Problems on Algebra : ICSE and CBSE

Algebraic Identities Problem Set

Master Algebra through Practice Problems. Prime Maths

About This Problem Set

This collection of problems is designed for Class IX students following CBSE, ICSE, and State Board curricula. The problems cover fundamental algebraic identities, inequalities, factorization, and polynomial expansions. Work through these problems systematically to strengthen your understanding of algebraic concepts and their applications.

Problem 1

Problem 1 of 22

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Practice these problems to master algebraic identities. Remember to attempt each problem before checking the hint!

Designed for Class IX Mathematics

Designed by Vinod Singh, 9038126497

Indices Interactive Chapter Test: ICSE and CBSE

Prime Maths

25 Question MCQ Chapter on Indices & Exponents for ICSE, CBSE, WBBSE and other State Boards

👨‍🏫 Author: Vinod Singh

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Prime Maths

Indices & Exponents Quiz

Test your understanding of mathematical indices

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• This quiz contains 25 multiple choice questions.
• Select only one correct answer per question.
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Question 1

\( \big( 125^{-4}\times 256^{-3/2}\big)^{-1/6} \times \big( (x^{2}y^{-4})^{1/3} \times \sqrt{y^{3}x^{-5}}\big)^{12}\times (x^{2})^{11}\)

A\( 10y^{2}\) B\( 100y^{2}\) C\( 10x^{2}\) D\( 100x^{2}\)

Question 2

The value of \( (5^{0} + 3^{0} + 2^{0}) ÷\bigg( \frac{2^{n}(2^{n-1})^n}{2^{n+1}.2^{n-1}} \times \bigg( \frac{\sqrt [3] {8^{n}}}{4}\bigg)^{-n} \bigg) \) is:

A0 B1 C2 D3

Question 3

Simplify: \( \big(\frac{1728}{729}\big)^{\frac{2}{3}}\times \frac{3^{2}}{\sqrt{144}}\times \sqrt{5} \)

A\( \frac{4\sqrt{5}}{3} \) B\( \frac{4\sqrt{5}}{7} \) C\( \frac{\sqrt{5}}{3} \) D\( \frac{7\sqrt{5}}{3} \)

Question 4

If \(5^{10x}=4900 \) and \( 2^{ \sqrt{y}}=25 \), the value of \(4^ { \sqrt{y}}\times 5^{5x-5} \) is:

A12 B16 C14 D13

Question 5

If \(\big( \frac{2a}{b}\big)^{2x-4} \) = \(\big( \frac{b}{2a}\big)^{2x-4} \), then the value of \( x \) is:

A2 B4 C3 D-2

Question 6

\( \big[1-\big(1-\big(1-n\big)^{-1}\big)^{-1} \big]^{-1} = \) where \(n \neq 0,1 \)

A\( n \) B\( 2n \) C\( -n \) D\( \frac{1}{n} \)

Question 7

If \( 2016 = 2^{a}\times 3^{b} \times 5^{c}, \) then the value of \(3^{a}\times 2^{-b} \times 5^{-c} \) is

A\( \frac{243}{4} \) B\( \frac{247}{4} \) C\( \frac{241}{4} \) D\( \frac{234}{4} \)

Question 8

If \( 2^{x}=3^{y}=6^{-z} \) then the value of \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z} =\)

A0 B1 C-1 D\( \frac{1}{2} \)

Question 9

If \( a^{x}=b^{y}=c^{z} \) and \(b^{2} = ac \) then the value of \( \frac{2xz}{z+x}\) is

Ay B2x Cx D-x

Question 10

The simplest value of \( \frac{(x^{a+b})^{2} . (x^{b+c})^{2} . (x^{c+a})^{2}}{(x^{a}.x^{b}.x^{c})^{4}} \) is

A0 B1 C2 D-1

Question 11

Simplest value of \( \big( \frac{2^{-1}\times 3^{2}}{2^{2}\times 3^{-4}}\big)^{7/2} \times \big( \frac{2^{-2}\times 3^{3}}{2^{3}\times 3^{-5}}\big)^{-5/2} \) is

A12 B22 C2 D11

Question 12

The value of \(x\) satisfying \( 9^{x}-9^{x-1}=648 \) is

A3 B\( \frac{1}{3} \) C2 D-3

Question 13

The simplest value of \( \big[ 5\big(8^{1/3}+27^{1/3}\big)^{3}\big]^{\frac{1}{4}} \) is

