| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Composite transformation sketch |
| Difficulty | Moderate -0.3 This is a slightly below-average A-level question. Part (i) requires finding where the square root is defined (routine domain work), part (ii) is direct observation of range from the function form, and part (iii) involves standard transformations (horizontal stretch and vertical translation). All techniques are straightforward C3 content with no problem-solving insight required, though the combination of transformations adds minor complexity beyond pure recall. |
| Spec | 1.02u Functions: definition and vocabulary (domain, range, mapping)1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (i) | 1 9a2 = 0 |
| a2 = 1/9 a = 1/3 | M1 |
| Answer | Marks |
|---|---|
| [2] | or 1 9x2 = 0 |
| or 0.33 or better √(1/9) is A0 | √(1 – 9a2) = 1 – 3a is M0 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (ii) | Range 0 ≤ y ≤ 1 |
| [1] | or 0 ≤ f(x) ≤ 1 or 0 ≤ f ≤ 1, not 0 ≤ x ≤ 1 | |
| 0 ≤ y ≤ √1 is B0 | allow also [0,1], or 0 to 1 inclusive, |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (iii) | 1 1 |
| 1 | M1 |
| Answer | Marks |
|---|---|
| [3] | curve goes from x = −3a to x = 3a |
| Answer | Marks |
|---|---|
| vertex at O and correct scaling) | must have evidence of using s.f. 3 |
Question 4:
4 | (i) | 1 9a2 = 0
a2 = 1/9 a = 1/3 | M1
A1
[2] | or 1 9x2 = 0
or 0.33 or better √(1/9) is A0 | √(1 – 9a2) = 1 – 3a is M0
not a = ± 1/3 nor x = 1/3
4 | (ii) | Range 0 ≤ y ≤ 1 | B1
[1] | or 0 ≤ f(x) ≤ 1 or 0 ≤ f ≤ 1, not 0 ≤ x ≤ 1
0 ≤ y ≤ √1 is B0 | allow also [0,1], or 0 to 1 inclusive,
but not 0 to 1 or (0,1)
4 | (iii) | 1 1
1 | M1
M1
A1
[3] | curve goes from x = −3a to x = 3a
(or −1 to 1)
vertex at origin
curve, ‘centre’ (0,−1), from (−1, −1) to
(1, −1) (y-coords of −1 can be inferred from
vertex at O and correct scaling) | must have evidence of using s.f. 3
allow also if s.f.3 is stated and
stretch is reasonably to scale
allow from (−3a, −1) to (3a, −1)
provided a = 1/3 or x = [±] 1/3 in (i)
A0 for badly inconsistent scale(s)Fig. 4 shows the curve $y = \text{f}(x)$, where $\text{f}(x) = \sqrt{1 - 9x^2}$, $-a < x < a$.
\includegraphics{figure_4}
\begin{enumerate}[label=(\roman*)]
\item Find the value of $a$. [2]
\item Write down the range of f(x). [1]
\item Sketch the curve $y = \text{f}(\frac{1}{3}x) - 1$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 Q4 [6]}}