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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | GCSE Higher |
(a) Write down the exact value of \(\tan 60^o\).
(b) Find the exact area of this triangle.
2. | IB Analysis and Approaches |
Solve for x where \( -\pi \le x \le \pi \).
$$ \sin{2x} = \cos{x} $$3. | IB Analysis and Approaches |
(a) Show that \(2x+15+\dfrac{40}{x-3}= \dfrac{2x^2+9x-5}{x-3}, \quad x \in \mathbb{R}, x \neq 3\)
(b) Hence or otherwise, solve the equation \( 2\cos{2\theta}+15+\dfrac{40}{\cos{2\theta}-3}=0, \quad \text{ for } 0 \le \theta \le \pi\)
4. | A-Level |
(a) Solve the following trigonometric equation for \(–360° \lt x \lt 360°\):
$$ 5 \sin^2 x + 2\sin x + 3 = 7 \cos^2 x $$giving your answers to the nearest integer.
(b) Hence find the smallest positive solution of the equation
$$ 5 \sin^2(3\theta + 20°) + 2\sin (3\theta + 20°) + 3 = 7 \cos^2 (3\theta + 20°) $$giving your answer to 2 decimal places.
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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