Geometry — Free IB MYP1 Mathematics Questions

1QuestionSolving Surface Area Problems in ContextConcept Practice

3 marks~5 minCriterion C

A student worked out the surface area of a cuboid with dimensions 3 cm, 4 cm, and 5 cm:

\text{Area} = 3 \times 4 + 4 \times 5 + 3 \times 5 = 12 + 20 + 15 = 47 \text{ cm}^2

a

Identify the error the student made. [1]

b

Describe why a cuboid has more than three faces to consider. [1]

c

Calculate the correct total surface area of the cuboid. [1]

Solutions

2QuestionSolving Surface Area Problems in ContextConcept Practice

2 marks~3 minCriterion A

The net of a cube is shown below. One edge is labeled 4 cm and another edge is labeled

x

.

a

State what is true about the lengths of all edges of a cube. [1]

b

Write down the value of

x

in centimeters. [1]

Solutions

3QuestionUnderstanding Surface Area ConceptuallyConcept Practice

3 marks~5 minCriterion B

The bar graph shows the surface area of four cubes with side lengths of 1 cm, 2 cm, 3 cm, and 4 cm.

a

Identify which cube has the greatest surface area. [1]

b

Describe what happens to the surface area as the side length increases. [1]

c

Calculate the surface area of a cube with a side length of 5 cm using

SA = 6s^2

. [1]

Solutions

4QuestionVolume of a CubeConcept Practice

2 marks~3 minCriterion B

A cube has a side length of 5 cm.

Side length (cm)	1	2	3	4
Volume (cm³)	1	8	27	64

a

Calculate the volume of the cube with side length 5 cm. [1]

b

Describe the relationship between the side length and the volume of a cube. [1]

Solutions

5QuestionIntroduction to Volume of CylindersConcept Practice

2 marks~3 minCriterion D

A farmer has a cylindrical water tank she uses for irrigation.

a

State one way the farmer could use the formula

V = \pi r^2 h

when planning her irrigation. [1]

b

Describe one assumption the farmer must make for this formula to give an accurate result. [1]

Solutions

6QuestionIntroduction to Volume of CylindersConcept Practice

2 marks~3 minCriterion A

The diagram shows a cylinder with two measurements labelled A and B. Measurement A goes from the centre of the circular face to its edge. Measurement B goes from one circular face to the other.

a

Identify which measurement shows the radius of the cylinder. [1]

b

Describe in one sentence what the height of a cylinder means, and state which measurement shows it. [1]

Solutions

7QuestionCreating and Interpreting Scale DiagramsConcept Practice

3 marks~5 minCriterion A

A scale diagram shows a rectangular garden. The diagram length is 4 cm and the diagram width is 3 cm. The actual length of the garden is 8 m.

a

Identify the scale of the diagram. [1]

b

Describe how you use the scale to find the actual width of the garden. [1]

c

Calculate the actual width of the garden in metres. [1]

Solutions

8QuestionUnderstanding Scale in Maps and BlueprintsConcept Practice

5 marks~8 minCriterion B

A bedroom wall measures 85 cm in real life. An architect draws the same wall at four different scales.

Scale:

1:10

,

1:20

,

1:50

,

1:100

Plan length (cm):

8.5

,

4.25

,

1.7

,

0.85

a

Calculate the actual length of the wall for each scale. Show your working. [2]

b

Describe what happens to the actual length as the scale changes. [2]

c

The architect draws the same wall at scale

1:200

. The plan length is

0.425

cm. State the actual length of the wall. [1]

Solutions

9QuestionCreating and Interpreting Scale DiagramsConcept Practice

2 marks~3 minCriterion D

A tourist map of a park has a scale of

1 \text{ cm} = 10 \text{ m}

. The distance between the playground and the pond on the map measures

4 \text{ cm}

.

a

Calculate the actual distance between the playground and the pond in metres. [1]

b

Identify one reason why the actual walking distance might be longer than your answer to part (a). [1]

Solutions

10QuestionCreating and Interpreting Scale DiagramsConcept Practice

2 marks~3 minCriterion A

A map uses a scale where 1 cm represents 5 m in real life. Two trees are 4 cm apart on the map.

a

State the scale of this map. [1]

b

Calculate the real distance between the two trees in metres. [1]

Solutions

11QuestionCommon Mistakes in Unit ConversionConcept Practice

3 marks~5 minCriterion C

A student works out the area of a rectangular garden that is 3 m long and 40 cm wide. They write:

3 \times 40 = 120

.

a

Identify the mistake the student made. [1]

b

Describe how to fix the mistake before calculating the area. [1]

c

Calculate the correct area of the garden in m². [1]

Solutions

12QuestionConverting Between Metric Length UnitsConcept Practice

2 marks~3 minCriterion B

The table below shows lengths in metres and centimetres.

