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 2012

Short Answer Type

If A = $[\begin{matrix} 3 & 1 \\ - 1 & 2 \end{matrix}]$ and B = $[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ , Find A² - 5A + 7I

The monthly pocket money of Ravi and Sanjeev are in the ratio 5:7. Their expenditures are in the ratio 3:5. If each saves Rs. 80 every month, find their monthly pocket money

Using the Remainder Theorem factorise completely the following polynomial.

3x³ + 2x² – 19x + 6

On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5% p.a.?

ABC is an isosceles right angled triangle with ∠ABC = 90 $°$ . A semi-circle is drawn with AC as the diameter. If AB = BC = 7 cm, find the area of the shaded region.
Take ( $π = \frac{22}{7}$ )

Given a line segment AB joining the points A(– 4, 6) and B(8, – 3). Find

(i) The ratio in which AB is divided by y-axis.

(ii) Find the coordinates of the point of intersection.

(iii) The length of AB.

In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm. Calculate the radius of circle.

Evaluate without using trigonometric tables:

$\cos^{2} (26 °) + \cos (64 °) \sin (26 °) + \frac{\tan (36 °)}{\cot (54 °)}$

9.
Marks obtained by 40 students in a short assessment is given below, where a and b are two missing data.

Marks 5 6 7 8 9

Number of Students 6 a 16 13 b

If the mean of the distribution is 7.2, find a and b.

It is given that the number of students is 40.

$∴ 35 + a + b = 40$ $\Rightarrow a + b - 5 = 0$ ...(i)

We have,Mean = $\frac{\sum fx}{\sum f}$ $\Rightarrow \frac{246 + 6 a + 9 b}{35 + a + b} = 7.2$

$\Rightarrow 246 + 6 a + 9 b = 7.2 (35 + a + b)$

$\Rightarrow 246 + 6 a + 9 b = 252 + 7.2 a + 7.2 b$

$\Rightarrow 0 = 252 - 246 + 7.2 a - 6 a + 7.2 b - 9 b$

$\Rightarrow 6 + 1.2 a - 1.8 b = 0$

$\Rightarrow 10 + 2 a - 3 b = 0$ ...(ii)

Solving equation (i) and (ii), we have

5a - 5 = 0Thus, a = 1

From equation (i), we get b = 4

Hence, value of a and b are 1 and 4 respectively.

Marks(x)	Number of Students(f)	fx
5	6	30
6	a	6a
7	16	112
8	13	104
9	b	9b
	$\sum$ f = 35 + a + b	$\sum$ fx = 246 + 6a + 9b

10.

Kiran deposited Rs. 200 per month for 36 months in a bank’s recurring deposit account. If the bank pays interest at the rate of 11% per annum, find the amount she gets on maturity.