Scientific calculation questions

Scientific calculation 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, don't just write the answer down. Calculation errors carried forward are worked through to give credit for later working.

In some maths questions you will be required to give the units. This may earn you an additional mark. Don't forget to check whether you need to do this. Take extra care when converting between units.

Maths questions might include graphs and tables as well as calculations. Don't forget to take a ruler and scientific calculator into the exam.

If drawing graphs, make sure you:

  1. put the independent variable on the x-axis and the dependent variable on the y-axis
  2. costruct regular scales for the axes
  3. label the axes appropriately
  4. plot each point accurately
  5. 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 - Foundation

The graph shows measurements of the heart rate of an athlete taken before, during and after exercise.

A graph showing the measurements of the heart rate of an athlete taken before, during and after exercise.

Use the graph to answer the following questions:

Question

What was the resting heart rate of the athlete? [1 mark]

61 beats per minute (bpm).

Question

What is the maximum heart rate of the athlete? [1 mark]

118 beats per minute (bpm).

Question

How long after exercise does the heart rate return to normal? [1 mark]

13 minutes.

This is the time taken from the end of exercise - 25 minutes - taken away from the time when the heart rate was back to normal - 38 minutes, ie 38 - 25.

Sample question 2 - Foundation

The table shows the result of an experiment investigating the effect of temperature on photosynthesis by counting the rate of formed bubbles per minute.

TemperatureRate
5°C3
10°C9
15°C15
20°C30
28°C30
30°C27
Question

Plot a graph of the results.

Join the points with straight lines. [4 marks]

Your graph should look like this:

The image shows how a plotted results graph should look

Axes and scales correct and labelled [1].

All points plotted correctly [2], or two to three points plotted correctly [1].

Points joined together correctly [1].

Follow the instructions on the exam paper when connecting points on a graph.

Join points dot-to-dot when told to do so, or draw lines of best fit to illustrate trends.

Question

At which temperatures is the rate of photosynthesis most rapid?

From 15°C to 20°C.

The examiner is looking for a range of values. Look for the steepest part of the graph.

Question

At which temperatures is the rate of photosynthesis stable?

Between 20°C and 28°C. This is the plateau of the graph.

Question

At which temperatures is the rate of photosynthesis decreasing?

Between 28°C and 30°C.

Sample question 3 - Higher

The data in the table shows the carbon dioxide produced by measuring the volume of respiring yeast cells.

Time in minutesVolume in microlitres
00 μl
1046 μl
20101 μl
30145 μl
40196 μl
50235 μl
Question

Plot a graph of the results.

Draw a line of best fit. [4 marks]

A graph showing the measurements of the heart rate of an athlete taken before, during and after exercise.

Axes and scales correct and labelled [1].

All points plotted correctly [2], or two to three points plotted correctly [1].

Appropriate line of best fit [1 ].

Question

Calculate the rate of carbon dioxide production in microlitres (μl) per hour. [4 marks]

You need to calculate the gradient of the graph - and not take values from the table of results.

You could base your calculation on values of volume of carbon dioxide produced at any two times, but:

  • make sure the region of your graph that you select is linear in this case, there's a clear linear relationship
  • choose as wide an interval along the x-axis as is possible
  • try to make sure that these correspond with values of y that you can read accurately.

Example calculation, using points P and Q:

A graph showing the measurements of the heart rate of an athlete taken before, during and after exercise.

\text{Rate of increase} = \frac{\text{increase in y}}{\text{increase in x}} \times 60 \text{ \mu l per hour}

\frac{\text{volume at point Q - volume at point P}}{\text{time at point Q - time at point P}} \times 60 \text{ \mu l per hour}

\frac{\text{volume at 50 minutes - volume at 0 minutes}}{\text{50 min - 0 min}} \times 60 \text{ \mu l per hour}

\frac{\text{240 \mu l - 0 \mu l}}{\text{50 min - 0 min}} \times 60 = \frac{240}{50} \times 60

288 \text{\mu l per hour}

Sample question 4 - Higher

The data below shows the volume of carbon dioxide produced by measuring the volume of yeast, in microlitres (μl) at different temperatures.

TemperatureVolume
0°C0 μl
10°C46 μl
20°C101 μl
30°C145 μl
40°C196 μl
50°C235 μl
Question

Draw a graph of the results.

Draw a line of best fit. [4 marks]

A graph measuring the volume of carbon dioxide produced.

Axes and scales correct and labelled [1].

All points plotted correctly [2], or two to three points plotted correctly [1].

Appropriate line of best fit [1].

Question

Predict the temperature at which yeast activity would stop.

Your graph will need to show evidence of extrapolation of the curve. Always make sure that you show this.

A graph measuring the volume of carbon dioxide produced.

You will be allowed some leeway in your answer.

In this instance, it would be 73°C ± 1°C.