Science calculations
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; don't 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. Don't forget to check whether you need to do this.
Maths questions might include graphs and tables as well as calculations. Don't forget to take a ruler and calculator.
If drawing graphs, make sure you:
- put the independent variable on the x-axis and the dependant variable on the y-axis
- construct regular scales for the axes
- label the axes appropriately
- plot each point accurately
- decide whether the origin should be used as a data point
- 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 use 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 would also be to two significant figures. 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
Question
A student measured the change in mass of potato cylinders placed in different concentrations of salt solution.
Their results are shown below.
| Concentration (mol dm-3) | 0.0 | 0.1 | 0.2 | 0.3 | 0.4 |
| Average change in mass (%) | +10 | +2 | -3 | -6 | -8 |
| Concentration (mol dm-3) |
|---|
| 0.0 |
| 0.1 |
| 0.2 |
| 0.3 |
| 0.4 |
| Average change in mass (%) |
|---|
| +10 |
| +2 |
| -3 |
| -6 |
| -8 |
Plot these points on graph paper. Draw a line of best fit. [4 marks]
Axes and scales correct – 1 mark.
All points plotted correctly – 2 marks.
or 2 to 3 points plotted correctly – 1 mark.
Appropriate line of best fit – 1 mark.
You should have concentration on the x-axis and change on the y-axis. The y-axis has a positive and negative scale. Your divisions on your scales should be regular. Your axes should be labelled and include units.
All points should be plotted accurately.
You should have drawn an appropriate line of best fit. In this case, it is a curve.
Sample question 2 - Foundation
Question
Describe how the surface area to volume ratio changes as an organism becomes larger. Specifically compare an organism of 1 cm3 with one of 3 cm3. [4 marks]
Four from:
- An organism 1 cm3 in size has a surface area of 6 cm3 and a volume of 1 cm3.
- So has 6:1 surface area:volume ratio.
- An organism 3 cm3 in size has a surface area of 54 cm3 and a volume of 27 cm3.
- So has 2:1 surface area: volume ratio.
- So surface area:volume ratio decreases with an increase in size.
Sample question 3 - Higher
Question
The diameter of an alveolus can range in size from 200 to 400 μm.
Alveoli are roughly spherical.
The surface area of a sphere can be calculated using the formula:
\(\text{surface area of a sphere} = 4 \pi r^2\)
The volume of a sphere can be calculated using the formula:
\(\text{volume of a sphere} = \frac{4}{3} \pi r^3\)
Where \(\pi = pi\). Use the value of \(π\) as 3.14 for your calculations. \(r\) = the radius of the sphere.
In this example, assume that an alveolus is a perfect sphere.
Calculate the surface area to volume ratios of:
- an alveolus 200 μm in diameter
- an alveolus 400 μm in diameter
Show all your working. [6 marks]
For:
- an alveolus 200 μm in diameter – surface area to volume ratio is 0.030
- an alveolus 400 μm in diameter – surface area to volume ratio is 0.015
Award:
- One mark each for the calculation of surface areas.
- One mark each for the calculation of volumes.
- One mark each for the calculation of surface area to volume ratios.
Note that if the question says that you must show all the stages of your working out, then you must do that.
Calculations:
The radius of a circle is half the diameter.
For an alveolus 200 μm in diameter – radius 100 μm - the surface area to volume ratio is:
\(\text{surface area of a sphere} = 4 \pi r^2\)
\(= 4 \times 3.14 \times (100 \times 100) = 125600~μm^2\)
\(\text{volume of a sphere} = \frac{4}{3} \pi r^3\)
\(= \frac{4}{3} \times 3.14 \times (100 \times 100 \times 100)= 4186667~ μm^3\)
\(\text{surface area to volume ratio} = \frac{125600}{4186667} = 0.030:1\)
For an alveolus 400 μm in diameter:
\(\text{surface area of a sphere} = 4 \pi r^2\)
\(= 4 \times 3.14 \times (200 \times 200) = 502400~μm^2\)
\(\text{volume of a sphere} = \frac{4}{3} \pi r^3\)
\(= \frac{4}{3} \times 3.14 \times (200 \times 200 \times 200)= 33493333~μm^3\)
\(\text{surface area to volume ratio} = \frac{502400}{33493333} = 0.015:1\)
