Linear Functions

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Linear Functions — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionPoint-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.

Calculate the rate of change (cost per kilometre) using the two data points. [1]

Deduce the equation of the cost function in the form

y = mx + b

, where

x

is distance in kilometres and

y

is total cost in dollars. [2]

The company advertises "no connection fee." Justify whether this claim is accurate. [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

m_1 = \dfrac{2}{3}

Deduce the slope of the second pathway. [1]

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

3QuestionSlopeAssessment 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)

and

(4, 8)

Calculate the slope of the line using the two labelled points. [1]

Show that the slope is constant by calculating the rise and run between a different pair of points on the line. [2]

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

4QuestionGraphing linesAssessment Practice

4 marks~6 minCriterion D

A city's water authority monitors reservoir levels during a drought. Sensors show the water volume is decreasing at a constant rate. At the start of monitoring (week 0), the reservoir holds

-2

units relative to the target level, and by week 4 it holds

1

unit relative to the target level, where each unit represents 10 million litres.

Calculate the slope of the line passing through

(0, -2)

and

(4, 1)

. [1]

Deduce the equation of the line in the form

y = mx + c

. [1]

Interpret what the slope and

y

-intercept reveal about the reservoir's situation, and advise the authority whether action is still required to safeguard the water supply. [2]

Solutions

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