Year 12 trigonometry test to download as PDF

This Year 12 trigonometry test lasts 60 minutes and is marked out of 20. It covers the whole chapter for pupils aged 16-17, and the full answers are on a separate page.

⏱️ Duration : 60 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Cosine rule and area
In triangle \(ABC\), \(AB=7\) cm, \(AC=10\) cm and angle \(A=58^\circ\).
1. Find \(BC\) to 3 significant figures. (2 marks)
2. Find the area of the triangle to 3 significant figures. (2 marks)
Question 2 – Radians
A sector of a circle has radius 9 cm and angle 0.8 radians.
1. Find the arc length. (1 mark)
2. Find the area of the sector. (1 mark)
3. Find the area of the segment cut off by the chord to 2 decimal places. (2 marks)
Question 3 – Proving an identity
Prove that \(\dfrac{\sin\theta}{1+\cos\theta}+\dfrac{1+\cos\theta}{\sin\theta}\equiv\dfrac2{\sin\theta}\).
Question 4 – Solving an equation
Solve \(2\sin^2\theta=1+\cos\theta\) for \(0^\circ\le\theta\le360^\circ\).
Question 5 – Problem: a harbour
A boat leaves harbour \(H\) and travels 12 km on a bearing of \(065^\circ\) to \(A\). It then travels 9 km on a bearing of \(140^\circ\) to \(B\).
1. Show that angle \(HAB=105^\circ\). (1 mark)
2. Find the distance \(HB\). (2 marks)
3. Find the bearing of \(B\) from \(H\) to the nearest degree. (1 mark)

How to use this Year 12 trigonometry test

First, revise with the trigonometry lesson and the worksheet. Then sit the test in one go, with a timer set to 60 minutes. After that, mark your work with the trigonometry test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 12 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.