Challenging +1.2 This FP2 question requires understanding that y² = f(x) means y = ±√f(x), so the curve is reflected in the x-axis and only exists where f(x) ≥ 0. Students must identify which portions of the original curve to keep (between the roots) and apply the square root transformation. While it requires careful geometric reasoning about transformations and domain restrictions, it's a standard FP2 technique with straightforward coordinate identification once the concept is grasped.
3 The diagram shows the curve \(y = \mathrm { f } ( x )\). Points \(A , B , C\) and \(D\) on the curve have coordinates ( \(- 1,0 ) , ( 2,0 )\), \(( 5,0 )\) and \(( 0,2 )\) respectively.
\includegraphics[max width=\textwidth, alt={}, center]{a31997f4-7890-42c1-9725-1b7058e8741f-2_593_1221_1041_406}
On the copy of this diagram in the Printed Answer Book, sketch the curve \(y ^ { 2 } = \mathrm { f } ( x )\), giving the coordinates of the points where the curve crosses the axes.
# Question 3:
| Answer | Mark | Guidance |
|--------|------|----------|
| Sketch: symmetric but not reflecting original curve | B1 | Symmetric but not for reflecting original curve |
| Both ranges only and nothing more | B1 | Both ranges only and nothing more |
| All parts cut $x$-axis at $90°$ | B1 | All parts cut $x$-axis at $90°$ |
| Both parts cut original curve at $y=k$ and central part "egg shaped", $k$ only approximately 1 | B1 | Approximate consistency |
| Points: $(-1,0),\ (2,0),\ (5,0)$; $\left(0,\sqrt{2}\right),\ \left(0,-\sqrt{2}\right)$ | B1 | All 5 points given |
| | **[5]** | |
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3 The diagram shows the curve $y = \mathrm { f } ( x )$. Points $A , B , C$ and $D$ on the curve have coordinates ( $- 1,0 ) , ( 2,0 )$, $( 5,0 )$ and $( 0,2 )$ respectively.\\
\includegraphics[max width=\textwidth, alt={}, center]{a31997f4-7890-42c1-9725-1b7058e8741f-2_593_1221_1041_406}
On the copy of this diagram in the Printed Answer Book, sketch the curve $y ^ { 2 } = \mathrm { f } ( x )$, giving the coordinates of the points where the curve crosses the axes.
\hfill \mbox{\textit{OCR FP2 2016 Q3 [5]}}