Maths questions
Maths questions will appear throughout both exam papers (Breadth and Depth), and at both Foundation tier and Higher tier.
Don't 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鈥檛 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鈥檛 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鈥 (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 91热爆 Sounds.
Brush up on the maths you need for your exam - percentages, averages and converting units.
Sample question 1 - Foundation
Question
A car accelerates uniformly from rest at a rate of 0.4 m/s2 for 10 seconds, and then decelerates to rest over the next 8 seconds.
Calculate the change in velocity for the car in the first 10 seconds. [3 marks]
In your answer use the equation:
acceleration = change in velocity 梅 time
OCR 21st Century Science, GCE Physics, Paper J259, 2016.
Rearrange equation to give: change in velocity = acceleration 脳 time [1]
= 0.4 脳 10 [1]
= 4 (m/s) [1]
A lot of information is given in this question so it's important to work out which pieces of data you need to use. The second part referring to the deceleration is not needed in this part of the question so just focus on what happens during the first 10 seconds. Once you鈥檝e extracted the two pieces of data you need (the acceleration and the time) it is simply a case of rearranging the equation, putting the data in and doing the calculation.
Sample question 2 - Higher
Question
Tom drops a ball from the top of a building that is 13.5 m tall. He finds that it takes an average of 1.8 seconds for the ball to fall. Use this time to calculate the average speed of the falling ball and use this value to find the acceleration due to gravity, g. [5 marks]
OCR 21st Century Science, GCE Physics, Paper J259, 2016 - Higher.
Recall speed = distance 梅 time [1]
average speed = 13.5 m 梅 1.8 s
= 7.5 m/s
average speed = (initial speed + final speed) 梅 2 [1]
7.5 = 0 + final speed 梅 2
final speed = 7.5 脳 2
Therefore final speed = 15 m/s [1]
Recall: acceleration = change in speed 梅 time [1]
acceleration = (15 - 0) 梅 1.8
= 8.3 m/s2 [1]
This is a difficult calculation with quite a few steps and marks. You need to recall two equations: the equation for speed and the equation for acceleration so a good first step is to write both of these equations down.
Next calculate the average speed using the equation: speed = distance 梅 time. Many students will then use this number in the acceleration calculation but this is the average speed, not the final speed. As it started from rest, you can multiple the average speed by 2 to get the final speed.
Sample question 3 - Higher
Question
Neil observes a stream of bubbles rising in a glass of fizzy cola. The bubbles are produced at a steady rate.
In a stream of bubbles, each bubble has an acceleration of 0.175 m/s2. Assume that each bubble has a mass of 1 x 10-6 g.
Calculate the resultant force on each bubble. [3 marks]
OCR 21st Century Science, GCE Physics, Paper J260, 2016 - Higher.
First convert g to kg so: 1 x 10-6 g = 1 x 10-9 kg. [1]
1 x 10-9 kg x 0.175 m/s2 [1]
= 0.175 x 10-9 (N) [1]
The first step here is to notice that the mass has been given in grams rather than kg so it will need to be converted. This is done by dividing by 1,000.
Although the numbers make the question appear harder than it is as it uses power of 10s, so long as you are comfortable with using this function on your calculator this shouldn't cause too many issues.