AllRounder.ai

Enrol to start learning

Reading is open to everyone. Enrolling is free, and it is what unlocks the audio lessons, practice tests and progress tracking.

Enrol free

2. Algebra

The chapter covers fundamental concepts in algebra, including linear inequations, quadratic equations, factorization of polynomials, ratios, proportions, matrices, and progressions. Each section explains the principles, provides examples, and demonstrates methods for solving problems associated with each topic. The chapter concludes with exercises and group activities that reinforce the learned concepts.

Sections

Algebra

This section explores key algebraic concepts, including linear inequations, quadratic equations, polynomials, ratios, matrices, and progressions.

2 Section Overview

Start current section content and materials

2.1 Linear Inequations (in one variable)

Linear inequations express the inequality between two expressions, and solving these involves finding the values that satisfy the inequality while preserving the inequality signs.

2.2 Quadratic Equations

Quadratic equations are mathematical expressions in the form ax² + bx + c = 0 and can be solved using factorization or the quadratic formula.

2.3 Factorisation of Polynomials

This section covers the concept of factorising polynomials, essential for simplifying algebraic expressions and solving equations.

2.4 Ratio and Proportion

This section introduces the concepts of ratio and proportion, focusing on their definitions and practical applications.

2.5 Matrices (Order 2 × 2)

This section introduces matrices as rectangular arrays of numbers and covers the operations of addition, subtraction, and multiplication specific to 2x2 matrices.

2.6 Arithmetic Progression (A.P.)

Arithmetic Progression (A.P.) refers to a sequence of numbers where the difference between consecutive terms is constant.

2.7 Geometric Progression (G.P.)

Geometric Progression involves sequences formed by multiplying each term by a constant ratio, with formulas governing the nth term and the sum of the series.

Learning Objectives

  • An inequation expresses the inequality between two expressions.

  • Quadratic equations can be solved using factorization or the quadratic formula.

  • Factorization of polynomials involves writing them as a product of their factors through various methods.

Key Concepts

Inequation

A mathematical sentence that expresses the inequality between two expressions.

Quadratic Equation

An equation in the form ax² + bx + c = 0, where a ≠ 0, which can be solved using factorization or the quadratic formula.

Factorization

The process of writing a polynomial as a product of its factors.

Ratio

A comparison between two quantities expressed as a fraction a:b = a/b.

Matrix

A rectangular array of numbers that can be added, subtracted, or multiplied under certain conditions.

Arithmetic Progression (A.P.)

A sequence where the difference between consecutive terms is constant.

Geometric Progression (G.P.)

A sequence where each term is obtained by multiplying the previous term by a constant (common ratio).

Practice Exercises

Total Questions

4

Estimated Time

8 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting