Maths questions
Maths questions will appear throughout both exams papers (Breadth and Depth), and at both Foundation Tier and Higher Tier.
Don鈥檛 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 question 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
Learn maths skills with Dr Alex Lathbridge
Listen to the full series on 大象传媒 Sounds.
Brush up on the maths you need for your exam - percentages, averages and converting units.
Sample question 1 - Higher
Question
Radon鈥222 is a dense radioactive gas. The diagram below shows the alpha decay of radon-222.
\(_{86}^{222}\textrm{Rn}\rightarrow_{84}^{x}\textrm{Po}+_{2}^{x}\textrm{He}\)
Complete the above equation by adding the two missing numbers to the products produced. [1 mark]
OCR 21st Century Science, GCE Physics, Paper J259, 2016 - Higher.
\(_{84}^{218}\textrm{Po}~,~ _{2}^{4}\textrm{He}\)
This question involves simple substitution. You should be able to recall that the mass number of the helium nuclei is 4. Then you just need to subtract it from the mass number of radon, so 222 鈥 4 = 218.
Sample question 2 - Foundation
Question
Radioactive isotopes are widely used in medicine to treat cancer. Some people are concerned that using radiotherapy treatment for cancer may itself cause a second cancer.
In a recent study of over 600,000 cancer patients who had been treated with radiotherapy, it was found that about 5 in 1,000 of them developed a further cancer within 15 years as a result of the treatment.
Calculate approximately how many cancer patients involved in the study developed a further cancer within 15 years of treatment. Use the data given above in your answer. [2 marks]
OCR 21st Century Science, GCE Physics, Paper J259, 2016.
\(600,000 \times (\frac{5}{1000}) = 3,000\)
The difficulty in this question comes from finding the relevant data in the question. Once you've picked out the data it's a relatively straight-forward calculation.
Sample question 3 - Foundation
Question
A hospital uses technetium-99 as a radioisotope.
The half-life of technetium-99 is 6 hours.
How long will it take for the activity of a sample of technetium-99 to fall to one eighth of its starting value? [2 marks]
OCR 21st Century Science, GCE Physics, Paper J260, 2016.
One eighth is equal to 3 half-lives =\(\frac{\textbf{1}}{\textbf{2}}\), \(\frac{\textbf{1}}{\textbf{4}}\), \(\frac{\textbf{1}}{\textbf{8}}\)
Therefore it will take 3 脳 6 = 18 hours
The first step in the calculation is to work out how many times the number has to half until it becomes an eighth of its original value. The answer to this is three times. Then you just need to multiple the half-life by three to get the time in hours.