| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find tangent equation at point |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question with standard techniques. Part (i) requires applying the chain rule to differentiate sin(2x) and tan(y), then rearranging for dy/dx. Part (ii) is routine substitution into y - y₁ = m(x - x₁) with given coordinates. The trigonometric functions involved are standard C4 material, and the question follows a predictable two-part structure with no novel problem-solving required. Slightly easier than average due to the guided nature and verification format of part (ii). |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
3. A curve has the equation
$$2 \sin 2 x - \tan y = 0$$
(i) Find an expression for $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in its simplest form in terms of $x$ and $y$.\\
(ii) Show that the tangent to the curve at the point $\left( \frac { \pi } { 6 } , \frac { \pi } { 3 } \right)$ has the equation
$$y = \frac { 1 } { 2 } x + \frac { \pi } { 4 } .$$
\hfill \mbox{\textit{OCR C4 Q3 [7]}}