QTS Numeracy Model Solutions – Test 2, Q16

In this series of blog posts, we look at some of the detailed methods that you could use to tackle the questions on the QTS Numeracy practice papers from the Department for Education.

In this post, we look at question 16 from practice test 2. The full practice paper can be downloaded here​.

The Question

At a staff meeting, the head teacher presented the following table, showing the number of pupils in each class in a school who are having extra music lessons.

What percentage of pupils in the school are having extra music lessons?

Give your answer to the nearest whole number.

Worked Solution

This question is looking for you to calculate a percentage from data that is given in a table.

Percentages are one of the forms of proportion that you need to work with (the others are fractions and decimals). This means that a percentage compares one part to the whole – in this case, it will compare the number of pupils having extra music lessons to the total number of pupils in the school.

The way a percentage works is by telling you how many out of every 100 pupils have the extra music lessons (the words ‘per cent’ literally mean ‘out of one hundred’). You can work percentage out by dividing the number of pupils who have the extra lessons by the total number of pupils, and then multiply the result by 100.

Percentage = Number Having Extra Lessons ÷ Total Number of Pupils × 100

Although the data is given for each of the individual classes, the question is asking about the percentage for the school as a whole, so before you work out the percentage you will need to add up the total number of pupils in the school and the total number who are having the extra music lessons (you don’t need to work out the percentages for the individual classes).

You can perform these calculations using your on-screen calculator (it might be a good idea to do the calculations twice just to check, as there are quite a lot of numbers involved).

Total number of pupils:

25 + 30 + 30 + 28 + 26 + 29 + 18 + 24 = 210

5 + 5 + 5 + 7 + 5 + 6 + 6 + 5 = 44

Put these numbers in to the formula to work out the percentage.

Percentage = 44 ÷ 210 × 100 = 20.952381

The question states that you should give your answer to the nearest whole number.

The answer given on the calculator is a decimal, and it is between 20 and 21. You need to decide whether you round it down to 20 or round it up to 21. To do this, look at the digit immediately to the right of the decimal point. If the digit is a 5 or above then you round up. If it is a 4 or below then you need to round down.

In this case the digit immediately after the decimal point is a 9, so you need to round up to 21%.

Final Answer: 21%

Note – I have made a point of being thorough in this method to ensure you understand each point as we go. When you sit your QTS Skills Tests, your process will probably be much quicker as these techniques start to become second nature to you.

Further Help

If you require any further help with questions like this, we have created a selection of resources to provide all the help you need.

Revision Book – The Guide to the QTS Skills Tests book devotes a whole chapter to each QTS numeracy topic, with detailed methods, worked examples and plenty of practice questions for you to have a go at. The book also includes three practice tests and fully worked solutions to every question.

Practice Tests – Want more practice tests to see how ready you are? Take a look at our selection of practice papers for the QTS numeracy test (including some totally free papers as our gift to you).

Revision Cheat Sheets – Our cheat sheets boil down everything you need to know to just the key points on the topic. They are a perfect resource for your last minute revision!