# QTS Numeracy Model Solutions – Test 2, Q22

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 22 from practice test 2. The full practice paper can be downloaded **here**.

## The Question

As part of a review programme a teacher compared the marks for 10 pupils in each of two English tests.

Circle the letters in the table for the pupils who scored at least 10 percentage points more in Test 2 than in Test 1.

## Worked Solution

This is a percentages question, and particularly about percentage points. Understanding what the phrase ‘percentage points’ means and how it applies to this kind of question can make things much simpler for you and can help you to avoid a common mistake.

Percentage points means that you need to use the original test as your frame of reference. You are not working out a percentage of each score, but simply a percentage of the total number of marks available that you can then compare with each of the students.

The question states that the tests are each out of 50 marks, and you are looking for students whose scores have improved by at least 10 percentage points. To do this, you simply need to work out 10% of 50.

You can work out 10% by dividing the number by 10 (this works because there are 10 tens in 100).

50 ÷ 10 = 5.

This means that you need to look at each of the pupils in turn and see which of them had a score in paper 2 that was at least 5 marks higher than their score in paper 1.

Pupil A scored 28 in paper 1 and 30 in paper 2. This is an increase of 2 marks.

Pupil B scored 14 in paper 1 and 18 in paper 2. This is an increase of 4 marks.

Pupil C scored 16 in paper 1 and 15 in paper 2. This is a decrease of 1 mark.

Pupil D scored 17 in paper 1 and 22 in paper 2. This is an increase of 5 marks.

Pupil E scored 20 in paper 1 and 24 in paper 2. This is an increase of 4 marks.

Pupil F scored 20 in paper 1 and 29 in paper 2. This is an increase of 9 marks.

Pupil G scored 16 in paper 1 and 18 in paper 2. This is an increase of 2 marks.

Pupil H scored 8 in paper 1 and 13 in paper 2. This is an increase of 5 marks.

Pupil I scored 6 in paper 1 and 6 in paper 2. This is exactly the same score.

Pupil J scored 14 in paper 1 and 24 in paper 2. This is an increase of 10 marks.

As you can see, there are eight pupils that scored higher in paper 2 than in paper 1, but only pupils D, F and J increased their score by 5 or more marks.

## Final Answer: Pupils D, F & J

*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

**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!