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ICSE Class 10 Mathematics Solved Question Paper 2010

Short Answer Type

21.

The Mean of the following distribution is 52 and the frequency of class interval 30-40 is ‘f’. Find ‘f’.

Class Interval	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
Frequency	5	3	f	7	2	6	13

22.

Use the Remainder Theorem to factorise the following expression:

2x³ + x² – 13x + 6

23.

If x, y, z are in continued proportion, prove that $\frac{(x + y)^{2}}{(y + z)^{2}} = \frac{x}{z}$

24.

From the top of a light house 100 m high the angles of depression of two ships on opposite sides of it are 48 $°$ and 36 $°$ respectively. Find the distance between the two ships to the nearest metre.

25.

Evaluate $[\begin{matrix} 4 \sin (30 °) & 2 \cos (60 °) \\ \sin (90 °) & 2 \cos (0 °) \end{matrix}] [\begin{matrix} 4 & 5 \\ 5 & 4 \end{matrix}]$

26.

In the given figure ABC is a triangle with $∠$ EDB = $∠$ ACB.

Prove that $∆$ ABC $~ ∆$ EBD. If BE = 6 cm, EC = 4 cm, BD = 5 cm. And area of
$∆$ BED = 9
cm2. Calculate the

(i) length of AB

(ii) area of $∆ ABC$

27.

Vivek invests Rs 4500 in 8%. Rs. 10 shares at Rs. 15. He sells the shares when the price rises to Rs. 30, and invests the proceeds in 12% Rs. 100 shares at Rs. 125. Calculate.

(i) the sale proceeds

(ii) the number of Rs. 125 shares he buys.

(iii) the change in his annual income from dividend.

28.

A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.

29.
The monthly income of a group of 320 employees in a company is given below:

Monthly Income No. of employees

6000 - 7000 20

7000 - 8000 45

8000 - 9000 65

9000 - 10000 95

10000 - 11000 60

11000 - 12000 30

12000 - 13000 5

Draw an ogive the given distribution on a graph sheet taking 2 cm = Rs. 1000 on one axis and 2 cm = 50 employees on the other axis. From the graph determine:
(i) the median wage
(ii) the number of employees whose income is below Rs. 8500.
(iii) if the salary of a senior employee is above Rs. 11,500, find the number of senior employees in the company.
(iv) the upper quartile.

Here, n = 320

(i) Median = ${(\frac{n}{2})}^{th} term = {(\frac{320}{2})}^{th} term = 160^{th} term$

From the graph, the corrosponding x - coordinate is 9400

Thus, the median wage = 9400 approx.

(ii) The number of employees whose income is below Rs. 8500 = 95 (approx.)

(iii) The number of senior employees whose salary is above Rs. 11500 = 320 – 305 = 15 (approx.)

(iv) The upper quartile, Q₃ = ${(\frac{3 n}{4})}^{th} term = 240^{th} term$

From the graph, the corresponding x co-ordinate is 10,300 (approx.)

Monthly Income	No. of employees	c.f.
6000 - 7000	20	20
7000 - 8000	45	65
8000 - 9000	65	130
9000 - 10000	95	225
10000 - 11000	60	285
11000 - 12000	30	315
12000 - 13000	5	320