H2 Maths Notes (JC 1-2): 1.2) Graphs and Transformations

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07 Oct 2025, 00:00 Z

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Marcus Pang·Managing Director (Maths)

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Q: What does H2 Maths Notes (JC 1-2): 1.2) Graphs and Transformations cover?
A: Sketching workflows, asymptotes, parametric curves, and transformation chains for H2 Maths Topic 1.2.

Before you revise
Keep a doodle pad next to your graphing calculator (GC). Sketch every curve by hand even if technology can plot it-the mark scheme rewards annotations and reasoning, not just the final picture.

Status: SEAB H2 Mathematics (9758) syllabus last checked 2026-01-13. Topic 1.2 scope unchanged; Pure Mathematics is assessed in Paper 1 (100 marks) and Paper 2 Section A (40 marks).

Core Sketching Strategy

Intercepts: Solve $f(x) = 0$ for x-intercepts; evaluate $f(0)$ for the y-intercept.
Asymptotes: Inspect denominators for vertical asymptotes and examine end behaviour (long division) for horizontal or oblique asymptotes.
Stationary Points: Solve $f'(x) = 0$

Expression	Effect on base graph $y = f(x)$
$y = a f(x)$	Vertical stretch by $\lvert a \rvert$ and reflection if $a < 0$ .
$y = f(x) + b$	Shift up by $b$ .
$y = f(x - h)$	Shift right by $h$ .
$y = f(ax)$	Horizontal compression by $\lvert a \rvert$ .
$y = f(\lvert x \rvert)$	Mirror the right-half across the y-axis.
$y = \lvert f(x) \rvert$	Reflect sections below the x-axis upward.
$y = \tfrac{1}{f(x)}$	Reciprocal curve with vertical asymptotes where $f(x) = 0$ .

H2 Maths Notes (JC 1-2): 1.2) Graphs and Transformations

Core Sketching Strategy

Common Function Families

Transformation Toolkit

Parametric and Polar Sketches

Graphs of Inverses and Moduli

Calculator Support

Exam Watch Points

Practice Quiz

Quick Revision Checklist

Sources

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