| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2013 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Convert to Cartesian (sin/cos identities) |
| Difficulty | Moderate -0.3 Part (i) requires standard differentiation using the chain rule (dy/dx = (dy/dθ)/(dx/dθ)) with basic trigonometric functions, then substitution. Part (ii) uses the double angle formula sin 2θ = 2sin θ cos θ and the identity cos²θ = 1 - sin²θ to eliminate the parameter—this is a routine textbook exercise in parametric-to-Cartesian conversion. Both parts are straightforward applications of standard techniques with no problem-solving insight required, making this slightly easier than average. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(t(P,A) = t(P,B)\) | B1 | Accept equivalent correct description [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| A is at approximately (6, 4); diamond shape with radius 3 visible | ||
| \(t(P,A) = 3\) | B1 | Accept equivalent [1] |
# Question 3(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| $t(P,A) = t(P,B)$ | B1 | Accept equivalent correct description [1] |
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# Question 3(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| A is at approximately (6, 4); diamond shape with radius 3 visible | | |
| $t(P,A) = 3$ | B1 | Accept equivalent [1] |
---3 The parametric equations of a curve are
$$x = \sin \theta , \quad y = \sin 2 \theta , \quad \text { for } 0 \leqslant \theta \leqslant 2 \pi .$$
(i) Find the exact value of the gradient of the curve at the point where $\theta = \frac { 1 } { 6 } \pi$.\\
(ii) Show that the cartesian equation of the curve is $y ^ { 2 } = 4 x ^ { 2 } - 4 x ^ { 4 }$.
\hfill \mbox{\textit{OCR MEI C4 2013 Q3 [7]}}