MM8: Graph Transformations, Modulus and Roots
Official Cambridge & Imperial ESAT specification requirements for Graph Transformations, Modulus and Roots 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
- 1Translations: f(x + a) shifts left by a, f(x) + a shifts up by a
- 2Stretches: f(ax) stretches horizontally by factor 1/a, a f(x) stretches vertically by factor a
- 3Reflections: -f(x) reflects in x-axis, f(-x) reflects in y-axis
- 4Modulus transformations: |f(x)| reflects negative parts upward, f(|x|) reflects positive x across y-axis
- 5Counting intersection roots of transformed curves
- 6Vertical, horizontal, and oblique asymptotes
Sub-90 Exam Speed Tips
How top candidates solve this spec under the 88.8s clock
For combined transformations like f(ax + b), factorise to f(a(x + b/a)): translate left by b/a first, then stretch horizontally by 1/a.
To sketch |f(x)|, reflect everything below the x-axis upward; for f(|x|), erase x < 0 and mirror x > 0 across the y-axis.
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 MM8
Master the individual question patterns and Sub-90 shortcuts for this specification.
Multi-Step Graph Transformations (af(bx+c)+d), Modulus Reflections & Root Counting
Track a single landmark point (vertex or intercept) through the equation: if (x₀, y₀) is on y = f(x), solve bx(new) + c = x₀ for x(new) and set y(new) = a*y₀ + d.
Ready to Master Specification MM8 Under Exam Conditions?
Practice timed questions under the authentic Pearson VUE interface with live split stopwatch pacing, dry-wipe scratchpad, and distractor forensics.