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Applications of Functions — Free MYP5 Mathematics (Extended) Practice Questions
1QuestionPredictionConcept Practice
2 marks~3 minCriterion D
A car travels at a constant speed. A distance–time graph for the journey passes through the origin and the point , where distance is measured in kilometres and time is measured in hours.
a
Deduce the equation of the line that models this relationship. [1]
b
The car must complete a 200 km journey within 3 hours. Justify whether the car's speed is sufficient to meet this requirement. [1]
Solutions
2QuestionReal-life modelsAssessment Practice
4 marks~6 minCriterion B
A student compares two savings plans. The total saved (in dollars) at the end of each week is recorded below.
Week (): 1, 2, 3, 4, 5
Plan A (): 50, 100, 150, 200, 250
Plan B (): 50, 105, 170, 245, 330
Week (): 1, 2, 3, 4, 5
Plan A (): 50, 100, 150, 200, 250
Plan B (): 50, 105, 170, 245, 330
a
Deduce the type of pattern (linear or quadratic) for each plan and derive a formula for total savings after weeks. [2]
b
Construct a prediction for the total savings under each plan after 10 weeks. [1]
c
Advise the student which savings plan to follow over a 52-week year, supporting your recommendation with calculated evidence. [1]
Solutions
3QuestionPredictionAssessment Practice
6 marks~9 minCriterion D
A projectile is launched at 10 m/s. The maximum height (in metres) reached at launch angle is given by
Angle (degrees): 15, 30, 45, 60, 75
Maximum height (m): ?, ?, ?, ?, ?
Angle (degrees): 15, 30, 45, 60, 75
Maximum height (m): ?, ?, ?, ?, ?
a
Calculate for each angle and complete the table. Round to two decimal places. [2]
b
Explain how changes as increases from 15° to 75°, and identify the mathematical relationship between and . [2]
c
A sports engineer claims that launching at 90° gives the greatest possible height. Advise the engineer whether a 90° launch angle is appropriate for a projectile intended to cover horizontal distance. [2]
Solutions
4QuestionInterpret contextAssessment Practice
6 marks~9 minCriterion A
A taxi company charges a fixed flag-fall fee plus a constant rate per kilometre travelled. The table below shows sample fares.
| Distance (km) | 1 | 3 | 5 |
|---|---|---|---|
| Total cost (dollars) | 7.50 | 14.50 | 21.50 |
a
Deduce the rate of change and the flag-fall fee, and hence write the general formula for the total cost (in dollars) in terms of distance (in km). [3]
b
A rival company charges according to . Construct a calculation to determine the distance at which both companies charge the same fare. [1]
c
A passenger must travel 8 km and has exactly 32.00 dollars. Advise the passenger which company to use, justifying your recommendation with numerical evidence. [2]
Solutions
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