| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2010 |
| Session | January |
| Marks | 1 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Prove identity then solve equation |
| Difficulty | Standard +0.3 This is a straightforward two-part question: proving a standard double angle identity using known formulae (cot 2θ = cos 2θ/sin 2θ, then applying tan forms) followed by a routine algebraic equation. The proof requires recall of double angle formulae and basic manipulation. The equation solving involves substituting the identity, clearing fractions, and solving a quadratic in tan θ—all standard C4 techniques with no novel insight required. Slightly above average difficulty due to the two-part structure and algebraic manipulation, but well within typical C4 scope. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| THE MATHEMATICIAN | B1 |
### Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| THE MATHEMATICIAN | B1 | |2 Show that $\cot 2 \theta = \frac { 1 - \tan ^ { 2 } \theta } { 2 \tan \theta }$.\\
Hence solve the equation
$$\cot 2 \theta = 1 + \tan \theta \quad \text { for } 0 ^ { \circ } < \theta < 360 ^ { \circ }$$
\hfill \mbox{\textit{OCR MEI C4 2010 Q2 [1]}}