State — 4 marks
A student conducted an experiment to investigate how the resistance of a wire varies with its length. She measured the resistance of nichrome wire at different lengths and plotted her results on a line graph. The graph shows resistance in ohms (Ω) on the y-axis and length in cm on the x-axis. The points form a straight line passing through the origin.
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State the relationship between the resistance of the wire and its length, as shown by the graph.
[1 mark]
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State two pieces of information that can be obtained from the fact that the line passes through the origin (0,0).
[2 marks]
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State one reason why plotting the data on a line graph, rather than as a bar chart, was the most appropriate choice of representation for this experiment.
[1 mark]
Show mark scheme
Explain — 4 marks
A student investigated how the temperature of water affects the time taken for sugar to dissolve. She heated water to different temperatures and timed how long it took for a fixed mass of sugar to completely dissolve. She recorded her results in a table and then plotted a scatter graph with temperature on the x-axis and time to dissolve on the y-axis.
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Identify the independent variable in this investigation.
[1 mark]
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The student's scatter graph shows all points lie close to a straight line sloping downwards from left to right. What does this tell you about the relationship between temperature and the time taken for sugar to dissolve?
[1 mark]
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Explain why plotting the results on a scatter graph is more useful than displaying them in a table for understanding this relationship.
[2 marks]
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Describe — 3 marks
A student conducted an experiment to investigate how the resistance of a wire varies with its length. They measured the resistance of nichrome wire at different lengths and plotted their results on a line graph. The graph shows resistance in ohms (Ω) on the y-axis and length in centimetres (cm) on the x-axis. The plotted points show a clear linear relationship, and the student has drawn a best-fit line through the data.
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Describe the relationship shown between the resistance of the wire and its length.
[1 mark]
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Describe what information the gradient of the best-fit line provides about the wire.
[1 mark]
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The student's graph shows one anomalous data point that lies significantly away from the best-fit line. Describe how this anomalous point should be treated when drawing conclusions from the experiment.
[1 mark]
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Calculate — 2 marks
A stationery shop recorded the number of rulers sold each day for one week. The bar chart shows the results: Monday 12, Tuesday 18, Wednesday 15, Thursday 20, Friday 25, Saturday 30, Sunday 8.
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(01.1) Calculate the total number of rulers sold on Saturday and Sunday.
[1 mark]
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(01.2) Calculate the mean number of rulers sold per day for the whole week.
[1 mark]
Show mark scheme
- (01.1) 38 rulers (accept 38)
- (01.2) 18.3 or better (accept 18) OR 128 ÷ 7 seen
Show — 3 marks
A shop owner records the number of customers each morning for five days.
| Day | Number of customers |
|-----|---------------------|
| Monday | 24 |
| Tuesday | 36 |
| Wednesday | 18 |
| Thursday | 30 |
| Friday | 42 |
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(01.1) Show how to work out the total number of customers over the five days.
[1 mark]
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(01.2) Draw a bar chart to represent this information.
[2 marks]
Show mark scheme
- (01.1) Correct method shown: 24 + 36 + 18 + 30 + 42 = 150
- (01.2) Axes correctly labelled with 'Day' and 'Number of customers' with appropriate scale
- (01.2) All five bars drawn to correct height (±½ square)
GCSE Perfect