Linear Equations in One Variable
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Linear Equations in One Variable — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionChecking Solutions and SubstitutionConcept Practice
4 marks~6 minCriterion A
A mobile data plan charges a monthly fee. The total monthly cost, yy (in dollars), for using xx gigabytes of data is modelled by the equation y=2x+1y = 2x + 1.
a
Show that the point (2,5)(2, 5) lies on the line y=2x+1y = 2x + 1. [1]
b
A customer uses 3 gigabytes in a month. Calculate their total monthly cost. [1]
c
A customer's budget allows a maximum monthly spend of 6 dollars. Advise the customer whether this budget is sufficient for 3 gigabytes of data usage, justifying your answer with a numerical comparison. [2]
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Solutions

2QuestionSolving One-Step and Two-Step EquationsAssessment Practice
4 marks~6 minCriterion C
A mobile data plan charges a fixed monthly fee of 4 dollars plus a cost per gigabyte used. In January, a customer used 6 GB and paid a total usage fee modelled by:

x+4=10x + 4 = 10

In February, the customer doubled their data usage, giving a total usage fee modelled by:

2x+4=162x + 4 = 16

where xx is the cost per gigabyte in dollars.
a
Calculate the value of xx for each equation. [2]
b
Explain why Equation B requires one more algebraic step than Equation A to isolate xx. [1]
c
Justify whether the February plan offers the customer better value per gigabyte than the January plan. [1]
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Solutions

3QuestionSolving One-Step and Two-Step EquationsAssessment Practice
6 marks~9 minCriterion D

A student tracks the battery percentage of a phone over time. The data collected is:

Time (h): 0, 1, 2, 3

Battery (%): 100, 82, 64, 46

The student models the battery drain with the equation B=100−18tB = 100 - 18t, where BB is the battery percentage and tt is the time in hours.

a
[2 marks] Use the model to predict the battery percentage after 4 hours.
b
[2 marks] Use the model to find the time when the battery reaches 0%.
c
[2 marks] Discuss two limitations of using this linear model to represent the phone's battery drain over time.
Question diagram

Solutions

4QuestionChecking Solutions and SubstitutionAssessment Practice
6 marks~9 minCriterion B

Data

x+2=5,x=3x + 2 = 5, \quad x = 3
2x+4=10,x=32x + 4 = 10, \quad x = 3
3x+6=15,x=33x + 6 = 15, \quad x = 3
4x+8=20,x=34x + 8 = 20, \quad x = 3
A water treatment plant adjusts chemical dosing using equations of the form ax+2a=5aax + 2a = 5a, where aa is a non-zero real number and xx represents the dosing multiplier.

The following equations and proposed solutions are
a
Deduce the solution to 10x+20=5010x + 20 = 50. [1]
b
Show that every equation of the form ax+2a=5aax + 2a = 5a, where a≠0a \neq 0, has solution x=3x = 3. [3]
c
The plant requires a dosing multiplier strictly greater than 3 to safely treat a new water source. The engineer models this situation with the equation 100x+200=500100x + 200 = 500. Solve this equation and advise the engineer whether the plant can safely treat the new water source under this model. [2]

Solutions

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