OCR MEI C2 — Question 1 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard trigonometric equations
TypeEquation with non-equation preliminary part (sketch/proof/identity)
DifficultyModerate -0.8 Part (i) is a standard geometric proof using an equilateral triangle that appears in most textbooks. Part (ii) is a routine trigonometric equation requiring basic knowledge of the unit circle and symmetry. Both parts involve direct recall and application of fundamental techniques with no problem-solving insight required. This is easier than average for A-level.
Spec1.05g Exact trigonometric values: for standard angles1.05o Trigonometric equations: solve in given intervals
  1. Starting with an equilateral triangle, prove that \(\cos 30° = \frac{\sqrt{3}}{2}\). [2]
  2. Solve the equation \(2 \sin \theta = -1\) for \(0 \leqslant \theta \leqslant 2\pi\), giving your answers in terms of \(\pi\). [3]
Question 1:
AnswerMarks Guidance
1(i) clear diagram or explanation starting with
equilateral triangle correctly showing 30 as
half angle and sides 1 and 2 or multiples of
these lengths
correct use of Pythagoras and adjacent and
hypotenuse correctly identified to obtain
3
given result cos30
AnswerMarks
2B1
B1
AnswerMarks
[2]adjacent and hypotenuse may be identified
on diagramunits for sides and angle not required
condone abbreviations
AnswerMarks Guidance
1(ii)  5
 or  soi
6 6
11
6
7
AnswerMarks
6M1
A1
A1
AnswerMarks
[3]may be implied by correct answer or
±0.523598775…, or may appear on quadrant
diagram or graph
if A0A0, SC1 for 1.8333333π and
1.16666666π to 3 or more sf or SC1 for 330°
AnswerMarks
and 210° wwwcondone ±30° or − 150°
ignore extra values outside the range
if full marks or SC1 awarded, subtract
1 for extra values in the range
Question 1:
1 | (i) | clear diagram or explanation starting with
equilateral triangle correctly showing 30 as
half angle and sides 1 and 2 or multiples of
these lengths
correct use of Pythagoras and adjacent and
hypotenuse correctly identified to obtain
3
given result cos30
2 | B1
B1
[2] | adjacent and hypotenuse may be identified
on diagram | units for sides and angle not required
condone abbreviations
1 | (ii) |  5
 or  soi
6 6
11
6
7
6 | M1
A1
A1
[3] | may be implied by correct answer or
±0.523598775…, or may appear on quadrant
diagram or graph
if A0A0, SC1 for 1.8333333π and
1.16666666π to 3 or more sf or SC1 for 330°
and 210° www | condone ±30° or − 150°
ignore extra values outside the range
if full marks or SC1 awarded, subtract
1 for extra values in the range
\begin{enumerate}[label=(\roman*)]
\item Starting with an equilateral triangle, prove that $\cos 30° = \frac{\sqrt{3}}{2}$. [2]

\item Solve the equation $2 \sin \theta = -1$ for $0 \leqslant \theta \leqslant 2\pi$, giving your answers in terms of $\pi$. [3]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI C2  Q1 [5]}}
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