| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2019 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Find tangent equation |
| Difficulty | Moderate -0.3 This question involves standard parametric differentiation techniques and coordinate substitution. Part (a) requires finding dy/dx using the chain rule (dy/dθ ÷ dx/dθ) and evaluating at a given parameter value—routine A-level calculus. Part (b) involves substituting the parametric equations into a linear equation and solving a trigonometric equation. Both parts are textbook-standard with no novel problem-solving required, making this slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
| \(\mathbf { 0 }\) | 7 |
A curve $C$ has parametric equations $x = \sin \theta , y = \cos 2 \theta$.
a) The equation of the tangent to the curve $C$ at the point $P$ where $\theta = \frac { \pi } { 4 }$ is $y = m x + c$. Find the exact values of $m$ and $c$.\\
b) Find the coordinates of the points of intersection of the curve $C$ and the straight line $x + y = 1$.
\begin{center}
\begin{tabular}{ | l | l }
$\mathbf { 0 }$ & 7 \\
\hline
\end{tabular}
\end{center} The diagram below shows a sketch of the graph of $y = f ( x )$. The graph crosses the $y$-axis at the point $( 0 , - 2 )$, and the $x$-axis at the point $( 8,0 )$.
\includegraphics[max width=\textwidth, alt={}, center]{966abb82-ade0-4ca8-87a4-26e806d5add7-3_784_1080_1407_513}\\
a) Sketch the graph of $y = - 4 f ( x + 3 )$. Indicate the coordinates of the point where the graph crosses the $x$-axis and the $y$-coordinate of the point where $x = - 3$.\\
b) Sketch the graph of $y = 3 + f ( 2 x )$. Indicate the $y$-coordinate of the point where $x = 4$.
\hfill \mbox{\textit{WJEC Unit 3 2019 Q6}}