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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | IB Analysis and Approaches |
In triangle ABC, the length of AB = 5cm, AC = 13cm and \( \cos B \hat AC = \frac18 \).
(a) find the value of \( \sin B \hat AC \)
(b) Find the area of triangle ABC.
Diagram not to scale
2. | IB Analysis and Approaches |
(a) Show that:
$$ \cos 2x - \sin 2x + 1 = 2 \cos x ( \cos x - \sin x) $$(b) Hence or otherwise, solve the following equation for \( \pi \lt x \lt 3\pi \).
$$ \cos 2x - \sin 2x + 1 = \sin x - \cos x $$3. | IB Analysis and Approaches |
(a) Show that the equation \( 2 \sin^2 x - 5 \cos x = -1\) may be written in the form \( 2 \cos^2 x + 5 \cos x = 3\)
(b) Hence, solve the equation \( 2 \sin^2 x - 5 \cos x = -1 \), \( 2\pi \lt x \lt 4\pi \).
4. | IB Standard |
Consider a right-angled triangle, ABC, with the right angle at vertex C and where \(\sin A = \frac{12}{13}\)
(a) Show that \(\cos A = \frac{5}{13}\)
(b) Find \(\sin 2A\).
5. | A-Level |
The cosine of acute angle \( \alpha \) is \( \frac{1}{ \sqrt 5} \)
The angle \( \beta \) is obtuse and \( \sin \beta = \sqrt \frac{2}{3} \).
(a) Find exact values of \( \tan \alpha \) and \( \tan \beta \).
(b) Hence show that \( \tan( \alpha - \beta ) \) can be written as \(a+b \sqrt 2 \) where \(a\) and \(b\) are rational numbersIf you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.
The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
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