Conversion of Units Length Area Volume
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Conversion of Units Length Area Volume — Free MYP3 Mathematics Practice Questions

1QuestionConverting Area UnitsConcept Practice
2 marks~3 minCriterion A
A rectangle has a length of 4 cm and a width of 3 cm. Each small square on the grid measures 1 cm by 1 cm.
a
Calculate the area of the rectangle in cm2\text{cm}^2. [1]
b
Calculate the area of the rectangle in mm2\text{mm}^2. Show your conversion clearly. [1]
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2QuestionCommon Mistakes in Unit ConversionAssessment Practice
6 marks~9 minCriterion C
A homeowner measures a rectangular room: length 5 m5\ \text{m}, width 4 m4\ \text{m}. The flooring supplier charges per square centimetre. The homeowner calculates the area as 20 m220\ \text{m}^2, then converts it as 20×100=2000 cm220 \times 100 = 2000\ \text{cm}^2 and orders flooring for 2000 cm22000\ \text{cm}^2.
a
Identify the error in the homeowner's unit conversion. [1]
b
Calculate the correct area of the room in cm2\text{cm}^2. [2]
c
The supplier quotes a price based on the homeowner's order of 2000 cm22000\ \text{cm}^2. Analyse how the conversion error affects the total cost, and explain one assumption about the room that could affect the accuracy of the area. [3]
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3QuestionConverting Area UnitsConcept Practice
3 marks~5 minCriterion B
The diagram shows a square with a side length of 1 m1\ \text{m}, divided into a grid of smaller squares each measuring 10 cm×10 cm10\ \text{cm} \times 10\ \text{cm}.
a
Calculate the total number of smaller squares in the grid. [1]
b
Calculate the area of the large square in square centimetres (cm2\text{cm}^2). [1]
c
Explain what your answers to (a) and (b) show about the conversion factor between square metres and square centimetres. [1]
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4QuestionConverting Between Metric Length UnitsAssessment Practice
6 marks~9 minCriterion D
An architect creates a scale model of a building using a scale of 1:2001 : 200, where 1 cm1\ \text{cm} on the model represents 2 m2\ \text{m} in reality. A wall on the model measures 12.5 cm12.5\ \text{cm}. Construction workers measure to the nearest centimetre.
a
Calculate the real length of the wall in metres. [2]
b
Explain why rounding the real length to the nearest whole metre would cause problems for construction workers. [2]
c
The architect considers rounding the real length to the nearest centimetre instead. Analyse whether this is a more suitable level of precision for construction, given the limitations of the scale model. [2]
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