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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→B assigns each x∈A to one output f(x)∈B
Want weekly guided practice on Functions? Our H2 Maths tuition programme builds fluency in this topic through structured problem sets and exam-style drills.
Common exam mistakes
Giving the range of f as the domain of f−1 without checking: The domain of f−1 equals the range of f, but only over the restricted domain. If you have restricted f to make it one-to-one, compute the range of the restricted f before stating the domain of f−1.
Attempting composition fg when the range of g is not a subset of the domain of f: The composition f∘g only exists when every output of g is a valid input for f
Restricting the domain to make f injective without verifying injectivity: Simply stating "restrict to x≥0" is insufficient if f is still not one-to-one on that interval. Always verify the horizontal-line test or use the derivative to confirm monotonicity.
Swapping x and y without keeping track of variable meaning: When deriving f−1, many students swap x↔y mid-working and lose track of which variable is the input. Write y=f(x)
Omitting the domain and range when stating the inverse function: A complete answer for an inverse function must state both f−1(x)=… and explicitly give the domain of f−1 (which equals the range of f). Omitting either loses a mark.
Frequently asked questions
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)⇒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.
