| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Finding quadratic constants from algebraic conditions |
| Difficulty | Moderate -0.8 This question tests basic understanding of vertex form of a quadratic and simple transformations. Part (a) requires recognizing that the vertex form y = a(x+b)² + c has its stationary point at (-b, c), making b=3 and c=2 immediate. Part (b) involves applying a horizontal translation and substituting a point to find a. All steps are routine with no problem-solving insight required, making this 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 | Marks | Guidance |
| Stationary point at \((-3, 2) \Rightarrow b = 3,\ c = 2\) | B2 (1.1, 1.1) | B1 for one correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Translated curve is \(y = a(x + (b-4))^2 + c\) | M1* | Translates \(y\) by either \(\binom{\pm4}{0}\) only. Possible to translate \((3,-18)\) by \(\binom{\pm4}{0}\) and use original curve to find \(a\) |
| \(-18 = a(3 + (b-4))^2 + c \Rightarrow a = \ldots\) | M1dep* | Substitutes \((3, -18)\) into translated curve and finds a value for \(a\) |
| \(a = -5\) | A1 |
# Question 5:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Stationary point at $(-3, 2) \Rightarrow b = 3,\ c = 2$ | B2 (1.1, 1.1) | B1 for one correct |
**[2 marks]**
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Translated curve is $y = a(x + (b-4))^2 + c$ | M1* | Translates $y$ by either $\binom{\pm4}{0}$ only. Possible to translate $(3,-18)$ by $\binom{\pm4}{0}$ and use original curve to find $a$ |
| $-18 = a(3 + (b-4))^2 + c \Rightarrow a = \ldots$ | M1dep* | Substitutes $(3, -18)$ into translated curve and finds a value for $a$ |
| $a = -5$ | A1 | |
**[3 marks]**5 A curve has equation $y = a ( x + b ) ^ { 2 } + c$, where $a , b$ and $c$ are constants. The curve has a stationary point at $( - 3,2 )$.
\begin{enumerate}[label=(\alph*)]
\item State the values of $b$ and $c$.
When the curve is translated by $\binom { 4 } { 0 }$ the transformed curve passes through the point $( 3 , - 18 )$.
\item Determine the value of $a$.
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q5 [5]}}