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Linear Functions — Free MYP5 Mathematics (Extended) Practice Questions
1QuestionSlopeConcept Practice
4 marks~6 minCriterion B
A city's water authority monitors daily water usage at a treatment plant. The graph shows total water processed (in megalitres) against time (in days), modelled as a straight line passing through the labelled points and .
a
Calculate the slope of the line using the two labelled points. [1]
b
Show that the slope is constant by calculating the rise and run between a different pair of points on the line. [2]
c
The authority states: "Usage is increasing at a steady rate, so we can reliably forecast demand using this model." Assess whether the mathematical properties of the graph support this statement. [1]
Solutions
2QuestionParallel & perpendicularAssessment Practice
2 marks~3 minCriterion C
A city planner is designing two straight pedestrian pathways that must cross at a right angle to ensure safe sightlines at the intersection.
The first pathway has a slope of .
The first pathway has a slope of .
a
Deduce the slope of the second pathway. [1]
b
The planner states: "A steeper crossing angle improves pedestrian safety." Justify whether the slopes of the two pathways satisfy the planner's safety condition. [1]
Solutions
3QuestionPoint-slope formConcept Practice
4 marks~6 minCriterion A
A delivery company charges a fixed connection fee plus a constant rate per kilometre. A driver records that a 1 km trip costs 2 dollars and a 4 km trip costs 8 dollars.
a
Calculate the rate of change (cost per kilometre) using the two data points. [1]
b
Deduce the equation of the cost function in the form , where is distance in kilometres and is total cost in dollars. [2]
c
The company advertises "no connection fee." Justify whether this claim is accurate. [1]
Solutions
4QuestionSlopeAssessment Practice
4 marks~6 minCriterion D
A distance–time graph shows a cyclist's journey from A to D, with points A(0, 0), B(20, 5), C(60, 5), and D(80, 20), where time is in minutes and distance is in kilometres.
a
Show that the slope of segment AB is 0.25 km/min. [1]
b
Explain what the slope of segment AB represents in the context of the cyclist's journey. [1]
c
The cyclist must maintain an average speed of at least 0.20 km/min over the entire journey from A to D. Justify whether this condition is met. [2]
Solutions
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