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Algebra — Free MYP1 Mathematics Practice Questions
1QuestionExpanding Single Bracket ExpressionsConcept Practice
2 marks~3 minCriterion B
The diagram shows a rectangular garden with a length of m and a total width of m. A dividing line splits it into two smaller rectangles: one of width m and one of width m.
a
State the area of each smaller rectangle. [1]
b
Describe how the two smaller areas show that . [1]
Solutions
2QuestionCreating Equivalent Expressions through ExpansionAssessment Practice
6 marks~9 minCriterion C
A gardener uses the expression to calculate the number of paving stones needed for a straight rectangular path of width meters. The path is shown in the diagram.
a
[2 marks] Explain why the expression gives the number of stones for a straight rectangular path, assuming each stone covers 1 square meter.
b
[2 marks] The actual path has a curved section and a small flower bed in the middle, as shown in the diagram. Discuss whether the model is still valid for this actual path. Identify one limitation of the model.
c
[2 marks] Suggest a different expression that would be more accurate for the actual path, and explain why your expression is better.
Solutions
3QuestionExpanding Single Bracket ExpressionsConcept Practice
6 marks~9 minCriterion A
You are buying 5 packs of juice for a class party. Each pack costs 8 dollars, and the delivery fee is 3 dollars per pack. The total cost can be written as .
a
Calculate the total cost by expanding . Show all your working. [2]
b
Describe what the numbers 8 and 3 inside the brackets represent in this situation. [2]
c
The delivery fee changes to 2 dollars per pack. Write the new expression for the total cost and describe how it is different from . [2]
Solutions
4QuestionCreating Equivalent Expressions through ExpansionAssessment Practice
6 marks~9 minCriterion D
You are tiling a rectangular patio. The width is 5 metres. The length is (x + 3) metres, where x is the length (in metres) of an extension that will be built later.
a
[2 marks] Write an expression for the area of the patio in expanded form.
b
[2 marks] The tiles cost 20 dollars per square metre. Write an expression for the total cost of the tiles in expanded form.
c
[4 marks] Suppose you measure the extension length x with a tape measure that has an accuracy of ±0.1 m. Evaluate the real-world significance and limitations of using the algebraic expression from part (b) to predict the total cost. In your response, discuss how the measurement error affects the reliability of the cost estimate and suggest one way to improve the accuracy of the prediction.
Solutions
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