Maths questions

Don't forget to take a ruler and scientific calculator into the exam.

Maths questions often start with the command word 'calculate'. You need to use numbers given in the question to work out the answer.

When an answer to a maths question is marked:

  • full marks are given for the right answer
  • marks may be given for working, including substitution and rearrangement
  • calculation errors carried forward are worked through to give credit for later working
curriculum-key-fact
Always show working in calculation questions. You can get marks for correct working, even if the answer is wrong.

Make sure you give answers to a suitable number of significant figures.

Maths questions might ask you to plot or complete a graph or table. When you draw a graph, make sure you:

  • plot each point accurately
  • draw a best fit straight line or curve, where appropriate

You may be given a grid with axes labelled and scales already given. Sometimes you may be given an empty grid for you to supply your own axes. When you do this:

  • put the independent variable on the x-axis and the dependent variable on the y-axis
  • choose even scales and make sure that the points cover at least half the given grid
  • label the axes with their quantity and unit, eg time (s)

Take extra care when converting between units.

This page contains AQA material which is reproduced by permission of AQA.

Sample question 1 – Foundation

Question

Scientists investigated the effect of light intensity on the rate of photosynthesis.

The graph below shows the scientists' results.

The graph indicates that rate of photosynthesis increases as light intensity

Describe the effect of increasing light intensity on the rate of photosynthesis.

You should include numbers from the graph in your description. [3 marks]

These terms should be used to gain all marks:

  • increases [1]
  • levels off / reaches a maximum / remains constant / stays the same / plateaus [1]
  • goes up to / reaches a maximum / levels off at 200 (arbitrary units) or levels off at 225-240 light units [1]

Sample question 2 – Foundation

Question

An athlete is running on a treadmill.

Group of runners on treadmills

After running for several minutes, the athlete's leg muscles began to ache.

This ache was caused by a high concentration of lactic acid in the muscles.

Scientists investigated the production of lactic acid by an athlete running at different speeds.

In the investigation:

  • the athlete ran on the treadmill at 4 km per hour
  • the scientists measured the concentration of lactic acid in the athlete's blood after 2 minutes of running

The investigation was repeated for different running speeds.

The scientists' results are presented in the graph below.

The graph shows the concentration of lactic acid increasing as so does the speed

How much more lactic acid was there in the athlete's blood when he ran at 14 km per hour than when he ran at 8 km per hour? [2 marks]

4.4 mmol per dm3 [2]

Correct readings from graph in the ranges of 6.7 to 6.9 and 2.3 to 2.5, but no answer or a wrong answer gains 1 mark.

Question 3 – Higher

Question

The nervous system allows humans to respond to their surroundings.

The figure below shows two nerve pathways.

Nerve pathway A is 92 cm long.

Two forms of nerve pathways

A nerve impulse travels along pathway A at 76.2 m/s.

Calculate how long it takes for the nerve impulse to travel the length of the pathway.

Use the equation:

distance = speed × time

0.92 = 76.2 × time [1]

time = 0.92 ÷ 76.2 [1]

= 0.012 s/sec/seconds [1]

Question 4 – Higher

Two students compare their reactions using a ruler.

This is the method used.

  1. Student A sits with his elbow on a table top.
  2. Student B holds the ruler so the bottom of the ruler is level with the top of student A's thumb.
  3. Student B drops the ruler.
  4. Student A catches the ruler.
  5. Record the drop distance.
  6. Repeat steps 1 to 5 four more times.
  7. Repeat the whole experiment with student A dropping the ruler and student B catching it.
On the left-hand side two hands hold both end of a ruler from top to bottom. On the right hand side one hand has just let go and the second hand at the bottom has caught ruler.

Both students are right-handed.

The students are testing the hypothesis:

The drop distance of the ruler is smaller when a right-handed person uses their right hand to catch the ruler.

Student A uses his right hand to catch the ruler.

Student B uses her left hand to catch the ruler.

The table shows the students' results.

The drop distance is measured in mm.

Test 1Test 2Test 3Test 4Test 5
Student A – right hand203167140156163
Student B – left hand230211279215264
Question

a) What is the range of student A's results? [1 mark]

140 – 203 [1]

Question

b) Student A's mean reaction time was 0.19 s.

Mean reaction time can be calculated using the equation:

\text{Mean reaction time} = \sqrt{\frac{2 \times \text{mean drop distance in mm}}{9.8 \text{m/s}^{2}}}

Calculate the mean reaction time for student B.

Give your answer to 2 significant figures. [4 marks]

Mean drop distance = (230 + 211 + 279 + 215 + 264) ÷ 5 = 239.8 [1]

239.8 mm = 0.2398 m

mean reaction time =  \sqrt{\frac{2 \times 0.2398}{9.8}} [2]

= 0.221 seconds [1]