OCR MEI AS Paper 2 2020 November — Question 8 6 marks

Exam BoardOCR MEI
ModuleAS Paper 2 (AS Paper 2)
Year2020
SessionNovember
Marks6
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Mark schemeDownload PDF ↗
TopicQuadratic trigonometric equations
TypeDirect solve: tanθ equation factorisation
DifficultyStandard +0.3 This is a straightforward trigonometric equation requiring substitution of tan θ = sin θ/cos θ, leading to a quadratic in cos θ. While it involves multiple steps (substitution, algebraic manipulation, solving quadratic, finding angles in range), these are all standard AS-level techniques with no novel insight required. Slightly above average difficulty due to the algebraic manipulation needed and finding all solutions in the given range.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals
8 In this question you must show detailed reasoning.
Solve the equation \(3 \cos \theta + 8 \tan \theta = 0\) for \(0 ^ { \circ } < \theta < 360 ^ { \circ }\), giving your answers correct to the nearest degree.
Question 8:
AnswerMarks Guidance
\(3\cos\theta + 8\frac{\sin\theta}{\cos\theta} [=0]\)M1* (1.2)
\(3\cos^2\theta + 8\sin\theta = 0\)M1dep* (1.1) multiplication of all terms by \(\cos\theta\); condone sign errors and number errors for the three M marks
\(3(1-\sin^2\theta) + 8\sin\theta = 0\)M1 (2.4) dependent on award of previous M1
\(3\sin^2\theta - 8\sin\theta - 3 = 0\)A1 (1.1)
\(\sin\theta = -\frac{1}{3}\) wwwA1 (1.1a) from factorising or quadratic formula; may see \(\sin\theta = 3\)
\(\theta = 341, 199\)A1 (2.4) [6] No wrong values; accept 199.47, 340.53 
## Question 8:

$3\cos\theta + 8\frac{\sin\theta}{\cos\theta} [=0]$ | M1* (1.2) | 

$3\cos^2\theta + 8\sin\theta = 0$ | M1dep* (1.1) | multiplication of all terms by $\cos\theta$; condone sign errors and number errors for the three M marks

$3(1-\sin^2\theta) + 8\sin\theta = 0$ | M1 (2.4) | dependent on award of previous M1

$3\sin^2\theta - 8\sin\theta - 3 = 0$ | A1 (1.1) |

$\sin\theta = -\frac{1}{3}$ www | A1 (1.1a) | from factorising or quadratic formula; may see $\sin\theta = 3$

$\theta = 341, 199$ | A1 (2.4) **[6]** | No wrong values; accept 199.47, 340.53

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8 In this question you must show detailed reasoning.\\
Solve the equation $3 \cos \theta + 8 \tan \theta = 0$ for $0 ^ { \circ } < \theta < 360 ^ { \circ }$, giving your answers correct to the nearest degree.

\hfill \mbox{\textit{OCR MEI AS Paper 2 2020 Q8 [6]}}
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