Metres (m)	0.1	0.2	0.3	0.4
Centimetres (cm)	10	20	30	40

a

Identify the pattern between the metres column and the centimetres column. [1]

b

Describe, in one sentence, the rule you would use to convert any length in metres into centimetres. [1]

Solutions

13QuestionCommon Mistakes in Unit ConversionConcept Practice

2 marks~3 minCriterion A

A rectangle has a length of 45 mm and a width of 3 cm.

a

Calculate the length in centimetres. [1]

b

Calculate the area of the rectangle in square centimetres (

\text{cm}^2

). Show your working. [1]

Solutions

14QuestionConverting Between Metric Length UnitsConcept Practice

2 marks~3 minCriterion D

A carpenter measures a table top as

1.5

m long. The design plan needs the length in centimetres. (

1

m

= 100

cm)

a

Calculate the length of the table top in centimetres. [1]

b

Identify one problem that could happen if the carpenter uses

1.5

m instead of the correct length in centimetres. [1]

Solutions

15QuestionArea of Rectangles Triangles and ParallelogramsConcept Practice

6 marks~9 minCriterion C

A garden patio is made up of two rectangles and a right triangle.

Rectangle A:

6 \text{ cm} \times 8 \text{ cm}

Rectangle B:

4 \text{ cm} \times 5 \text{ cm}

Right triangle: base

4 \text{ cm}

, height

3 \text{ cm}

a

State the formula used to find the area of a rectangle. [1]

b

Calculate the area of each shape. Show your working. [3]

c

A classmate says: "The total area is exactly 84 cm²." Describe whether your classmate is correct, and explain how you know. [2]

Solutions

16QuestionArea of Trapeziums and Compound ShapesConcept Practice

2 marks~3 minCriterion A

A trapezium has parallel sides of 8 cm and 12 cm. Its area is 50 cm².

Using

A = \frac{1}{2}(a + b)h

, calculate the height

h

of the trapezium. [2]

Solutions

17QuestionArea of Rectangles Triangles and ParallelogramsConcept Practice

4 marks~6 minCriterion B

A rectangle has a length of 10 cm. The table shows its area for different widths.

Width (cm)	1	2	3	4	5
Area (cm²)	10	20	30	40	50

a

Identify the area when the width is 3 cm. [1]

b

Describe what happens to the area as the width increases. [1]

c

A second rectangle also has a length of 10 cm. Its width is 4 cm. A third rectangle has the same length but a width of 8 cm. Compare the areas of these two rectangles. [2]

Solutions

18QuestionSurface Area of a Rectangular PrismAssessment Practice

2 marks~3 minCriterion D

A toy company wraps gift boxes shaped like rectangular prisms. Each box measures 20 cm by 15 cm by 10 cm, giving a surface area of

1300 \text{ cm}^2

.

Describe one reason why the actual amount of wrapping paper used could be more than

1300 \text{ cm}^2

. [2]

Solutions

19QuestionVolume of a Rectangular PrismAssessment Practice

5 marks~8 minCriterion C

A storage box has a length of 4 cm, a width of 3 cm, and a height of 5 cm.

a

Calculate the volume of the box. [1]

b

A new box is made with double the length and double the width, but the same height. Calculate the volume of the new box. [2]

c

A student says: "Doubling the length and width also doubles the volume." Describe whether the student is correct, using your two answers. [2]

Solutions

20QuestionFinding Perimeter of Irregular ShapesAssessment Practice

4 marks~6 minCriterion D

A student traces around the edge of a garden bed with a piece of string, then stretches the string out and measures it with a ruler.

a

State whether this method gives the exact perimeter or an approximation. [1]

b

Describe one reason why the measurement might not be perfectly accurate. [1]

c

The student now tries the same method on a very large garden and then on a very small garden. Describe one problem with using string for each size, and explain how each problem affects the accuracy of the measurement. [2]

Solutions

Geometry — Free MYP1 Mathematics Practice Questions