OCR MEI C4 — Question 2 4 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicParametric curves and Cartesian conversion
TypeVerify parametric equations
DifficultyEasy -1.2 This is a straightforward verification question requiring only basic manipulation: square both equations, use the Pythagorean identity cos²θ + sin²θ = 1, and read off the centre and radius. It's more routine than average, involving direct application of a standard technique with no problem-solving or insight required.
Spec1.03g Parametric equations: of curves and conversion to cartesian
2 Show that the curve, given by the parametric equations given below, represents a circle. $$x = 2 \cos \theta + 3 , y = 2 \sin \theta - 3$$ State the radius and centre of this circle.
Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
\(x = 2\cos\theta + 3 \Rightarrow 2\cos\theta = x - 3\)M1 Getting cos and sin as subject
\(y = 2\sin\theta - 3 \Rightarrow 2\sin\theta = y + 3\)A1
\(\Rightarrow (x-3)^2 + (y+3)^2 = 4\cos^2\theta + 4\sin^2\theta\)A1
\(= 4\) — circle, centre \((3, -3)\) radius \(2\)A1
Total: 4 marks 
## Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $x = 2\cos\theta + 3 \Rightarrow 2\cos\theta = x - 3$ | M1 | Getting cos and sin as subject |
| $y = 2\sin\theta - 3 \Rightarrow 2\sin\theta = y + 3$ | A1 | |
| $\Rightarrow (x-3)^2 + (y+3)^2 = 4\cos^2\theta + 4\sin^2\theta$ | A1 | |
| $= 4$ — circle, centre $(3, -3)$ radius $2$ | A1 | |
| **Total: 4 marks** | | |

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2 Show that the curve, given by the parametric equations given below, represents a circle.

$$x = 2 \cos \theta + 3 , y = 2 \sin \theta - 3$$

State the radius and centre of this circle.

\hfill \mbox{\textit{OCR MEI C4  Q2 [4]}}
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Q1 4 Q2 4 Q3 5 Q4 8 Q5 7 Q6 4 Q7 4 Q8 18 Q9 18