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

1QuestionSolving One-Step and Two-Step EquationsConcept Practice
4 marks~6 minCriterion A
A mobile phone plan charges a fixed monthly fee plus a cost per gigabyte of data used. Last month, a customer used 7 GB of additional data and paid a total bill of 15 dollars. This situation is modelled by the equation x+7=15x + 7 = 15, where xx is the fixed monthly fee in dollars.
a
Calculate the fixed monthly fee xx. [1]
b
Deduce the operation applied to both sides of the equation to isolate xx, and state the property of equality that justifies this step. [2]
c
Advise the customer, who budgets 10 dollars per month for fixed fees, whether this plan is within their budget. Justify your advice using your answer to part (a). [1]
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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

4QuestionSolving One-Step and Two-Step EquationsAssessment Practice
8 marks~12 minCriterion B
A mobile data plan charges a fixed monthly fee of bb dollars plus aa dollars per gigabyte used. Last month, a customer paid exactly 17 dollars in total.
a
With b=5b = 5, calculate the number of gigabytes xx used for each per-gigabyte rate: a=2,3,4,6,12a = 2, 3, 4, 6, 12. Show your algebraic working for each case. [2]
b
With a=3a = 3, calculate the number of gigabytes xx used for each fixed fee: b=2,8,11,14,17b = 2, 8, 11, 14, 17. Show your algebraic working for each case. [2]
c
Analyse how changes in aa affect xx using your results from part (a), and how changes in bb affect xx using your results from part (b). [2]
d
The plan is advertised as suitable for customers who use at least 1 gigabyte per month. With b=5b = 5, advise whether a per-gigabyte rate of a=15a = 15 keeps the plan suitable for a customer who paid exactly 17 dollars. Justify your answer using the pattern identified in part (c). [2]

Solutions

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