Edexcel IAL P3 Functions Questions
Domain, range, composite and inverse functions; the modulus function y = |f(x)| and y = f(|x|); combinations of transformations.
- P3 · Pure Mathematics 3
- Calculator allowed
- 35 practice questions
What the questions test
The 35 P3 functions practice questions cover:
Worked example 1
Solve the inequality $|2x + 1| \le |x - 5|$.
Mark scheme
- M1 for squaring both sides to remove the modulus signs: $(2x+1)^2 \le (x-5)^2$.
- M1 for expanding the brackets: $4x^2 + 4x + 1 \le x^2 - 10x + 25$.
- M1 for rearranging to form a quadratic inequality: $3x^2 + 14x - 24 \le 0$.
- M1 for factorising to find the critical values: $(3x-4)(x+6) \le 0$, yielding critical values $-6$ and $\frac{4}{3}$.
- A1 for stating the correct closed interval $-6 \le x \le \frac{4}{3}$.
Worked example 2
Given that $f(x) = \frac{x+1}{x-2}$, $x \ne 2$, find an expression for $ff(x)$ in its simplest form.
Mark scheme
- M1 for substituting $f(x)$ into itself: $ff(x) = \frac{\frac{x+1}{x-2} + 1}{\frac{x+1}{x-2} - 2}$.
- M1 for multiplying the numerator and the denominator by $(x-2)$ to clear the nested fractions.
- M1 for obtaining the expanded fraction $\frac{(x+1) + (x-2)}{(x+1) - 2(x-2)}$.
- A1 for fully simplifying to $\frac{2x-1}{5-x}$ (or $\frac{1-2x}{x-5}$).
FAQ
What functions is in Edexcel IAL P3?
Domain, range, composite and inverse functions; the modulus function y = |f(x)| and y = f(|x|); combinations of transformations.
Is P3 a calculator paper?
Yes, a calculator is allowed in P3, but method marks are only given for working you write down.
How are P3 functions questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.