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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(a) State the relationship between the resistance of the wire and its length, as shown by the graph.
[1 mark]
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(b) 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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(c) 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
- (a) Resistance is directly proportional to length / increases linearly with length / positive correlation between resistance and length
- (b) When length is zero, resistance is zero
- (b) There is no resistance when there is no wire / no fixed/constant resistance value independent of length
- (c) Both variables are continuous/numeric data
- (c) It shows the continuous relationship/trend between the two variables
- (c) Length and resistance are not categories
- (c) It allows identification of the relationship/pattern between variables more clearly than a bar chart
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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(a) Identify the independent variable in this investigation.
[1 mark]
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(b) 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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(c) Explain why plotting the results on a scatter graph is more useful than displaying them in a table for understanding this relationship.
[2 marks]
Show mark scheme
- (a) Temperature (of water) / the variable that was changed/manipulated
- (b) There is a negative/inverse correlation between temperature and time to dissolve, OR as temperature increases, time to dissolve decreases
- (c) A graph shows the trend/pattern/relationship more clearly than a table
- (c) The straight line allows us to see that the variables are directly/inversely related, OR we can easily identify the correlation visually
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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(a) Describe the relationship shown between the resistance of the wire and its length.
[1 mark]
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(b) Describe what information the gradient of the best-fit line provides about the wire.
[1 mark]
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(c) 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]
Show mark scheme
- (a) Resistance increases as length increases / positive correlation
- (a) The relationship is linear / proportional
- (b) The gradient represents the resistance per unit length
- (b) It shows the resistivity / resistance characteristics of the material
- (b) It indicates how much the resistance changes for each centimetre of wire
- (c) The anomalous point should be ignored / disregarded when drawing conclusions
- (c) It may have resulted from a measurement error or experimental error
- (c) The best-fit line should not pass through the anomalous point
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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(a) Calculate the total number of rulers sold on Saturday and Sunday.
[1 mark]
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(b) Calculate the mean number of rulers sold per day for the whole week.
[1 mark]
Show mark scheme
- (a) 38 rulers (accept 38)
- (b) 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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(a) Show how to work out the total number of customers over the five days.
[1 mark]
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(b) Draw a bar chart to represent this information.
[2 marks]
Show mark scheme
- (a) Correct method shown: 24 + 36 + 18 + 30 + 42 = 150
- (b) Axes correctly labelled with 'Day' and 'Number of customers' with appropriate scale
- (b) All five bars drawn to correct height (±½ square)
GCSE Perfect