Year 12 binomial expansion and sequences test to download as PDF

This Year 12 binomial expansion and sequences 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 – Binomial expansion
Expand \((2-3x)^4\) up to and including the term in \(x^2\). (3 marks)
Hence estimate \(1.97^4\) (use \(x=0.01\)). (1 mark)
Question 2 – Term in an expansion
Find the coefficient of \(x^3\) in \((1+2x)^5(1-x)\).
Question 3 – Arithmetic series
The 3rd term of an arithmetic sequence is 11 and the 8th term is 31.
1. Find the first term and the common difference. (2 marks)
2. Find the sum of the first 20 terms. (2 marks)
Question 4 – Geometric series
A geometric series has first term 18 and common ratio \(\tfrac23\).
1. Find the sum to infinity. (2 marks)
2. Find the smallest \(n\) such that the sum of the first \(n\) terms exceeds 53. (2 marks)
Question 5 – Problem: a savings pot
A child saves £2 in week 1, £3 in week 2, £4 in week 3 and so on, increasing by £1 each week.
1. How much is saved in week 25? (1 mark)
2. How much in total after 25 weeks? (1 mark)
3. After how many weeks will the total first exceed £500? (2 marks)

How to use this Year 12 binomial expansion and sequences test

First, revise with the binomial expansion and sequences 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 binomial expansion and sequences test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 12 binomial expansion and sequences 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.

Binomial expansion and sequences – Year 12 A level maths test to download as PDF

Question 1 – Binomial expansion

Question 2 – Term in an expansion

Question 3 – Arithmetic series

Question 4 – Geometric series

Question 5 – Problem: a savings pot

How to use this Year 12 binomial expansion and sequences test

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