M4: Algebra, Equations and Inequalities
Official Cambridge & Imperial ESAT specification requirements for Algebra, Equations and Inequalities on the Mathematics 1 paper. Understand the syllabus boundaries, spot distractor traps engineered by examiners, and master the 2-step Sub-90 shortcuts that compress solve time well below the 88.8-second cutoff.
Official Syllabus Subtopics
Requirements specified in the UAT-UK framework
- 1Algebraic subject rearrangement with nested radicals and rational fractions
- 2Completing the square: a(x + p)² + q and turning point coordinates
- 3Simultaneous linear equations and linear combinations
- 4Linear and quadratic inequalities with sign interval charts
- 5Difference of two squares factorisation and algebraic identities
Sub-90 Exam Speed Tips
How top candidates solve this spec under the 88.8s clock
When completing the square with a leading coefficient a ≠ 1, always factor out `a` from both x terms first.
Never multiply or divide an inequality by an unknown expression without establishing its sign.
Examiners engineer distractor options using common algebraic expansions and sign slips. Always test structural ratios or invariants before calculating arithmetic values.
Tested Topics in Specification M4
Master the individual question patterns and Sub-90 shortcuts for this specification.
Algebraic Subject Rearrangement, Rational Fractions & Completing the Square
For y = (ax+b)/(cx+d), the inverse rearrangement swaps (a, d) with a sign flip: x = (-dy+b)/(cy-a). For p(x+q)²⁺r, evaluate at x=0 and x=-q to find r in 10 seconds without full expansion.
Simultaneous Linear Combinations, Straight-Line Gradients & Inequalities
Check if the target expression (e.g. 6a+2c) is a direct linear combination of the given equations (2*(4a+4c) - (2a+3c)) before solving for individual variables. For ax+by=c, gradient is -a/b.
Ready to Master Specification M4 Under Exam Conditions?
Practice timed questions under the authentic Pearson VUE interface with live split stopwatch pacing, dry-wipe scratchpad, and distractor forensics.