Previous Year Paper year:2018 : ICSE-X-Mathematics

Home Learn Fast select Course

Change Unit Change Subject Last Menu

ICSE-X-Mathematics

Previous Year Paper year:2018

with Solutions -

#
ICSE Board
Class X Mathematics
(Two hours and a half)
Answers to this Paper must be written on the paper provided separately.
You will not be allowed to write during the first 15 minutes.
This time is to be spent in reading the question paper.
The time given at the head of this Paper is the time allowed for writing the answers.
Attempt all questions from Section I and any four questions from Section II.
All working, including rough work, must be clearly shown and must be done on the
same sheet as the rest of the answer.
Omission of essential working will result in loss of marks.
The intended marks for questions or parts of questions are given in brackets [].
Mathematical tables are provided.

# [40]
Section : A
Attempt all questions from this Section.

#1

#1-a [3]
Find the value of 'x' and 'y' if:
$$
2\cdot \begin{bmatrix}
x & 7 \\
9 & y-5 \\
\end{bmatrix}
+
\begin{bmatrix}
6 & -7 \\
4 & -5 \\
\end{bmatrix}
= \begin{bmatrix}
10 & 7 \\
22 & 15 \\
\end{bmatrix}
$$
Ans : $$2 \begin{bmatrix} x & 7 \\ 9 & y-5 \end{bmatrix} + \begin{bmatrix} 6 & -7 \\ 4 & 5 \end{bmatrix} = \begin{bmatrix} 10 & 7 \\ 22 & 15 \end{bmatrix}
$$
$$
\Rightarrow \begin{bmatrix} 2x & 14 \\ 18 & 2y-10 \end{bmatrix} + \begin{bmatrix} 6 & -7 \\ 4 & 5 \end{bmatrix} = \begin{bmatrix} 10 & 7 \\ 22 & 15 \end{bmatrix}
$$
$$
\Rightarrow \begin{bmatrix} 2x+6 & 14-7 \\ 22 & 2y-5 \end{bmatrix} = \begin{bmatrix} 10 & 7 \\ 22 & 15 \end{bmatrix}
$$
$$\Rightarrow 2x+6=10 \Rightarrow x = 2 $$
and ``2y-5 = 15 \Rightarrow y = 10 ``
$$Hence, x =2 \ and \ y = 10$$

#1-b [3]
Sonia had a recurring deposit account in a bank and deposited Rs. 600 per month
for ``2\frac12`` years. If the rate of interest was 10% p.a., find the maturity value of this
account.
Ans : Monthly investments ``(x) = 600 \ Rs.``
`` n = 30 \ months , r = 10\% ``
$$I = \frac{n(n+1)}{2} \times x \times \frac{1}{12} \times \frac{r}{100}$$
$$= \frac{30(31)}{2} \times 600 \times \frac{1}{12} \times \frac{10}{100}$$
$$= 2325 \ Rs. $$
Maturity value ``= x \times n + I = 600 \times 30 + 2325 = 20325 \ Rs. ``

#1-c [4]
Cards bearing numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 are kept in a bag. A card is
drawn at random from the bag. Find the probability of getting a card which is:
Ans : Cards $$: 2, 4, 6, 8, 10, 12, 14, 16, 18 \ and \ 20$$
``n(S) = 10``

#1-c-i
a prime number.
Ans : Prime numbers: 2
``n(E) = 1``
Probability (a prime number) ``= \frac{n(E)}{n(S)} = \frac{1}{10}``

#1-c-ii
a number divisible by 4.
Ans : Numbers divisible by 4: 4, 8, 12, 16, 20
``n(E) = 5``
Probability (a prime number)`` = \frac{n(E)}{n(S)} = \frac{5}{10} = 0.5``

#1-c-iii
a number that is a multiple of 6.
Ans : Numbers multiple of 6: 6, 12, 18
``n(E) = 3``
Probability (a prime number) ``= \frac{n(E)}{n(S)} = \frac{3}{10} = 0.5``

#1-c-iv
an odd number.
Ans : Odd numbers: None
``n(E) = 0``
Probability (a prime number)`` = \frac{n(E)}{n(S)} = \frac{0}{10} = 0``

#2

#2-a [3]
The circumference of the base of a cylindrical vessel is 132 cm and its height is 25
cm. Find the

#2-a-i
radius of the cylinder

Ans :
Circumference = ``132 \ cm``
Height ``= 25 \ cm``
Circumference ``= 2\pi r = 132``
``r = \frac{132 \times 7}{2 \times 22} = 21 \ cm``

#2-a-ii
volume of cylinder
(use ``\pi = \frac{22}{7}``)
Ans : Volume ``= \pi r ^2 h``
``= \frac{22}{7} \times 21 \times 21 \times 25``
``= 34650 \ cm^3``

#2-b [3]
If (k - 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value
of k.
Ans : (k-3), (2k+1) and (4k+3) are in AP
``\Rightarrow (2k+1) - (k-3) = (4k+3) -(2k+1)``
``\Rightarrow k+4 = 2k+2``
``\Rightarrow k = 2``
Therefore the terms are -1, 5, 11 and the common difference is 6