Chapter 4.1
Expanding double brackets (mastery)
Expand binomials efficiently using FOIL, grid, and algebra tiles.
Chapters15
Double/triple brackets, algebraic fractions, rearranging formulae.
Time invested11 hrs
Approximate guided learning.
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Chapter 4.2
Expanding triple brackets
Combine expansion strategies to handle cubics and product chains.
Chapter 4.3
Factorising quadratics (a = 1)
Use sum-product reasoning to factor trinomials with leading coefficient 1.
Chapter 4.4
Factorising quadratics (a ≠ 1)
Factor harder quadratics using grouping, AC method, or splitting middle term.
Chapter 4.5
Difference of two squares
Recognise and factor expressions like a² − b² quickly.
Chapter 4.6
Simplifying algebraic fractions
Cancel common factors and tidy rational expressions.
Chapter 4.7
Adding & subtracting algebraic fractions
Use common denominators and factor spotting to combine fractions.
Chapter 4.8
Multiplying & dividing algebraic fractions
Multiply numerators/denominators and simplify cross-cancellation.
Chapter 4.9
Algebraic proof
Construct proofs using substitution, expansion, and generalising.
Chapter 4.10
Rearranging formulae (simple)
Change the subject in single-step formulae and basic triangles.
Chapter 4.11
Rearranging formulae (complex)
Handle multi-step rearrangements with fractions, powers, and roots.
Chapter 4.12
Changing the subject when it appears twice
Use exponent rules and factoring to isolate repeated variables.
Chapter 4.13
Indices in algebra – all laws
Blend exponent rules with algebraic expressions and formulae.
Chapter 4.14
Substitution – complex formulae
Evaluate formulae with multiple variables, fractions, and powers.
Chapter 4.15
Writing & using formulae
Create algebraic models for geometric, financial, and scientific contexts.
Next steps
Need more proportion practice? Revisit Section 3, or continue into Section 5 for algebraic equations and inequalities mastery.