Year 12 vectors in two dimensions test to download as PDF

This Year 12 vectors in two dimensions 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 – Vector arithmetic
\(\mathbf a=4\mathbf i-3\mathbf j\) and \(\mathbf b=\mathbf i+2\mathbf j\).
1. Find \(3\mathbf a-2\mathbf b\). (2 marks)
2. Find \(|\mathbf a+2\mathbf b|\). (2 marks)
Question 2 – Parallel vectors
\(\mathbf p=(k+2)\mathbf i+9\mathbf j\) and \(\mathbf q=2\mathbf i+3\mathbf j\) are parallel.
1. Find \(k\). (2 marks)
2. Find the ratio \(|\mathbf p|:|\mathbf q|\). (2 marks)
Question 3 – Position vectors
\(A(1,4)\) and \(B(7,-2)\).
1. Find \(\overrightarrow{AB}\) and its magnitude. (2 marks)
2. The point \(P\) divides \(AB\) in the ratio \(2:1\). Find its position vector. (2 marks)
Question 4 – Velocity
A ship travels at 20 km/h on a bearing of \(150^\circ\).
1. Write its velocity as \(a\mathbf i+b\mathbf j\). (2 marks)
2. Find its position after 3 hours relative to its starting point. (1 mark)
3. How far east is it after 3 hours? (1 mark)
Question 5 – Geometric proof
In triangle \(OAB\), \(\overrightarrow{OA}=\mathbf a\) and \(\overrightarrow{OB}=\mathbf b\). \(M\) is the midpoint of \(OA\) and \(N\) is the midpoint of \(OB\). Prove that \(MN\) is parallel to \(AB\) and half its length.

How to use this Year 12 vectors in two dimensions test

First, revise with the vectors in two dimensions 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 vectors in two dimensions test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 12 vectors in two dimensions 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.