Chapter 5.1
Linear equations (complex multi-step)
Solve equations requiring multiple inverse operations and nested brackets.
Chapters16
Equations, quadratics, inequalities, iteration, graphical methods.
Time invested12 hrs
Approximate guided learning.
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Chapter 5.2
Equations with fractions
Clear denominators efficiently and solve fraction-based equations.
Chapter 5.3
Equations with brackets & fractions
Combine expansion and fraction clearing to solve demanding equations.
Chapter 5.4
Simultaneous equations (elimination – advanced)
Use elimination for larger coefficients and contextual problems.
Chapter 5.5
Simultaneous equations (substitution – advanced)
Solve systems requiring substitution into non-linear expressions.
Chapter 5.6
Simultaneous equations (one linear, one quadratic)
Find intersections analytically and interpret results graphically.
Chapter 5.7
Quadratic equations – factorising
Solve quadratics using factorisation and check solutions.
Chapter 5.8
Quadratic equations – formula
Use the quadratic formula, discriminant, and surd solutions.
Chapter 5.9
Completing the square
Rewrite quadratics in vertex form for solving and graphing.
Chapter 5.10
Solving equations by iteration
Use iterative processes and convergence ideas for non-linear equations.
Chapter 5.11
Linear inequalities (complex)
Solve inequalities with fractions, negative multipliers, and double bounds.
Chapter 5.12
Quadratic inequalities
Use quadratic graphs to determine solution intervals.
Chapter 5.13
Graphical solutions to equations
Interpret intersections of graphs to solve systems and check work.
Chapter 5.14
Solving equations graphically (applications)
Apply graphical methods to motion, economics, and science contexts.
Chapter 5.15
Trial and improvement
Use systematic trials for equations lacking analytic solutions.
Chapter 5.16
Equation problem solving (GCSE)
Blend all techniques to tackle real exam-style applications.
Next steps
Need more algebraic manipulation? Revisit Section 4, or continue into Section 6 for sequence mastery.