Algebra and Functions — Edexcel International A-Level Mathematics
Edexcel International A-Level Mathematics · Edexcel IAL Maths P1 · 25 min read
1. Algebraic Expression Simplification★★☆☆☆⏱ 6 min
Simplification relies on three core skills: factorising polynomials, cancelling common factors, and applying index rules: $a^m \times a^n = a^{m+n}$, $\frac{a^m}{a^n} = a^{m-n}$, $(a^m)^n = a^{mn}$.
Exam tip: Always state restrictions on x for rational expressions, as Edexcel awards explicit marks for this.
2. Domain and Range Calculation★★★☆☆⏱ 7 min
For Edexcel P1, you will calculate domain and range for four common function types: linear, quadratic, root, and rational. Key restrictions to check: denominators cannot equal 0, expressions under square roots must be ≥ 0.
3. Composite and Inverse Functions★★★★☆⏱ 7 min
Composite functions apply one function after another: $fg(x) = f(g(x))$, meaning you substitute $g(x)$ into $f(x)$ wherever $x$ appears. Inverse functions $f^{-1}(x)$ reverse the operation of $f(x)$, and only exist if $f(x)$ is one-to-one.
Exam tip: Never confuse $fg(x)$ with $f(x) \times g(x)$: Edexcel examiners frequently test this common misinterpretation.
4. Function Graph Transformations★★★☆☆⏱ 5 min
Transformations applied inside the function bracket affect x-values (with opposite sign to what you expect), while transformations outside affect y-values (with the same sign). Apply transformations in order: inner x changes first, then stretches/reflections, then outer y changes.
Common Pitfalls
Why: You can only cancel common factors of the entire numerator and denominator, not individual un-factorised terms.
Why: Function composition is sequential, not multiplicative, and order matters: $fg(x)$ applies g first, then f, which is not the same as $gf(x)$ in most cases.
Why: Edexcel awards explicit marks for stating valid x-values, and omitting them leads to lost marks even if simplification is correct.
Why: Quadratics have a minimum or maximum at their vertex, which is not always at y=0 unless the vertex lies on the origin.
Why: Inner x transformations apply first, then stretches/reflections, then outer y transformations, so wrong order gives incorrect coordinate values.