| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2016 |
| 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 C1 question testing completing the square (a routine algebraic procedure) and identifying transformations. Part (a)(i) is a standard textbook exercise, (a)(ii) requires simply reading off the minimum from completed square form, and part (b) involves recognizing a translation. All parts are procedural 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 |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\left(x-\frac{7}{2}\right)^2 \ldots\) | M1 | \((x-3.5)^2 \ldots\) OE |
| \(\left(x-\frac{7}{2}\right)^2 - \frac{41}{4}\) | A1 | \((x-3.5)^2 - 10.25\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Minimum value \(= -10.25\) OE | B1F | Must follow through their \(q\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Translation | E1 | Or translate(d) (by/through); no other transformation given |
| \(\begin{bmatrix} 0.5 \\ * \end{bmatrix}\) | M1 | |
| \(\begin{bmatrix} 0.5 \\ 10.25 \end{bmatrix}\) | A1 | Must express as vector to earn A1 mark |
## Question 3:
### Part (a)(i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\left(x-\frac{7}{2}\right)^2 \ldots$ | M1 | $(x-3.5)^2 \ldots$ OE |
| $\left(x-\frac{7}{2}\right)^2 - \frac{41}{4}$ | A1 | $(x-3.5)^2 - 10.25$ |
### Part (a)(ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Minimum value $= -10.25$ OE | B1F | Must follow through their $q$ |
### Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Translation | E1 | Or translate(d) (by/through); no other transformation given |
| $\begin{bmatrix} 0.5 \\ * \end{bmatrix}$ | M1 | |
| $\begin{bmatrix} 0.5 \\ 10.25 \end{bmatrix}$ | A1 | Must express as vector to earn A1 mark |3
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Express $x ^ { 2 } - 7 x + 2$ in the form $( x - p ) ^ { 2 } + q$, where $p$ and $q$ are rational numbers.
\item Hence write down the minimum value of $x ^ { 2 } - 7 x + 2$.
\end{enumerate}\item Describe the geometrical transformation which maps the graph of $y = x ^ { 2 } - 7 x + 2$ onto the graph of $y = ( x - 4 ) ^ { 2 }$.\\[0pt]
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA C1 2016 Q3 [6]}}