Free IB MYP Practice Questions | RevisionPrep

Linear Inequalities and Graphical Solutions — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionGraphical Representation of InequalitiesConcept Practice

2 marks~3 minCriterion A

A city planner models a budget constraint for two infrastructure projects. The total spending on Project A (

x

million) and Project B (

y

million) must remain below a fixed limit. The boundary line of the feasible region passes through

(0, 2)

and

(2, 0)

and is shown as a dashed line on the graph. The region below this line is shaded.

Write the inequality that represents the feasible spending region. [1]

The planner proposes spending

x = 0.8

million on Project A and

y = 1.4

million on Project B. Justify whether this combination is a feasible spending plan. [1]

Solutions

2QuestionSolving Linear Inequalities in One VariableAssessment Practice

4 marks~6 minCriterion C

A city regulation states that a food truck must be located more than 4 metres from the nearest fire hydrant. A number line is provided showing all permitted distances

x

(in metres) from a hydrant.

Interpret the number line: explain what the open circle at

x = 4

and the arrow pointing right each indicate about the solution set. [1]

Write an inequality in the form

ax + b > c

, where

a

b

, and

c

are integers and

a \neq 1

, that represents the same solution set. [1]

A rival truck parks at

x = 4.0

m. Justify whether this truck complies with the regulation. [2]

Solutions

3QuestionGraphical Representation of InequalitiesAssessment Practice

4 marks~6 minCriterion D

A farmer has 100 hectares of land and a budget of 120000 dollars to plant two crops: wheat and corn. Planting one hectare of wheat costs 1000 dollars, while one hectare of corn costs 1500 dollars. The profit per hectare of wheat is 5000 dollars, and the profit per hectare of corn is 8000 dollars.

Let

x

be the number of hectares of wheat and

y

be the number of hectares of corn. Write down two inequalities that represent the constraints on the land and budget.

Sketch a graph showing the feasible region defined by these inequalities, with

x

on the horizontal axis and

y

on the vertical axis. Label the axes clearly.

The farmer wants to maximize their profit. Discuss the strengths and limitations of using this linear programming model to determine the optimal number of hectares of each crop to plant. Consider factors such as unpredictable weather patterns, fluctuating market prices, and the assumption of constant profit per hectare.

Solutions

4QuestionGraphical Representation of InequalitiesAssessment Practice

6 marks~9 minCriterion B

A city planner is designing a pedestrian zone. The safe walking corridor must satisfy two constraints modelled by linear inequalities. Three trial corridor systems are tested:

System 1:

y \geq x + 1

and

y \leq -x + 5

System 2:

y \geq x + 3

and

y \leq -x + 3

System 3:

y \geq x + 5

and

y \leq -x + 1

A proposed corridor uses the system

y \geq x + 2

and

y \leq -x + 4

Analyse the three trial systems. For each, identify whether the feasible region is bounded, a single point, or empty, and explain how the relationship between the constants

c_1

and

c_2

determines this outcome. [2]

Deduce the nature of the feasible region for the proposed corridor system, justifying your answer using the pattern identified in part (a). [1]

Construct a graph of the proposed corridor system, clearly showing the boundary lines, the feasible region, and the coordinates of any intersection points. Hence advise the city planner whether the proposed corridor should be approved, justifying your recommendation with reference to the feasible region. [3]

Solutions

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