# QTS Numeracy Model Solutions – Test 2, Q19

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

## The Question

To set targets for the following year, the mathematics department analysed the percentage of mathematics GCSE grades A* – C achieved by pupils in the school.

Tick all the true statements:

– The mean percentage of GCSE grades A* – C for the last 5 years of the chart was 51%.

– The percentage of GCSE grades A* – C increased each year from 2004 – 2011.

– The percentage of mathematics GCSE grades A* – C more than doubled from 2004 – 2011.

## Worked Solution

Questions like this that give you a series of statements and ask you to indicate all of the true statements come up fairly often on the QTS Numeracy test. The best way to approach this kind of question is to take each of the statements one at a time and answer them as true or false questions.

**The mean percentage of GCSE grades A* – C for the last 5 years of the chart was 51%.**

This statement is asking you to use the data from the **bar chart** to calculate the mean. Don’t worry about the value they have given for now – you need to work out what you think the mean is first and then use your value to decide whether or not the statement is true.

In this case, reading the data from the bar chart is straight-forward because each of the bars has the percentage that it represents written at the top of the bar. Because the question asks about the **last 5 years** of the chart, the relevant values are 47, 46, 50, 54 and 58.

From these values, you need to work out the mean. Mean is one of the three **averages** that you could be asked to work out (the others are median and mode), and it is asking you to find one value that represents the percentages in these five years. Each of the averages does this in a different way – and mean does it by ‘sharing’ the values evenly across the five years.

The way you work this out is by **adding all of the values together, and then dividing by how many values there are**.

47 + 46 + 50 + 54 + 58 = 255

There are five values, so 255 ÷ 5 = 51

The mean percentage is 51%, which is what the statement says, so this statement is **TRUE**.

**The percentage of GCSE grades A* – C increased each year from 2004 – 2011.**

The best way to do this is to look at the percentages shown on the bar chart for **each of the years in turn** and check whether or not it is higher than the percentage in the previous year.

In 2004, the percentage was 22%.

In 2005, the percentage was 34%, which is an **increase** from 2004.

In 2006, the percentage was 38%, which is an **increase** from 2005.

In 2007, the percentage was 47%, which is an **increase** from 2006.

In 2008, the percentage was 46%. This is **less** than the percentage in 2007.

Because the percentage went down from 2007 to 2008, it did not increase every year and so the statement is **FALSE**.

**The percentage of Mathematics GCSE grades A* – C more than doubled from 2004 to 2011.**

This statement is asking you to **compare** the percentages from 2004 and 2011, so you need to start by reading these percentages from the bar chart.

In 2004, the percentage was 22%.

In 2011, the percentage was 58%.

If you double the percentage from 2004, you would get 22% × 2 = 44%.

The percentage from 2011 is bigger than this, so it has more than doubled from 2004 and the statement is **TRUE**.

## Final Answer: True, False, True

*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!