Subject

Mathematics

Class

ICSE Class 10

Pre Boards

Practice to excel and get familiar with the paper pattern and the type of questions. Check you answers with answer keys provided.

Sample Papers

Download the PDF Sample Papers Free for off line practice and view the Solutions online.

ICSE Class 10 Mathematics Solved Question Paper 2013

Short Answer Type

Given $A = [\begin{matrix} 2 & - 6 \\ 2 & 0 \end{matrix}], B = [\begin{matrix} - 3 & 2 \\ 4 & 0 \end{matrix}], C = [\begin{matrix} 4 & 0 \\ 0 & 2 \end{matrix}]$

Find the matrix X such that A + 2X = 2B + C.

At what rate % p.a. will a sum of Rs. 4000 yield Rs. 1324 as compound interest in 3 years?

The median of the following observation 11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24.

Find the value of x and hence find the mean.

What number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?

5.
If (x – 2) is a factor of the expression 2x³ + ax² + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.

Let consider p(x) = 2x³ + ax² + bx - 14

As given, (x – 2) is a factor of p(x),

$\Rightarrow$ Remainder = p(2) = 0

$\Rightarrow$ 2(2)² + a(2)² + b(2) - 14 = 0

$\Rightarrow$ 16 + 4a + 2b - 14 = 0

$\Rightarrow$ 4a + 2b + 2 = 0

$\Rightarrow$ 2a + b + 1 = 0 ...(i)

As given, when p(x) is divided by (x - 3), it leaves remainder 52.

Therefore, p (3) = 52

$\Rightarrow$ 2(3)² + a(3)² + b(3) - 14 = 52

$\Rightarrow$ 54 + 9a + 3b - 14 = 52

$\Rightarrow$ 9a + 3b - 12 = 0

$\Rightarrow$ 3a + b - 4 = 0 ...(ii)

By substracting equation (i) from equation (ii), we get,

a - 5 = 0

$\Rightarrow$ a = 5

By substituting a = 5 in equation (i), we get,

10 + b + 1 = 0

$\Rightarrow$ b = - 11

Draw a histogram from the following frequency distribution and find the mode from the graph:

Class 0 - 5 5 - 10 10 - 15 15 - 20 20 -25 25 - 30

Frequency 2 5 18 14 8 5