| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete the square |
| Difficulty | Moderate -0.8 This is a straightforward completing-the-square exercise with standard follow-up questions. Part (a) requires a routine algebraic manipulation, part (b) is direct reading from the completed square form, and part (c) tests basic understanding of transformations. All parts are textbook-standard with no problem-solving or novel insight required, making it easier than average. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\left(x - \frac{3}{2}\right)^2\) | B1 | |
| \(+ \frac{7}{4}\) | B1 | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Minimum value is \(\frac{7}{4}\) | B1 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Translation (and no other transformation stated) | E1 | |
| through \(\begin{bmatrix} 3/2 \\ 7/4 \end{bmatrix}\) (or equivalent in words) | M1, A1 | 3 |
**4(a)**
| $\left(x - \frac{3}{2}\right)^2$ | B1 | | Must have $()^2$, $p = 1.5$ |
| $+ \frac{7}{4}$ | B1 | 2 | $q = 1.75$ |
**4(b)**
| Minimum value is $\frac{7}{4}$ | B1 | 1 | ft their $q$ or correct value |
**4(c)**
| **Translation** (and no other transformation stated) | E1 | | (not shift, move, transformation etc) |
| through $\begin{bmatrix} 3/2 \\ 7/4 \end{bmatrix}$ (or equivalent in words) | M1, A1 | 3 | M1 for one component correct or ft their $p$ or $q$ values CSO; condone 1.5 right and 1.75 up etc |
---4
\begin{enumerate}[label=(\alph*)]
\item Express $x ^ { 2 } - 3 x + 4$ in the form $( x - p ) ^ { 2 } + q$, where $p$ and $q$ are rational numbers.\\
(2 marks)
\item Hence write down the minimum value of the expression $x ^ { 2 } - 3 x + 4$.
\item Describe the geometrical transformation that maps the graph of $y = x ^ { 2 }$ onto the graph of $y = x ^ { 2 } - 3 x + 4$.
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2008 Q4 [6]}}