Equations with Brackets and Fractions
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Equations with Brackets and Fractions — Free MYP3 Mathematics Practice Questions

1QuestionSolving Equations Involving FractionsConcept Practice
2 marks~3 minCriterion A
A triangle has angles measuring x°x°, x2°\dfrac{x}{2}°, and 30°30°.

(a) Write an equation using the angle sum property of a triangle. Calculate the value of xx. [2]
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Solutions

2QuestionClearing Fractions in EquationsAssessment Practice
6 marks~9 minCriterion D
A student receives a monthly allowance of 500 dollars. They plan to save xx dollars and spend the rest. The situation is modelled by the equation

x4+500−x3=150\frac{x}{4} + \frac{500 - x}{3} = 150
a
Calculate the value of xx by first clearing the fractions. [2]
b
Explain one assumption the model makes about the student's monthly spending, and describe how this assumption could limit the model's accuracy. [2]
c
The student uses this model over 12 months. Analyse how a rounding error of 0.50 dollars per month in the savings amount could affect the student's total annual budget prediction. [2]
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Solutions

3QuestionSolving Equations with Variables on Both SidesConcept Practice
3 marks~5 minCriterion C
The graph shows the lines y=2x+1y = 2x + 1 and y=x+5y = x + 5, which intersect at the point (4,9)(4, 9).
a
Calculate the value of each side of the equation 2x+1=x+52x + 1 = x + 5 when x=4x = 4. [1]
b
Explain what the equation 2x+1=x+52x + 1 = x + 5 is asking you to find. [1]
c
Interpret what the xx-coordinate of the intersection point represents in relation to solving the equation 2x+1=x+52x + 1 = x + 5. [1]
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Solutions

4QuestionExpanding Brackets Before SolvingConcept Practice
2 marks~3 minCriterion B
Each expression below has been expanded using the distributive property.

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
Describe the pattern you see in how each expression is expanded. [1]
b
Apply this pattern to expand 6(x+5)6(x + 5). Show your working. [1]

Solutions

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