| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2016 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Composite & Inverse Functions |
| Type | Find function from composite |
| Difficulty | Moderate -0.3 This is a slightly below-average A-level question. Part (i) is routine completing the square (standard GCSE/AS technique), part (ii) requires simple substitution to find g(x) once part (i) is done, and part (iii) involves finding an inverse function with domain consideration—all standard textbook exercises with no novel problem-solving required. The multi-part structure adds some length but each component is straightforward. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02v Inverse and composite functions: graphs and conditions for existence |
\begin{enumerate}[label=(\roman*)]
\item Express $4x^2 + 12x + 10$ in the form $(ax + b)^2 + c$, where $a$, $b$ and $c$ are constants. [3]
\item Functions $f$ and $g$ are both defined for $x > 0$. It is given that $f(x) = x^2 + 1$ and $fg(x) = 4x^2 + 12x + 10$. Find $g(x)$. [1]
\item Find $(fg)^{-1}(x)$ and give the domain of $(fg)^{-1}$. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2016 Q8 [8]}}