A5 B6 C8 D12

Question 14

If \( y= x^{1/3}-x^{-1/3}, \) then \( y^{3}+3y = \)

A\( x-x^{-1} \) B\( x^{2} - x^{-2} \) C\( x^{2}+x^{-2} \) D\( x+x^{-1} \)

Question 15

If \( (10^{11}+25)^{2}-(10^{11}-25)^{2} = 10^{n}\) then the value of \( n \) is

A11 B13 C17 D7

Question 16

The least value of the expression \( 4^{x}+4^{1-x} \) is

A2 B4 C8 D16

Question 17

Value of \(x\) and \(y\) satisfying the equations \( 5^{x}-3^{y}=16; \quad 5^{x-1}+3^{y+1}=32\) are

A\( x=2 \quad y = 2 \) B\( x=2 \quad y = -2 \) C\( x=-2 \quad y = 2 \) D\( x=-2 \quad y = -2 \)

Question 18

If \(\big( x^{n^{2}}\big)^{n}= \big( x^{2^{n}}\big)^{2}\), then the value of \( \sqrt[n+1]{n^{3}} \) is

A2 B4 C1 D\( 2^{4} \)

Question 19

If \( x = 3+3^{2/3}+3^{1/3}\) then the value of \( x^3-9x^2+18x-12 \) is

A0 B1 C3 D-3

Question 20

If \( a^{x}=bc, \quad b^{y}= ca, \quad c^{z}=ab\), then the value of \(\frac{x}{x+1}+\frac{y}{y+1}+\frac{z}{z+1} \quad \) is

A1 B2 C0 D-1

Question 21

The value of \(x\) satisfying \( 4^{x}-3^{x-1/2}=3^{x+1/2}-2^{2x-1}\) is

A\( \frac{3}{2} \) B2 C\( \frac{1}{2} \) D\( \frac{2}{3} \)

Question 22

The value of \( \frac{\big(2^{2n}-3.2^{2n-2}\big)\big(3^{n}-2.3^{n-2}\big)}{3^{n-4}\big( 4^{n+3}-2^{2n}\big)} \quad \) is

A\( \frac{1}{4} \) B\( \frac{3}{4} \) C\( \frac{-3}{4}\) D\( \frac{1}{3} \)

Question 23

If \( a^{x}=b^{y}\) and \( b^{x}=a^{y} \quad ( ab \neq 1)\) then which of the following relation is true

A\( a=b^{2} \) B\( a=b \) C\( b=a^{2} \) D\( ab=2 \)

Question 24

Solve for \(x \) and \( y: \quad 2^{x}+2^{y}=12; \quad x+y= 5\)

A\( x=3, \quad y = 2 \) B\( x=2, \quad y = 3 \) C\( x=4, \quad y = 1\) D\( x=1, \quad y = 4 \)

Question 25

The value of \( \bigg( \frac{9^{n+1/4}.\sqrt{3.3^{n}}}{3.\sqrt{3^{-n}}}\bigg)^{1/n}\) is

A3 B9 C27 D81

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Factorisation Worksheet | CBSE | ICSE | Class IX

ICSE & CBSE Class IX Factorisation - Prime Maths

Master the Art of Factorisation with 39 Progressive Problems

Factorisation Overview

What is Factorisation?

Factorisation is the process of breaking down algebraic expressions into simpler components called "factors" that, when multiplied together, give the original expression.

Worksheet Structure

• Problems 1-10: Basic factorisation
• Problems 11-20: Difference of squares
• Problems 21-30: Grouping techniques
• Problems 31-39: Challenge mastery

How to Use This Worksheet:

1. Work through problems one by one using the slides.

2. Try to solve before clicking "Next".

3. Use the list below to jump to specific questions.

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Problem 1 of 39

$$10xy - 15xz$$

Hint: Look for common factors

Full Problem List

ICSE Class IX Mathematics - Factorisation Worksheet

Worksheet Prepared By:

Vinod Singh

M.Sc. Pure Mathematics, Calcutta University (First Class)

B.Sc. Mathematics, St. Xavier's College Kolkata (First Class)

maths.programming@gmail.com