Cambridge International AS Level · Thinking Skills (9694)
5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Analyse data.
A small boutique records its sales over four days:
Day 1: \(50\) units
Day 2: \(25\) units
Day 3: \(25\) units
Day 4: \(100\) units
If this information is represented in a pie chart, what is the angle of the sector representing Day 4?
A company compares its regional sales for two years using a stacked bar chart. In \(2021\), Region A sold \(100\) units and Region B sold \(200\) units. In \(2022\), Region A sold \(150\) units and Region B sold \(120\) units.
Which of the following is a correct observation when transforming this table into the stacked bar chart?
The volume of water in a storage tank is monitored over time. From \(0\) to \(5\) minutes, the volume increases at a constant rate from \(100\) L to \(300\) L. From \(5\) to \(10\) minutes, the volume continues to increase at a constant rate, reaching \(400\) L at the \(10\)-minute mark.
What is the most likely explanation for the change in the graph's gradient at \(t = 5\)?
A meteorologist records monthly rainfall for a city: January: \(10\) mm, February: \(15\) mm, March: \(20\) mm, and April: \(25\) mm.
Which linear model correctly represents the rainfall \(R\) (in mm) based on the month number \(n\), where January is \(n=1\)?
A graph shows the distance a cyclist travels over a period of \(30\) minutes. The line is straight and sloping upwards from \(t = 0\) to \(t = 10\) minutes, becomes perfectly horizontal from \(t = 10\) to \(t = 20\) minutes, and then slopes upwards again from \(t = 20\) to \(t = 30\) minutes.
Which of the following is the most likely explanation for the trend between \(t = 10\) and \(t = 20\)?
In a small competition, the top three scores were 95, 88, and 82. The range of all six participants was 25. What is the lowest possible score achieved in the competition?<\/p>
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A survey of 200 people showed that 120 prefer tea, 100 prefer coffee, and 40 prefer both. How many people surveyed prefer neither tea nor coffee?<\/p>
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A city's bike-sharing usage data shows a strong positive correlation between temperature and the number of rentals. However, when the temperature exceeds \(35^\circ \text{C}\), the number of rentals drops sharply.
Suggest a plausible reason for this non-linear trend and explain how a researcher could modify a simple linear model to better represent this change in the data pattern.
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The following table shows the number of visitors to a local museum over four months:
January: 1200
February: 1500
March: 1800
April: 2100
The museum manager claims that the number of visitors is increasing by a constant percentage each month.
a) Use the data to show whether the manager's claim of a constant percentage increase is correct.
b) If the trend in the number of additional visitors per month continues linearly, how many visitors should be expected in May?
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The height of water in a rectangular storage tank was recorded over 40 minutes as it was being filled. For the first 10 minutes, the height increased at a constant rate from \(0\) cm to \(30\) cm. At \(t = 10\) minutes, a second identical pipe was opened, and the filling continued until \(t = 25\) minutes. At that point, both pipes were closed, and a drain was opened that emptied the tank at a rate of \(3\) cm per minute until the tank was empty.
a) What was the height of the water at \(t = 25\) minutes?
b) Determine the rate of increase in water height (in cm/min) between \(t = 10\) and \(t = 25\).
c) At what time \(t\) will the tank be completely empty?
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