Linear Equations in One Variable
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Linear Equations in One Variable — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionEquations Involving Brackets and FractionsConcept Practice
2 marks~3 minCriterion A
A personal trainer designs a 45-minute session split into three identical blocks. Each block includes a 5-minute warm-up plus 2x2x minutes of circuit training, where xx is the number of circuit rounds.
a
Show that the total session time gives the equation 3(2x+5)=453(2x + 5) = 45, and solve for xx. [1]
b
The trainer states: "Each block has time for at least 4 circuit rounds." Using your value of xx, justify whether this statement is correct. [1]
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2QuestionWord Problems Involving Linear EquationsAssessment Practice
4 marks~6 minCriterion D
An architect is designing a rectangular garden bed with a perimeter of 94 cm. The length is 5 cm more than twice the width.
a
Write a linear equation in one variable that represents the perimeter condition of the rectangle. [1]
b
Determine the length and width of the rectangle. Show your working. [2]
c
The architect considers redesigning the garden bed as a square with the same perimeter. Advise the architect whether switching to the square design is worthwhile for maximising planting area. [1]
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3QuestionEquations Involving Brackets and FractionsConcept Practice
2 marks~3 minCriterion B
A mobile data plan charges a fixed monthly fee. The total cost CC (in dollars) after nn months satisfies the sequence of equations below, where xx is the monthly fee.

x2=5,x+13=5,x+24=5,x+35=5\frac{x}{2} = 5, \quad \frac{x+1}{3} = 5, \quad \frac{x+2}{4} = 5, \quad \frac{x+3}{5} = 5

Analyse the pattern in the sequence. Write the next equation and deduce the value of xx it gives. [2]

Solutions

4QuestionSolving One-Step and Two-Step EquationsAssessment Practice
4 marks~6 minCriterion C
A student solves 5x−10=205x - 10 = 20 and produces the following working:

Step 1: 5x=20−10=105x = 20 - 10 = 10

Step 2: x=105=2x = \dfrac{10}{5} = 2
a
Identify the step in which the error occurs and state what the student did incorrectly. [1]
b
Show that the correct solution is x=6x = 6. [2]
c
An engineer uses the equation 5x−10=205x - 10 = 20 to model the load (in kilonewtons) on a structural beam, where xx represents the number of support columns. Advise the engineer whether the student's solution should be used to determine the number of columns, justifying your answer in terms of structural safety. [1]
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