# Algebraic expressions, equations and inequalities notes > CAPS-aligned study notes for Algebraic expressions, equations and inequalities in Grade 12 Mathematics. Browse the sections below for explanations, worked examples and exam preparation. - Page: https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities Breadcrumbs: [Home](https://www.hlayiso.com/) › [Grade 12](https://www.hlayiso.com/grade-12) › [Mathematics](https://www.hlayiso.com/grade-12/mathematics) › [Notes](https://www.hlayiso.com/grade-12/mathematics/notes) › [Algebraic expressions, equations and inequalities](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities) ## Sections in Algebraic expressions, equations and inequalities Each entry shows the free preview (about 200 characters). Create a free Hlayiso account to read the full notes, practise every question and track your progress. - [Algebraic Expressions](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/algebraic-expressions) — Algebraic Expressions Algebra forms the backbone of Grade 12 Mathematics and appears in almost every topic you will encounter in the NSC examination. Before tackling equations and inequalities, you… - [Addition and Subtraction](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/addition-and-subtraction) — Addition and Subtraction of Algebraic Expressions Adding and subtracting algebraic expressions is one of the most fundamental operations you will perform in Grade 12 Mathematics. Getting this right… - [Multiplication and Division](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/multiplication-and-division) — Multiplication and Division of Algebraic Expressions Once you are comfortable adding and subtracting expressions, the next step is multiplying and dividing them. These operations appear in almost… - [Factorising](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/factorising) — Factorising Factorising is the reverse of expanding. Instead of removing brackets, you put them back in. This skill is essential because it is the first step in solving quadratic equations,… - [Notes on Factorising a Trinomial](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/notes-on-factorising-a-trinomial) — Notes on Factorising a Trinomial Factorising trinomials of the form $ax^2 + bx + c$ is one of the most tested skills in the Grade 12 exam. Many students struggle with this when $a \\neq 1$. This… - [Quadratic Equations](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/quadratic-equations) — Quadratic Equations A quadratic equation is any equation that can be written in the standard form $ax^2 + bx + c = 0$ where $a \\neq 0$. There are three methods for solving quadratic equations, and… - [Quadratic Inequalities](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/quadratic-inequalities) — Quadratic Inequalities A quadratic inequality looks like a quadratic equation but uses an inequality sign instead of an equals sign. For example: $x^2 - 5x + 6 \> 0$ or $2x^2 + x - 3 \\leq 0$. The… - [Simultaneous Equations](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/simultaneous-equations) — Simultaneous Equations Simultaneous equations are two or more equations that share the same unknowns and must be solved together. In Grade 12, you work with systems where one equation is linear and… - [The Nature of the Roots](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities/the-nature-of-the-roots) — The Nature of the Roots The nature of the roots of a quadratic equation tells you what type of solutions the equation has — without actually solving it. This is determined by the discriminant, which… ## Other Mathematics topics - [Exponents and Surds](https://www.hlayiso.com/grade-12/mathematics/notes/exponents-and-surds) - [Number patterns](https://www.hlayiso.com/grade-12/mathematics/notes/number-patterns) - [Functions and graphs](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs) - [Trig Functions](https://www.hlayiso.com/grade-12/mathematics/notes/trig-functions) - [Finance, growth and decay](https://www.hlayiso.com/grade-12/mathematics/notes/finance-growth-and-decay) - [Differential Calculus](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus) - [Counting principle and probability](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability) - [Analytical Geometry](https://www.hlayiso.com/grade-12/mathematics/notes/analytical-geometry) - [Trigonometry](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry) - [Trigonometry: Sine, Cosine and Area Rules](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry-sine-cosine-and-area-rules) - [Euclidean Geometry](https://www.hlayiso.com/grade-12/mathematics/notes/euclidean-geometry) - [Statistics](https://www.hlayiso.com/grade-12/mathematics/notes/statistics) ## Frequently asked questions ### What is covered in Algebraic expressions, equations and inequalities for Grade 12 Mathematics? The Algebraic expressions, equations and inequalities section covers all key concepts from the Grade 12 Mathematics CAPS curriculum, including detailed explanations, worked examples, and exam preparation tips. ### Are the Algebraic expressions, equations and inequalities notes free? Yes. Each section has a free preview, and a free Hlayiso account lets you read the full notes. ### How do these notes help with exam preparation? Our Algebraic expressions, equations and inequalities notes are CAPS-aligned and include worked examples, common mistakes to avoid, and exam tips — everything you need to prepare for your Grade 12 Mathematics exams. ### Are there quizzes for Algebraic expressions, equations and inequalities? Yes. Hlayiso has quizzes for Algebraic expressions, equations and inequalities in Grade 12 Mathematics. Test your understanding after reading the notes. --- Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. 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