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MathematicsGrade 10Quality review 0/4

Solving Linear & Quadratic Equations

From your first balance-scale equation to the quadratic formula: a complete, CAPS-aligned Grade 10 journey through solving equations. Every concept comes in two modes — rigorous Theory and intuition-first Visual — with worked examples from everyday South African life and over a hundred practice problems with hints and full solutions.

≈ 14 h 45 min6 sections · 32 lessonsNo ratings yet
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What you'll learn

  • Solve linear equations, inequalities and simultaneous equations confidently — including brackets, fractions and changing the subject of a formula
  • Factorise expressions using common factors, difference of squares and trinomial methods, and verify factorisations by expansion
  • Solve quadratic equations by factorising, square roots, completing the square and the quadratic formula, and use the discriminant to predict the nature of the roots
  • Translate real-world problems into equations, solve them, and interpret which roots make sense in context

Before you start

  • Grade 9 algebra: simplifying expressions, integers and fractions
  • Basic number facts: multiplication tables, squares and square roots up to 12

Course content

0/32 lessons
1. Equation Foundations5 lessons
  1. What Is an Equation?Lesson20 min
  2. Checking a Solution by SubstitutionLesson20 min
  3. Undoing Operations: InversesLesson20 min
  4. One-Step EquationsLesson25 min
  5. Two-Step EquationsLesson25 min
2. Linear Equations7 lessons
  1. Solving Linear EquationsLesson30 min
  2. Variables on Both SidesLesson25 min
  3. Equations with BracketsLesson25 min
  4. Equations with FractionsLesson30 min
  5. Changing the Subject of a FormulaLesson30 min
  6. Linear InequalitiesLesson25 min
  7. Word Problems with Linear EquationsLesson30 min
3. Simultaneous Linear Equations4 lessons
  1. What Are Simultaneous Equations?Lesson20 min
  2. Solving by SubstitutionLesson30 min
  3. Solving by EliminationLesson30 min
  4. Word Problems with Two UnknownsLesson30 min
4. Factorising6 lessons
  1. Taking Out Common FactorsLesson25 min
  2. Difference of Two SquaresLesson25 min
  3. Factorising TrinomialsLesson30 min
  4. Factorising QuadraticsLesson30 min
  5. The Zero-Product PropertyLesson25 min
  6. Solving Quadratics by FactorisingLesson30 min
5. Quadratic Equations6 lessons
  1. Standard Form of a QuadraticLesson20 min
  2. Solving with Square RootsLesson25 min
  3. Completing the SquareLesson35 min
  4. The Quadratic FormulaLesson35 min
  5. The Discriminant: How Many Roots?Lesson25 min
  6. Choosing the Best MethodLesson25 min
6. Applications & Mastery4 lessons
  1. Word Problems with QuadraticsLesson35 min
  2. Graphs and RootsLesson30 min
  3. Mixed Practice: Linear & QuadraticLesson35 min
  4. Exam-Style RevisionLesson40 min