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Two groups of students go on a water sport holiday - OCR - GCSE Maths - Question 8 - 2018 - Paper 1
Question 8
Two groups of students go on a water sport holiday. Each student chooses one activity. Students in Group A choose from Diving, Swimming, Paddleboarding and Kayaking... show full transcript
Worked Solution & Example Answer:Two groups of students go on a water sport holiday - OCR - GCSE Maths - Question 8 - 2018 - Paper 1
Step 1
Complete this table for Group A.
Answer
To complete the table for Group A, we first calculate the total number of students:
Total = Students in Diving + Students in Swimming + Students in Paddleboarding + Students in Kayaking
Given:
Diving = 5 Swimming = 10 Paddleboarding = x (unknown) Kayaking = 9
Thus,
Total = 5 + 10 + x + 9 = 24 + x
Now calculate the angle of the sector for Paddleboarding. The total angle in a pie chart is 360°. The current angles are:
Angle for Diving + Swimming + Kayaking = 60° + 120° + 108° = 288°
Angle for Paddleboarding = 360° - 288° = 72°
Now we know:
Diving: 5 students, 60° Swimming: 10 students, 120° Paddleboarding: 10 students, 72° (since total students = 24) Kayaking: 9 students, 108°
Step 2
Complete the pie chart for Group A.
Answer
To complete the pie chart for Group A, plot the angles for each activity based on the previously calculated values:
- Diving: 60°
- Swimming: 120°
- Paddleboarding: 72°
- Kayaking: 108°
The chart should visually represent these angles proportionally, ensuring the sum equals 360°.
Step 3
One student in Group A changes activity.
Answer
If one student in Group A changes their activity, we need to take into account how this affects the total numbers and angles. For example, if the student changes from Swimming to Paddleboarding, then:
- Diving: 5 students, 60°
- Swimming: 9 students, 108° (1 student leaves)
- Paddleboarding: 11 students, updated angle is calculated as follows: Total = 23 students: New angle for Paddleboarding = (11/23) * 360°.
Step 4
The choices made by Group B are shown in this pie chart.
Answer
For Group B, we need to analyze the proportions based on the pie chart representation. A common misconception could arise because Group B may have different total numbers of participants, thus skewing the comparison when estimating participation in activities between the groups.