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 2015

Long Answer Type

21.
Three vertices of a parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2), Find (i) the coordinate of the fourth vertex D (ii) length of diagonal BD (iii) equation of the side AB of the parallelogram ABCD

Three vertices of a parallelogram taken in order are A(3, 6), B(5, 10) and C(3, 2)

(i) We need to find the coordinates of D.

We know that the diagonals of a parallelogram bisect each other.

Let (x,y) be the coordinates of D.

Therefore, Mid-point of diagonal AC = $(\begin{matrix} \frac{3 + 3}{2}, & \frac{6 + 2}{2} \end{matrix})$ = (3,4)

And, mid-point of diagonal BD = $(\begin{matrix} \frac{5 + x}{2} & \frac{10 + y}{2} \end{matrix})$

Thus we have

$\frac{5 + x}{2}$ = 3 and $\frac{10 + y}{2}$ = 4

Therefore, 5 + x = 6 and 10 + y = 8

x = 1 and y = -2

Therefore, D = (1, -2)

(ii) Length of diagonal BD = $\sqrt{(1 - 5)^{2} + (- 2 - 10)^{2}}$

= $\sqrt{(- 4)^{2} + (- 12)^{2}}$

= $\sqrt{16 + 44}$

= $\sqrt{160}$

= $4 \sqrt{10}$

(iii) A(3, 6) = (x₁, y₁) and B(5,10) = (x₂ , y₂)

Slope of line AB = m = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{10 - 6}{5 - 3} = \frac{4}{2} = 2$

Therefore , Equation of line AB is given by,

y - y₁ = m(x - x₁)

y - 6 = 2(x - 3)

y - 6 = 2x - 6

2x - y = 0

2x = y

22.

In the figure given below, O is the centre of the circle and SP is a tangent. If ∠SRT = $65^{°}$ , find the value of x, y and z.

23.

Katrina opened a recurring deposit account with a Nationalised Bank for a period of 2 years. If the bank pays interest at the rate 6% per annum and the monthly instalment is Rs. 1,000, find the: (i) Interest earned in 2 years. (ii) Matured valu

24.

Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation, (K + 2)x² – Kx + 6 = 0. Thus find the other root of the equation.

25.

Construct a regular hexagon of side 5 cm. Construct a circle circumscribing the hexagon. All traces of construction must be clearly shown.

26.

(a) Use a graph paper for this question taking 1 cm = 1 unit along both the x and y axis :

(i) Plot the points A(0, 5), B(2, 5), C(5, 2), D(5, -2), E(2, -5) and F(0, -5).

(ii) Reflect the points B, C, D and E on the y-axis and name them respectively as B’, C’, D’ and E’.

(iii) Write the coordinates of B’, C’, D’ and E’.

(iv) Name the figure formed by B C D E E’ D’ C’ B’.

(v) Name a line of symmetry for the figure formed.

27.

In the given figure ABC is a triangle and BC is parallel to the y – axis. AB and AC intersect the y–axis at P and Q respectively.

(i) Write the coordinates of A.

(ii) Find the length of AB and AC.

(iii) Find the ratio in which Q divides AC.

(iv) Find the equation of the line AC.

28.

Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed.

29.

Find 'a' of the two polynomials ax³ + 3x² – 9 and 2x³ + 4x + a, leaves the same remainder when divided by x + 3.

30.

The weight of 50 workers is given below :

Weight in Kg	50 - 60	60 -70	70 -80	80 -90	90 -100	100 -110	110 -120
No. of Workers	4	7	11	14	6	5	3

Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following:

(i) The upper and lower quartiles.

(ii) If weighing 95 kg and above is considered overweight, find the number of workers who are overweight.