Year 12 exponentials and logarithms test to download as PDF

This Year 12 exponentials and logarithms 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 – Laws of logarithms
Write as a single logarithm and simplify: \(2\log_53+\log_5 50-\log_5 18\). (3 marks)
Hence evaluate it. (1 mark)
Question 2 – Exponential equation
Solve \(4^x=7\times2^x-12\).
Question 3 – Logarithmic equation
Solve \(\log_3(2x+1)+\log_3(x-1)=2\).
Question 4 – Straight-line graph
The data satisfy \(y=ab^x\). A graph of \(\log_{10}y\) against \(x\) has gradient 0.2 and passes through \((0,1.3)\). Find \(a\) and \(b\) to 3 significant figures.
Question 5 – Problem: decay of a medicine
The mass of a drug in the blood is \(M=80e^{-0.15t}\) mg after \(t\) hours.
1. Find the mass after 4 hours. (1 mark)
2. Find the half-life to 3 significant figures. (2 marks)
3. When does the mass fall below 5 mg? (1 mark)

How to use this Year 12 exponentials and logarithms test

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

Finally, you can download this Year 12 exponentials and logarithms 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.