| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Read parameters from graph of transformed trig function |
| Difficulty | Moderate -0.8 This question requires reading amplitude, vertical shift, and period from sine graphs to determine parameters a, b, and c. While it involves multiple parameters and two parts, the process is mechanical: a is the midline, b is the amplitude, and c comes from the period formula. This is a standard textbook exercise testing graph interpretation rather than problem-solving, making it easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.05f Trigonometric function graphs: symmetries and periodicities |
## (i) Bounds
B1 bounds $-\pi + 1 < f(x) < \pi + 1$
B1 or $\ldots < y < \ldots$ or $(-\pi + 1, \pi + 1)$
B1 cao
[3]
## (ii) Inverse function
M1 attempt to invert formula
A1 $y - 1 = 2\arctan x$ or $\arctan y = \frac{x-1}{2}$ or $\arctan x = \frac{y-1}{2}$
A1 $y = \tan\left(\frac{x-1}{2}\right)$ or $f^{-1}(x) = \tan\left(\frac{x-1}{2}\right)$
B1 reasonable reflection in $y = x$
B1 $(1, 0)$ intercept indicated
[5]
**Guidance:** Not $\ldots < x < \ldots$, not 'between $\ldots$'; one step is enough, i.e. $y - 1 = 2\arctan x$ or $x - 1 = 2\arctan y$; need not have interchanged $x$ and $y$ at this stage; allow $y = \ldots$; curves must cross on $y = x$ line if present (or close enough to imply intention); curves shouldn't touch or cross in the third quadrant.
---2 The curves in parts (i) and (ii) have equations of the form $y = a + b \sin c x$, where $a , b$ and $c$ are constants. For each curve, find the values of $a , b$ and $c$.\\
(i)\\
\includegraphics[max width=\textwidth, alt={}, center]{11877196-83d9-4283-9eef-e617bea50c63-1_449_681_834_408}\\
(ii)\\
\includegraphics[max width=\textwidth, alt={}, center]{11877196-83d9-4283-9eef-e617bea50c63-1_376_681_1344_408}
\hfill \mbox{\textit{OCR MEI C3 Q2 [4]}}