H2 Maths Functions and Graphs | Free Notes

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07 Oct 2025, 00:00 Z· Last updated 13 Jan 2026

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Marcus Pang·Managing Director (Maths)

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Q: What does H2 Maths Notes (JC 1-2): 1) Functions and Graphs cover?
A: Detailed guide to MOE Topic 1 -- functions, transformations, equations, and inequalities -- with worked examples and calculator workflows.

Before you begin\ Make sure your Additional Maths foundations are fresh (logarithms, surds, quadratic inequalities). Keep the graphing calculator (GC) in Exam Mode while you revise so keystrokes become automatic.

For the full topic map, paper weightings, and official PDF link, see our H2 Maths Syllabus 2026-27 overview.

Status: SEAB H2 Mathematics (9758, first exam 2026) syllabus last checked 2026-01-13 (PDF last modified 2024-10-16). Topic 1 coverage unchanged; Pure Mathematics is assessed in Paper 1 (100 marks) and Paper 2 Section A (40 marks).

1.1 | Functions

Core ideas

A function maps each input in its domain to exactly one output in its range.
Injective (one-to-one) functions pass the horizontal-line test and admit inverses on their natural domain.
Composition $(f \circ g)(x) = f\bigl(g(x)\bigr)$

Transformation	Effect on $y = f(x)$	Notes
$y = a f(x)$	Vertical stretch by $\lvert a \rvert$ (reflect if $a < 0$ )	Multiply y-values.
$y = f(x) + a$	Shift up by $a$	Add to the output.
$y = f(x + a)$	Shift left by $a$	Replace $x$ with $x + a$
$y = f(ax)$	Horizontal compression by $\lvert a \rvert$ (reflect if $a < 0$ )	Divide x-values by $a$
$y = \lvert f(x) \rvert$	Reflect negative parts above the x-axis	Ensure the range is non-negative.
$y = f(\lvert x \rvert)$	Mirror the right-half graph across the y-axis	Only the right half is independent.
$y = \frac{1}{f(x)}$	Reciprocal graph	Watch for new vertical asymptotes where $f(x) = 0$

H2 Maths Functions and Graphs | Free Notes

1.1 | Functions

Core ideas

Domain/range checks

Composition pitfalls

1.2 | Graphs and Transformations

Essential graph features

Transformation cheat sheet

Parametric sketches

1.3 | Equations and Inequalities

General equation strategy

Systems of linear equations

Inequalities

Graphical method with GC

Practice Quiz

1.4 | Quick Revision Checklist

Sources

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