Maths questions
Maths questions will appear throughout both exams papers (Breadth and Depth), and at both Foundation Tier and Higher Tier.
Don't forget to take a ruler and a calculator into the exams.
Maths questions often start with the command word 'calculate', followed by a blank space for your working. It is important that you show your working - don't just write the answer down. You might earn marks for your working even if you get the answer wrong.
Always include the correct units for your answer, unless they are already given on the answer line. This may earn you an additional mark.
Check carefully to see if the question tells you to round your answer to a particular number of significant figures or decimal places. And don't forget to check your rounding.
If the question does not tell you to round your answer but it has lots of decimal places, you should give your answer to the same number of significant figures as the data in the question. For example, if two significant figures are used in the question, then usually your answer should also be given to two significant figures.
Other command words you might see in maths questions include:
- 'predict' (look at some data and suggest an outcome - don't just guess, look at trends in the data and use your scientific knowledge and understanding to make a sensible suggestion)
- 'estimate' (suggest a rough value without doing a calculation - don't just guess, use your scientific knowledge and understanding to make a sensible suggestion)
- 'show' (write down the details, steps or calculations to prove that an answer is correct).
Maths questions might include tables and graphs as well as calculations. When drawing a graph, make sure you:
- put the independent variable (the factor you changed) on the x-axis
- put the dependent variable (the factor you measured) on the y-axis
- construct regular scales for the axes
- label each axis with the quantity and units, eg time(s)
- plot each point accurately
- decide whether the origin (0, 0) should be used as a data point
- draw a straight or curved line of best fit if appropriate
These questions have been written by Bitesize consultants as suggestions to the types of questions that may appear in an exam paper.
Sample question 1 - Foundation
Question
A Year 11 form tutor recorded the number of students off sick each day for a week. The results are shown in the table below.
| Monday | Tuesday | Wednesday | Thursday | Friday | |
| Number of students off sick | 7 | 3 | 9 | 5 | 6 |
| Number of students off sick | |
|---|---|
| Monday | 7 |
| Tuesday | 3 |
| Wednesday | 9 |
| Thursday | 5 |
| Friday | 6 |
Calculate the mean number of students off sick. [1 mark]
To calculate a mean all the values must be added up and then divided by the total number of values.
\( \text{Mean} = \frac{7+3+9+5+6} {5}\)
\( = \frac{30}{5} = 6\).
Sample question 2 - Foundation
Question
The number of people living with HIV each year is recorded by the UN. The data for recent years is shown in the table below.
| Year | 2000 | 2005 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 |
| Number of infected people (millions) | 28.9 | 31.8 | 33.3 | 33.9 | 34.5 | 35.2 | 35.9 | 36.7 |
| Year | Number of infected people (millions) |
|---|---|
| 2000 | 28.9 |
| 2005 | 31.8 |
| 2010 | 33.3 |
| 2011 | 33.9 |
| 2012 | 34.5 |
| 2013 | 35.2 |
| 2014 | 35.9 |
| 2015 | 36.7 |
Plot these points on the graph paper below. Draw a line of best fit.
[4 marks]
Your graph should look like this.
Answer four from:
You should have years on the x-axis and number of infected people (millions) on the y-axis (2 marks). Your scales should be regular (1 mark). Your axes should be labelled (1 mark). All points should be accurate (1 mark) and you should have drawn a curve of best fit (1 mark).
Sample question - Higher
Question
A father recorded the temperature of his young child when they had the measles. The table below shows the results.
| Time after symptoms first noticed (hours) | Temperature (°C) |
| 24 | 37.9 |
| 48 | 38.3 |
| 72 | 39.2 |
| 96 | 37.5 |
| Time after symptoms first noticed (hours) | 24 |
|---|---|
| Temperature (°C) | 37.9 |
| Time after symptoms first noticed (hours) | 48 |
|---|---|
| Temperature (°C) | 38.3 |
| Time after symptoms first noticed (hours) | 72 |
|---|---|
| Temperature (°C) | 39.2 |
| Time after symptoms first noticed (hours) | 96 |
|---|---|
| Temperature (°C) | 37.5 |
Calculate the rate of change per hour for the first three days. Give your answer to two significant figures. [1 mark]
rate of change = \( \frac{change~in~value}{change~in~time}\)
change in value = 39.2 - 37.9 (°C)
= 1.3 (°C)
change in time = 72 hours
so rate of change (per hour) = \( \frac{1.3~(°C)}{72~(hour)}\)
72 (hour)
= 0.018 (°C/hour)
The question asks for the rate change per hour. So make sure you don't calculate the rate of change per day instead. You would do this by: \( \frac{1.3}{3}\) = 0.43.
