Is Topic 1.1 (Functions) in Paper 1 or Paper 2?

Topic 1.1 is Pure Mathematics and can appear in Paper 1 (100 marks) or Paper 2 Section A (40 marks). Functions questions are often in the early parts of structured questions and test precision with domain notation.

Do I need to prove injectivity algebraically, or is a GC sketch sufficient?

The GC can support your reasoning but is not a substitute for an algebraic or derivative-based proof. To prove \$f\$ is one-to-one, either show \$f(x1) = f(x2) \Rightarrow x1 = x2\$ algebraically, or show \$f'(x) > 0\$ (or \$< 0\$) on the domain to establish strict monotonicity.

What is the difference between "domain" and "natural domain"?

The natural domain is the largest set of real numbers for which \$f(x)\$ is defined (no division by zero, no negative square roots, etc.). A restricted domain is a subset chosen to make \$f\$ injective (for finding an inverse). Always check whether the question specifies a domain or asks you to state the natural domain. ---

H2 Maths Functions Notes | Domains, Inverses & Composites

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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): 1.1) Functions cover?
A: Domains, ranges, inverse checks, and composite workflows for Section A Topic 1.1 of the 2026 H2 Maths syllabus.

Before you revise
Keep a running list of domain restrictions (denominators, even roots, logarithms). Test every claim with quick substitutions or GC trace-functions questions are marked on precision.

Status: SEAB H2 Mathematics (9758) syllabus last checked 2026-01-13. Topic 1.1 expectations unchanged; Pure Mathematics is assessed in Paper 1 (100 marks) and Paper 2 Section A (40 marks).

Core Concepts

A function $f: A \to B$ assigns each $x \in A$ to one output $f(x) \in B$

Sources

SEAB H2 Mathematics (9758) Syllabus 2026

H2 Maths Functions Notes | Domains, Inverses & Composites

Core Concepts

Sources

Domain and Range Workflow

Inverse Functions

Composite Functions

Modelling with Functions

Calculator Workflow

Practice Quiz

Quick Revision Checklist

Common exam mistakes

Frequently asked questions

Sources

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