Year 13 further trigonometry test to download as PDF

This Year 13 further trigonometry test lasts 40 minutes and is marked out of 20. It covers the whole chapter for pupils aged 17-18, and the full answers are on a separate page.

⏱️ Duration : 40 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Small angles
(a) Use small-angle approximations to find an approximation for \(\dfrac{\theta\tan2\theta}{1-\cos3\theta}\) when \(\theta\) is small. [2 marks] (b) Evaluate the expression for \(\theta=0.1\) and find the percentage difference from your answer to part (a), to 2 significant figures. [2 marks]
Question 2 – A reciprocal equation
Solve \(2\tan^2x+\sec x=1\) for \(0^\circ\le x<360^\circ\), giving answers to 1 decimal place. [4 marks]
Question 3 – Compound angles
(a) Find the exact value of \(\sin105^\circ\). [2 marks] (b) The angles \(A\) and \(B\) are acute with \(\sin A=\dfrac5{13}\) and \(\cos B=\dfrac45\). Find the exact value of \(\cos(A-B)\). [2 marks]
Question 4 – A double angle equation
Solve \(2\cos2x+3\sin x=1\) for \(0^\circ\le x<360^\circ\). [4 marks]
Question 5 – Combining sine and cosine
(a) Express \(8\cos x+15\sin x\) in the form \(R\cos(x-\alpha)\) where \(R>0\) and \(0^\circ\lt \alpha<90^\circ\). [2 marks] (b) Solve \(8\cos x+15\sin x=10\) for \(0^\circ\le x<360^\circ\). [2 marks]

How to use this Year 13 further trigonometry test

First, revise with the further trigonometry lesson and the worksheet. Then sit the test in one go, with a timer set to 40 minutes. After that, mark your work with the further trigonometry test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 13 further trigonometry test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.