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Types of Functions — Free MYP4 Mathematics (Extended) Practice Questions
1QuestionLinear functionsConcept Practice
4 marks~6 minCriterion A
A cyclist's journey is shown on the distance–time graph below. The two labelled points are and , where the horizontal axis shows time in hours and the vertical axis shows distance in kilometres.
a
Interpret what the gradient of the line represents in the context of this journey. [1]
b
Calculate the cyclist's speed in km/h. [1]
c
A cycling event requires competitors to cover at least 40 km in the first 2.5 hours. Justify whether this cyclist meets that requirement. [2]
Solutions
2QuestionRational functionsAssessment Practice
3 marks~5 minCriterion D
A community centre charges a fixed booking fee of 250 dollars and an additional 15 dollars per person for catering. The average cost per person for guests is modelled by
a
Calculate the average cost per person when there are 50 guests. [1]
b
Explain what happens to the average cost per person as the number of guests increases, linking your answer to the structure of . [1]
c
The community centre manager claims the model is reliable for planning any event. Advise the manager on whether this claim is justified, identifying one real-world constraint that limits the model. [1]
Solutions
3QuestionIdentify from equationsAssessment Practice
4 marks~6 minCriterion B
A landscape architect is designing square garden plots. Each plot has a side length of cm, and the usable planting area cm² follows the pattern below.
(cm):
(cm²):
(cm):
(cm²):
a
Calculate the first differences and second differences for the -values. [2]
b
Deduce the type of function (linear or quadratic) that models this data, justifying your answer using the differences found in part (a). [1]
c
The architect needs the usable planting area to exceed 90 cm². Advise the architect whether a plot with side length cm is sufficient to meet this requirement. [1]
Solutions
4QuestionLinear functionsAssessment Practice
8 marks~12 minCriterion C
A logistics company purchases a delivery van for 30 000 dollars. The van depreciates at a constant rate of 4 000 dollars per year.
a
Construct a linear function that represents the value of the van, in dollars, after years. [2]
b
Deduce the value of the van after 3 years. Show all working. [2]
c
The company's accountant states: "We should sell the van before its value falls below 14 000 dollars." Determine after how many years this threshold is reached, then advise the accountant whether the van should be sold before or after the 4-year mark. Show all working. [4]
Solutions
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