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)
Calculate — 5 marks
A group of 120 students were asked how they travel to school. The results are shown in a pie chart. 45 students walk to school, 30 students cycle, and the angle of the sector representing students who travel by bus is 105°. The remaining students travel by car.
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(a) Calculate the angle of the sector representing students who walk to school.
[2 marks]
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(b) Calculate the number of students who travel to school by car.
[3 marks]
Show mark scheme
- (a) Method: 360 ÷ 120 or 3° per student, or 45/120 × 360 seen
- (a) Correct answer: 135°
- (b) Method to find number of bus students: 105 ÷ 360 × 120 or equivalent (35)
- (b) Method to find car students: 120 − 45 − 30 − 35 or equivalent complete method
- (b) Correct answer: 10
Show — 4 marks
A leisure centre records the number of visitors attending swimming lessons each day over a week. The data collected is: Monday 24, Tuesday 31, Wednesday 28, Thursday 35, Friday 29, Saturday 42, Sunday 38.
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(a) Show that the total number of visitors for the week is 227.
[2 marks]
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(b) Show that the mean number of visitors per day is approximately 32.4 (to 1 decimal place).
[2 marks]
Show mark scheme
- (a) Correctly adds at least 5 of the 7 daily values
- (a) Arrives at the total of 227 with correct arithmetic shown
- (b) Divides 227 by 7 (or equivalent working shown)
- (b) Correctly rounds to 1 decimal place to obtain 32.4
Show — 4 marks
A leisure centre tracks the number of visitors each day over one week. The data collected shows: Monday 45 visitors, Tuesday 52 visitors, Wednesday 38 visitors, Thursday 61 visitors, Friday 55 visitors, Saturday 78 visitors, Sunday 42 visitors. The leisure centre manager wants to represent this data clearly to show patterns in visitor numbers throughout the week.
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(a) Show that the total number of visitors for the week is 371.
[2 marks]
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(b) Show which day had the highest number of visitors and calculate how many more visitors attended on that day compared to the day with the lowest number of visitors.
[2 marks]
Show mark scheme
- (a) Correctly adds all seven daily values (45 + 52 + 38 + 61 + 55 + 78 + 42)
- (a) Arrives at the total of 371
- (b) Correctly identifies Saturday as the day with the highest number of visitors (78) and Wednesday as the day with the lowest (38)
- (b) Correctly calculates the difference: 78 − 38 = 40 visitors
GCSE Perfect
/ Mathematics