Equations with Brackets and Fractions
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Equations with Brackets and Fractions — Free MYP2 Mathematics Practice Questions

1QuestionSolving Equations Involving FractionsConcept Practice
3 marks~5 minCriterion A
The graph shows the line y=12x+3y = \dfrac{1}{2}x + 3.
a
Identify the xx-coordinate of the point on the line where y=7y = 7. [1]
b
Calculate the value of xx by solving the equation 12x+3=7\dfrac{1}{2}x + 3 = 7, showing all working. [1]
c
Compare your answer to part (b) with the value you read from the graph in part (a), and explain what this tells you about the two methods. [1]
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Solutions

2QuestionSolving Equations with Variables on Both SidesAssessment Practice
2 marks~3 minCriterion D
A student compares two mobile phone plans:

Plan A: 20 dollars per month + 0.10 dollars per text
Plan B: 10 dollars per month + 0.15 dollars per text

The equation 20+0.10x=10+0.15x20 + 0.10x = 10 + 0.15x shows when the plans cost the same, giving a solution of x=200x = 200 texts.
a
Identify one real-world limitation of this model. [1]
b
Explain how this limitation could affect the break-even result of 200 texts. [1]
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Solutions

3QuestionExpanding Brackets Before SolvingConcept Practice
2 marks~3 minCriterion B
Look at the four equations below.

2(x+1)=2x+22(x + 1) = 2x + 2
3(x+2)=3x+63(x + 2) = 3x + 6
4(x+3)=4x+124(x + 3) = 4x + 12
5(x+4)=5x+205(x + 4) = 5x + 20
a
Identify the pattern in how the left side expands to give the right side. [1]
b
State the general rule for expanding a(x+b)a(x + b). [1]

Solutions

4QuestionClearing Fractions in EquationsAssessment Practice
3 marks~5 minCriterion C
The graph shows the lines y=x+13y = \dfrac{x+1}{3} and y=2x−12y = \dfrac{2x-1}{2}.
a
Identify the x-coordinate of the point where the two lines intersect. [1]
b
Explain how this x-coordinate gives the solution to the equation x+13=2x−12\dfrac{x+1}{3} = \dfrac{2x-1}{2}. [1]
c
Calculate the exact solution algebraically and compare it with your answer in part (a). [1]
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Solutions

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