Maths questions
Maths questions often start with the command words 鈥楥补濒肠耻濒补迟别...鈥 or 鈥楧别迟别谤尘颈苍别...鈥. They will then have a blank space for you to show 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 incorrect.
In some maths questions you will be required to give the units. This may earn you an additional mark. Don鈥檛 forget to check whether you need to do this.
Maths questions might include graphs and tables as well as calculations. Don鈥檛 forget to take a ruler and calculator.
If drawing graphs, make sure you:
- put the independent variable on the x-axis and the dependent variable on the y-axis
- construct regular scales for the axes
- label the axes appropriately
- plot each point accurately
- draw a straight or curved line of best fit
If you are asked to calculate an answer and it has lots of significant figures, you should try to round it to the same number of significant figures you were given in the data in the question. Don鈥檛 forget to check your rounding.
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Sample question 1 - Foundation
Question
A student measured the distance between a lens and the image of an object.
Table 1 gives both of the distances measured and the magnification.
Table 1
| Distance between the lens and the image in cm | Distance between the lens and the object in cm | Magnification |
| 100 | 25 | 4.0 |
| 60 | 30 | 2.0 |
| 40 | 40 | 1.0 |
| 33 | 50 | 0.7 |
| 30 | 60 | 0.5 |
| 100 | |
|---|---|
| Distance between the lens and the object in cm | 25 |
| Magnification | 4.0 |
| 60 | |
|---|---|
| Distance between the lens and the object in cm | 30 |
| Magnification | 2.0 |
| 40 | |
|---|---|
| Distance between the lens and the object in cm | 40 |
| Magnification | 1.0 |
| 33 | |
|---|---|
| Distance between the lens and the object in cm | 50 |
| Magnification | 0.7 |
| 30 | |
|---|---|
| Distance between the lens and the object in cm | 60 |
| Magnification | 0.5 |
Consider the data in Table 1.
Give a second way that the student could have determined the magnification of the object.
Justify your answer with a calculation. [2 marks]
The student could divide the distance between the lens and the image by the distance between the lens and the object.
For example, 100 梅 25 = 4 which is the same as the measured magnification of 4.0.
This question requires you to spot a pattern in the table data.
Sample question 2 - Higher
Question
A student uses a ripple tank where all the water is the same depth.
She measures the wavelength of each wave as 0.34 m.
The period of each wave is 0.42 s.
Calculate the speed of the wave.
Use the correct equation from the Physics Equation Sheet. Give the unit. Give your answer to three significant figures. [5 marks]
0.809 m/s
This calculation must be done in two parts. Use the time period to find the frequency then use the frequency and wavelength to find the wave speed. Do not forget to give the unit and to give the answer to three significant figures.
Time period = 1 梅 frequency
0.42 = 1 梅 frequency
frequency = 1 梅 0.42
= 2.38 Hz
wave speed = frequency 脳 wavelength
wave speed = 2.38 脳 0.34
= 0.809 m/s
Sample question 3 - Higher
Question
The speed of a wave is calculated using the following equation:
wave speed = frequency 脳 wavelength
The water waves in a ripple tank have a wavelength of 1.2 cm and a frequency of 18.5 Hz.
How does the speed of these water waves compare to the typical speed of a person walking? [4 marks]
1.2 cm = 0.012 m
Wave speed = frequency 脳 wavelength
= 18.5 脳 0.012
= 0.22 m/s
Typical walking speed = 1.5 m/s so the water waves are much slower (than a typical walking speed).
In this question, it is important to convert centimetres into metres and to remember to make the final comparison with walking speed.