Question 4 - A-Level Maths

Edexcel C2 2013 January — Question 4 7 marks

Exam Board	Edexcel
Module	C2 (Core Mathematics 2)
Year	2013
Session	January
Marks	7
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Standard trigonometric equations
Type	Transformed argument solving
Difficulty	Moderate -0.3 This is a straightforward transformed argument trigonometric equation requiring inverse cosine, consideration of the second quadrant solution, and division by 3. While it involves multiple steps and careful angle manipulation, it follows a standard C2 procedure with no conceptual challenges beyond basic technique, making it slightly easier than average.
Spec	1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs 1.05o Trigonometric equations: solve in given intervals

4. Solve, for $0 \leqslant x < 180 ^ { \circ }$, $$\cos \left( 3 x - 10 ^ { \circ } \right) = - 0.4$$ giving your answers to 1 decimal place. You should show each step in your working.

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Question 4:

Answer	Marks	Guidance
Answer/Working	Mark	Guidance
$\cos^{-1}(-0.4) = 113.58\ (\alpha)$	B1	Awrt 114
$3x - 10 = \alpha \Rightarrow x = \dfrac{\alpha + 10}{3}$	M1	Uses their $\alpha$ to find $x$. Allow $x = \dfrac{\alpha \pm 10}{3}$, not $\dfrac{\alpha}{3} \pm 10$
$x = 41.2$	A1	Awrt
$(3x - 10 =)\ 360 - \alpha\ (246.4...)$	M1	$360 - \alpha$ (can be implied by $246.4...$)
$x = 85.5$	A1	Awrt
$(3x - 10 =)\ 360 + \alpha\ (= 473.57...)$	M1	$360 + \alpha$ (can be implied by $473.57...$)
$x = 161.2$	A1	Awrt

## Question 4:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\cos^{-1}(-0.4) = 113.58\ (\alpha)$ | B1 | Awrt 114 |
| $3x - 10 = \alpha \Rightarrow x = \dfrac{\alpha + 10}{3}$ | M1 | Uses their $\alpha$ to find $x$. Allow $x = \dfrac{\alpha \pm 10}{3}$, not $\dfrac{\alpha}{3} \pm 10$ |
| $x = 41.2$ | A1 | Awrt |
| $(3x - 10 =)\ 360 - \alpha\ (246.4...)$ | M1 | $360 - \alpha$ (can be implied by $246.4...$) |
| $x = 85.5$ | A1 | Awrt |
| $(3x - 10 =)\ 360 + \alpha\ (= 473.57...)$ | M1 | $360 + \alpha$ (can be implied by $473.57...$) |
| $x = 161.2$ | A1 | Awrt |

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4. Solve, for $0 \leqslant x < 180 ^ { \circ }$,

$$\cos \left( 3 x - 10 ^ { \circ } \right) = - 0.4$$

giving your answers to 1 decimal place. You should show each step in your working.\\

\hfill \mbox{\textit{Edexcel C2 2013 Q4 [7]}}

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