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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.

From right angle triangle ADC, we get

$\frac{AD}{CD} = \tan (36 °)$

$\Rightarrow \frac{100}{y} = 0.7265$

$\Rightarrow y = \frac{100}{0.7265} = 137.638$ m

From right angle Δ ADB, we have

$\frac{100}{x} = \tan (48 °)$

$\Rightarrow x = \frac{100}{1.1106}$ = 90.04 m

Thus, Distance between the ships = x + y

= 137.638 + 90.04

= 227.678 = 228 m (approx.)

Therefore, the distance between the two ships is 228 m.

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.