MM1: Algebra, Polynomials and Functions
Official Cambridge & Imperial ESAT specification requirements for Algebra, Polynomials and Functions on the Mathematics 2 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
- 1Polynomial long division and linear remainder theorem: f(x) = Q(x)D(x) + R(x)
- 2Factor theorem: f(c) = 0 ⟺ (x - c) is a factor
- 3Quadratic discriminant Δ = b² - 4ac (real distinct, repeated, or no real roots)
- 4Vieta’s formulas for root sums (-b/a) and root products (c/a)
- 5Disguised radical equations and principal square root domain filtering (√x ≥ 0)
- 6Function domain and range constraints
Sub-90 Exam Speed Tips
How top candidates solve this spec under the 88.8s clock
When dividing by a quadratic divisor, the remainder must be assumed linear: R(x) = mx + n.
Always substitute candidate roots back into radical equations to discard extraneous non-principal branch solutions.
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 MM1
Master the individual question patterns and Sub-90 shortcuts for this specification.
Polynomial Division by a Quadratic & Linear Remainder Theorem (R(x) = mx + n)
Never perform long division: write P(x) = Q(x)(x-a)(x-b) + mx + n, substitute x = a and x = b to get two instant linear equations ma + n = P(a) and mb + n = P(b).
Disguised Radical Equations & Principal Square Root Domain Filtering (√x ≥ 0)
In ESAT/TMUA, √(u) is strictly >= 0. Before squaring sqrt(f(x)) = g(x), write the mandatory filter g(x) >= 0 on your notepad and discard any root that fails it.
Quadratic Discriminant (b² - 4ac), Root-Difference Identities & Parameter Range Inequalities
For ax² + bx + c = 0, the positive difference between roots is ALWAYS |alpha - beta| = √(b² - 4ac) / |a|. For two distinct positive roots, intersect three conditions: Δ > 0, -b/a > 0, and c/a > 0.
Ready to Master Specification MM1 Under Exam Conditions?
Practice timed questions under the authentic Pearson VUE interface with live split stopwatch pacing, dry-wipe scratchpad, and distractor forensics.