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

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.

Find ‘a‘ if the two polynomials ax³ + 3x² – 9 and 2x³ + 4x + a, leave the same remainder when divided by x + 3. 

Using the Remainder Theorem, factorise each of the following completely. 

3x³ + 2x² − 19x + 6 

Using the Remainder Theorem, factorise the following completely:

2x³ + x² – 13x + 6 

Using the Remainder Theorem, factorise the following completely:

3x³ + 2x² – 23x – 30

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.