Paper 1: the mathematical core
The \(CF\) Maths Paper \(1\) sequence is Algebra & Functions, Sequences & Series, Coordinate Geometry, Trigonometry, Exponentials & Logarithms, Differentiation and Integration. Graph interpretation is woven through algebra, trigonometry, exponentials and calculus rather than treated as an isolated memorisation chapter.
The strongest preparation is cumulative: algebraic manipulation supports every later chapter; functions and graphs support root-counting; sequences feed into logarithms and trigonometry; differentiation and integration then reuse all of those structures.
- Algebra, functions, inequalities, polynomials, modulus and graph transformations
- Explicit and recurrent sequences, AP/GP, sigma notation and binomial structure
- Lines, circles, tangency, chords and coordinate geometry
- Exact trigonometry, equations, radians, sine/cosine rules and triangle logic
- Exponentials and logarithms with domain and monotonicity control
- Differentiation for tangents, normals, stationary points, optimisation and root counts
- Integration, signed area, definite-integral identities, trapezium rule and accumulated-area reasoning
Paper 2: mathematical logic around familiar content
Paper \(2\) uses familiar mathematics but changes the question being asked. Instead of simply solving an equation, you may need to decide whether a condition is necessary, sufficient, both or neither; identify a counterexample; recognise a contrapositive; preserve quantifier order; or find the first invalid line in a proof.
The \(CF\) Maths Proof & Logic material therefore trains the exact logical status of claims across algebra, calculus, sequences, number theory and geometry rather than treating proof as a separate abstract topic.
- Necessary and sufficient conditions
- Converses and contrapositives
- Counterexamples to universal claims
- Quantifiers: for all \(/\) there exists
- Proof-error analysis and reversible steps
- Number and divisibility reasoning
- Geometry and calculus sufficiency arguments
What is extension material?
Some \(CF\) Maths questions deliberately go beyond the most literal topic labels in order to create stronger admissions-test reasoning. Floor and ceiling functions are a good example: they are used as an advanced extension for interval splitting, exact reasoning and mixed-topic practice, not presented as a named core integration requirement.
Use extensions after the core is stable. They are valuable because they force unfamiliar reasoning, but they should not displace mastery of the published mathematical foundations.