ Total number of balls = x + 30

Probability of drawing black ball = $\frac{x}{x + 30}$

Probability of drawing white ball = $\frac{30}{x + 30}$

It is given that, P(Drawing a balck ball) = $\frac{2}{5} \times$ P(Drawing a white ball)

$\Rightarrow \frac{x}{x + 30} = \frac{2}{5} \times \frac{30}{x + 30}$

$\Rightarrow \frac{x}{x + 30} = \frac{12}{x + 30}$

$\Rightarrow x^{2} + 30 x = 12 x + 360$

$\Rightarrow x^{2} + 18 x - 360 = 0$

$\Rightarrow x^{2} + 30 x - 12 x - 360 = 0$

$\Rightarrow x (x + 30) (x - 12) = 0$

$\Rightarrow x = - 30 or x = 12$

Since number of balls cannot be negative, we reject x = - 30

$\Rightarrow x = 12$

Therefore, number of black balls in the box is 12.

26.

Find the mean of the following distribution by step deviation method:

Class Interval	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
Frequency	10	6	8	12	5	9

27.

Using a ruler and compasses only:

(i) Construct a triangle ABC with the following data:
AB = 3.5 cm, BC = 6 cm and $∠$ ABC = 120 $°$

(ii) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.

(iii) Measure $∠$ BCP.

28.

The marks obtained by 120 students in a test are given below:

Marks	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80	80 - 90	90 - 100
No. of students	5	9	16	22	26	18	11	6	4	3

Draw an ogive for the given distribution on a graph sheet.

Use suitable scale for ogive to estimate the following:

(i) The median.

(ii) The number of students who obtained more than 75% marks in the test.

(iii) The number of students who did not pass the test if minimum marks required to pass is 40.

29.

In the figure given below, the line segment AB meets X-axis at A and Y-axis at B. The point P(-3, 4) on AB divides it in the ratio 2:3. Find the coordinates of A and B.