Subject

Mathematics

Class

ICSE Class 10

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Sample Papers

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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.

2.
At what rate % p.a. will a sum of Rs. 4000 yield Rs. 1324 as compound interest in 3 years?

As given, P = Rs. 4000, C.I. = Rs. 1324, n = 3 years
Amount, A = P + C.I. = Rs. 4000 + Rs. 1324 = Rs. 5324

A = $P (1 + \frac{r}{100})^{n}$

$\Rightarrow 5324 = 4000 (1 + \frac{r}{100})^{3}$

$\Rightarrow (1 + \frac{r}{100}) 3 = \frac{5324}{4000} = \frac{1331}{1000}$

$\Rightarrow (1 + \frac{r}{100})^{2} = (\frac{11}{10})^{3}$

$\Rightarrow (1 + \frac{r}{100}) = \frac{11}{10}$

$\Rightarrow \frac{r}{100} = \frac{11}{10} - 1 = \frac{1}{10}$

$\Rightarrow r = 10 %$

Therefore, at rate 10% p.a. will a sum of Rs.4000 yield Rs.3124 as compound interest in 3years.

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?

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.

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