Maths questions
Maths questions often start with the command words 'Calculate...' or 'Determine...'. They will then have a blank space for you to show your working. It is important that you show your working, donât just write the answer down. You might earn marks for your working even if you get the answer incorrect.
In some maths questions you will be required to give the units. This may earn you an additional mark. Donât forget to check whether you need to do this.
Maths questions might include graphs and tables as well as calculations. Donât forget to take a ruler and calculator.
If drawing graphs, make sure you:
- put the independent variable on the x-axis and the dependent variable on the y-axis
- construct regular scales for the axes
- label the axes appropriate
- plot each point accurately
- draw a straight or curved line of best fit
If you are asked to calculate an answer and it has lots of decimal places, don't forget to only use one more than the data in the question. For example, if whole numbers are given in the question, then your answer would be to one decimal place. Don't forget to check your rounding.
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
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 | |
| Class 11A | 6 | 5 | 5 | 5 | 4 |
| Class 11A | |
|---|---|
| Monday | 6 |
| Tuesday | 5 |
| Wednesday | 5 |
| Thursday | 5 |
| Friday | 4 |
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.
\(6 + 5 + 5 + 5 + 4 = \frac{25}{5} = 5\)
Sample question 2
Question
A class of Year 9 students planted twelve barley seeds on cotton wool in petri dishes on a windowsill. Six were watered with fertilisers and six were given the same volume of pure water. The heights of the six seedlings were measured after two weeks.
| Plant | Height with fertiliser | Height without fertiliser |
| 1 | 2 cm | 2 cm |
| 2 | 3 cm | 3 cm |
| 3 | 4 cm | 2 cm |
| 4 | 3 cm | 1 cm |
| 5 | 6 cm | 2 cm |
| 6 | 5 cm | 2 cm |
| Plant | 1 |
|---|---|
| Height with fertiliser | 2 cm |
| Height without fertiliser | 2 cm |
| Plant | 2 |
|---|---|
| Height with fertiliser | 3 cm |
| Height without fertiliser | 3 cm |
| Plant | 3 |
|---|---|
| Height with fertiliser | 4 cm |
| Height without fertiliser | 2 cm |
| Plant | 4 |
|---|---|
| Height with fertiliser | 3 cm |
| Height without fertiliser | 1 cm |
| Plant | 5 |
|---|---|
| Height with fertiliser | 6 cm |
| Height without fertiliser | 2 cm |
| Plant | 6 |
|---|---|
| Height with fertiliser | 5 cm |
| Height without fertiliser | 2 cm |
What is the median result with and without fertilisers? [2 marks]
To calculate the median, place the set of numbers in increasing order of size. The median is the middle number. In increasing order of size with fertilisers: 2, 3, 3, 4, 5, 6. The answer is therefore 3.5. (If the median falls between two numbers, then the mean of these is used. Here it is 3.5 which is the mean of 3 and 4.) In increasing order of size without fertilisers: 1, 2, 2, 2, 2, 3. The answer is therefore 2.
Sample question 3
Question
The number of people living with HIV each year is recorded by the UN. The date for recent years is shown in the table below.
| Year | 2000 | 2005 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 |
| Infected people (millions) | 28.9 | 31.8 | 33.3 | 33.9 | 34.5 | 35.2 | 35.9 | 36.7 |
| Year |
|---|
| 2000 |
| 2005 |
| 2010 |
| 2011 |
| 2012 |
| 2013 |
| 2014 |
| 2015 |
| Infected people (millions) |
|---|
| 28.9 |
| 31.8 |
| 33.3 |
| 33.9 |
| 34.5 |
| 35.2 |
| 35.9 |
| 36.7 |
Plot these points on graph paper. Draw a line of best fit. [4 marks]
Your graph should look like this.
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 curved line of best fit [1 mark].
Sample question 4
Question
A mother recorded the temperature of her young child when they had the measles. The table below shows the results.
| Time after symptoms first noticed (hours) | 24 | 48 | 72 | 96 |
| Temperature | 37.9°°ä | 38.3°°ä | 39.2°°ä | 37.5°°ä |
| Time after symptoms first noticed (hours) |
| 24 |
| 48 |
| 72 |
| 96 |
| Temperature |
| 37.9°°ä |
| 38.3°°ä |
| 39.2°°ä |
| 37.5°°ä |
Calculate the rate of change per hour for the first three days. Give your answer to two significant figures. [1 mark]
\(\text{rate of change} = \frac{\text{change in value}}{\text{change in time}}\)
\(\text{change in value} = 39.2 - 37.9 = 1.3\)
\(\text{change in time} = 72 \text{hours}\)
\(\text{so rate of change (per hour)} = \frac{1.3}{72} = 0.018\)
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: \(\frac{1.3}{3} = 0.43\).
Remember to read the question closely. It asks for the first three days not four, so you should ignore the data for the fourth day.