Question 4 - A-Level Maths

OCR MEI C2 — Question 4 5 marks

Exam Board	OCR MEI
Module	C2 (Core Mathematics 2)
Marks	5
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Quadratic trigonometric equations
Type	Direct solve: sin²/cos² substitution
Difficulty	Standard +0.3 This is a standard C2 trigonometric equation requiring the identity sin²θ = 1 - cos²θ to convert to a quadratic in cos θ, then solving the resulting quadratic. It's slightly above average difficulty due to the multi-step process (substitution, rearranging, factorising/formula, finding angles in the given range), but follows a well-practiced routine with no novel insight required.
Spec	1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1 1.05o Trigonometric equations: solve in given intervals

4 Showing your method clearly, solve the equation $$5 \sin ^ { 2 } \theta = 5 + \cos \theta \quad \text { for } 0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ } .$$

Show mark scheme Show mark scheme source

Question 4:

Answer	Marks
M1	Substitution of $\sin^2 \theta = 1 - \cos^2 \theta$
M1	$-5\cos^2 \theta = \cos \theta$
A1	$\theta = 90$ and $270$
A1	$102$
A1	$258$
A1	$101$ and $259$
SC 1	soi or better

Guidance:

Accept $101.5(\ldots)$ and $258.(46\ldots)$ rounded to 3 or more sf

If M0, allow B1 for both of $90$ and $270$ and B1 for $102$ and B1 for $258$ (to 3 or more sf)

If the 4 correct values are presented, ignore any extra values which are outside the required range, but apply a penalty of minus 1 for extra values in the range

If given in radians deduct 1 mark from total awarded ($1.57, 1.77, 4.51, 4.71$)

**Question 4:**

M1 | Substitution of $\sin^2 \theta = 1 - \cos^2 \theta$

M1 | $-5\cos^2 \theta = \cos \theta$

A1 | $\theta = 90$ and $270$

A1 | $102$

A1 | $258$

A1 | $101$ and $259$

SC 1 | soi or better

**Guidance:**

Accept $101.5(\ldots)$ and $258.(46\ldots)$ rounded to 3 or more sf

If M0, allow B1 for both of $90$ and $270$ and B1 for $102$ and B1 for $258$ (to 3 or more sf)

If the 4 correct values are presented, ignore any extra values which are outside the required range, but apply a penalty of minus 1 for extra values in the range

If given in radians deduct 1 mark from total awarded ($1.57, 1.77, 4.51, 4.71$)

Show LaTeX source

4 Showing your method clearly, solve the equation

$$5 \sin ^ { 2 } \theta = 5 + \cos \theta \quad \text { for } 0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ } .$$

\hfill \mbox{\textit{OCR MEI C2  Q4 [5]}}

This paper (12 questions)

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Q1 3 Q2 5 Q3 5 Q4 5 Q5 3 Q6 3 Q7 3 Q8 3 Q9 3 Q10 5 Q11 5 Q12 5

OCR MEI C2 — Question 4 5 marks

Question 4:

Guidance:

Accept \(101.5(\ldots)\) and \(258.(46\ldots)\) rounded to 3 or more sf

If M0, allow B1 for both of \(90\) and \(270\) and B1 for \(102\) and B1 for \(258\) (to 3 or more sf)

If the 4 correct values are presented, ignore any extra values which are outside the required range, but apply a penalty of minus 1 for extra values in the range

If given in radians deduct 1 mark from total awarded (\(1.57, 1.77, 4.51, 4.71\))

This paper (12 questions)

Answer	Marks
M1	Substitution of \(\sin^2 \theta = 1 - \cos^2 \theta\)
M1	\(-5\cos^2 \theta = \cos \theta\)
A1	\(\theta = 90\) and \(270\)
A1	\(102\)
A1	\(258\)
A1	\(101\) and \(259\)
SC 1	soi or better