Linear Functions
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Linear Functions — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionSlopeAssessment 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 (1,2)(1, 2) and (4,8)(4, 8).
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]
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2QuestionSlopeAssessment Practice
4 marks~6 minCriterion A
A distance–time graph shows a cyclist's journey from A to D, with coordinates A(0, 0), B(20, 5), C(60, 5), and D(80, 20), where time is in minutes and distance is in kilometres.
a
Calculate the slope of segment AB. [1]
b
Interpret what the slope of segment AB represents in the context of the cyclist's journey. Include appropriate units in your answer. [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]
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3QuestionGraphing linesAssessment Practice
4 marks~6 minCriterion D
A city's water authority monitors its reservoir during a drought. Sensors record the water volume relative to a target level, where each unit represents 10 million litres. At week 0 the reservoir is at −2-2 units relative to target; by week 4 it is at 11 unit relative to target.
a
Calculate the slope of the line passing through (0,−2)(0, -2) and (4,1)(4, 1). [1]
b
Deduce the equation of the line in the form y=mx+cy = mx + c. [1]
c
Interpret what the slope and yy-intercept reveal about the reservoir's situation, and justify whether the authority should still take action to safeguard the water supply. [2]
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4QuestionSlope-intercept formAssessment Practice
4 marks~6 minCriterion C
A mobile data plan charges a fixed monthly fee plus a constant rate per gigabyte used. The total cost, in dollars, is modelled by a linear function. The graph passes through (0,−4)(0, -4) and (3,−2)(3, -2).
a
Calculate the slope of the line using the two given points. [1]
b
Deduce the equation of the line in slope-intercept form y=mx+by = mx + b. [1]
c
A technician claims the monthly fixed fee is a cost saving of 4 dollars. Justify whether this claim accurately describes the overall pricing structure of the plan. [2]
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