(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

Using the Remainder Theorem, factorise the following completely:  

4x³ + 7x² – 36x – 63

Using the Remainder Theorem, factorise the following completely:

x³ + x² – 4x – 4

Using the Remainder Theorem, factorise the expression 3x³ + 10x² + x – 6. Hence, solve the equation 3x³ + 10x² + x – 6 = 0

When x³ + 3x² – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.

Find the value of ‘m’, if mx³ + 2x² – 3 and x² – mx + 4 leave the same remainder when each is divided by x – 2.

Find the number which should be added to x² + x + 3 so that the resulting polynomial is completely divisible by (x + 3).

When the polynomial x³ + 2x² – 5ax – 7 is divided by (x – 1), the remainder is A and when the polynomial x³ + ax² – 12x + 16 is divided by (x + 2), the remainder is B. Find the value of ‘a’ if 2A + B = 0.

Draw histogram for the following frequency distributions: 

Draw histogram for the following frequency distributions: 

Draw histogram for the following frequency distributions: 

Draw histogram for the following frequency distributions:

Attempt this question on graph paper.

1. Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both the axes.
2. Reflect A and B in the x-axis to A’ and B’ respectively. Plot these points also on the same graph paper.
3. Write down:
   1. the geometrical name of the figure ABB’A’;
   2. the measure of angle ABB’;
   3. the image of A” of A, when A is reflected in the origin.
   4. the single transformation that maps A’ to A”.

Points (3, 0) and (–1, 0) are invariant points under reflection in the line L₁; points (0, –3) and (0, 1) are invariant points on reflection in line L₂.

1. Name or write equations for the lines L₁ and L₂.
2. Write down the images of the points P (3, 4) and Q (–5, –2) on reflection in line L₁. Name the images as P’ and Q’ respectively.
3. Write down the images of P and Q on reflection in L₂. Name the images as P” and Q” respectively.
4. State or describe a single transformation that maps P’ onto P''.

1. Point P (a, b) is reflected in the x-axis to P’ (5, –2). Write down the values of a and b.
2. P” is the image of P when reflected in the y-axis. Write down the co-ordinates of P”.
3. Name a single transformation that maps P’ to P”.

The point (–2, 0) on reflection in a line is mapped to (2, 0) and the point (5, –6) on reflection in the same line is mapped to (–5, –6).

1. State the name of the mirror line and write its equation.
2. State the co-ordinates of the image of (–8, –5) in the mirror line.

The points P (4, 1) and Q (–2, 4) are reflected in line y = 3. Find the co-ordinates of P’, the image of P and Q’, the image of Q.

A point P (–2, 3) is reflected in line x = 2 to point P’. Find the co-ordinates of P’.

A point P (a, b) is reflected in the x-axis to P’ (2, –3). Write down the values of a and b. P” is the image of P, reflected in the y-axis. Write down the co-ordinates of P”. Find the co-ordinates of P”’, when P is reflected in the line, parallel to y-axis, such that x = 4.

Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image:

1. A’ of A under reflection in the x-axis.
2. B’ of B under reflection in the line AA’.
3. A” of A under reflection in the y-axis.
4. B” of B under reflection in the line AA”.

1. Plot the points A (3, 5) and B (–2, –4). Use 1 cm = 1 unit on both the axes.
2. A’ is the image of A when reflected in the x-axis. Write down the co-ordinates of A’ and plot it on the graph paper.
3. B’ is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B’ and plot it on the graph paper.
4. Write down the geometrical name of the figure AA’BB’.
5. Name the invariant points under reflection in the x-axis.