Geometry – Measurement & Calculation — Free IB MYP2 Mathematics Questions

1QuestionSolving Surface Area Problems in ContextConcept Practice

2 marks~3 minCriterion A

The net of a cuboid is shown below. Three faces are labelled with their dimensions.

Dimensions given:
- Front face:

6 \, \text{cm}

wide,

3 \, \text{cm}

tall
- Top face:

6 \, \text{cm}

long,

4 \, \text{cm}

wide
- Left side face:

4 \, \text{cm}

wide,

3 \, \text{cm}

tall

a

Identify the width of the back face of the cuboid. [1]

b

Explain how you know the back face and front face must have the same dimensions. [1]

Solutions

2QuestionIntroduction to Volume of CylindersConcept Practice

2 marks~3 minCriterion A

A cylinder has a diameter of 10 cm and a height of 8 cm.

a

Identify the radius of the cylinder. [1]

b

Calculate the volume of the cylinder using

V = \pi r^2 h

. [1]

Solutions

3QuestionArea and Perimeter of Compound ShapesConcept Practice

2 marks~3 minCriterion A

The diagram shows a compound shape made from two rectangles joined side by side. The left rectangle has a top side of

5

cm and a height of

3

cm. The right rectangle has a top side of

4

cm and a height of

3

cm. The bottom side of the left rectangle is marked with a question mark.

a

Identify the missing side length. [1]

b

Explain the geometric property that allows you to find it. [1]

Solutions

4QuestionCreating and Interpreting Scale DiagramsConcept Practice

2 marks~3 minCriterion A

A map shows a line of

5

cm representing a real distance of

50

m.

a

Identify the map distance and the real distance in the same unit. [1]

b

Calculate the scale of the map. Express your answer as a ratio in the form

1 : n

, showing all working. [1]

Solutions

5QuestionConverting Area UnitsConcept Practice

2 marks~3 minCriterion A

A rectangle has a length of 300 cm and a width of 40 cm.

a

Calculate the area of the rectangle in square centimetres (cm²). Use the formula

\text{Area} = \text{length} \times \text{width}

. [1]

b

Convert your answer to square metres (m²). Use the conversion factor

1 \text{ m}^2 = 10\,000 \text{ cm}^2

. [1]

Solutions

6QuestionUsing Unit Conversion in Word ProblemsConcept Practice

3 marks~5 minCriterion B

The graph shows the relationship between the side length and area of squares.

Points on the graph:

(1, 1)

,

(2, 4)

,

(3, 9)

,

(4, 16)

.

a

Identify the shape of the graph. [1]

b

Explain why the area of a square with side length

3 \text{ cm}

is

9 \text{ cm}^2

. [1]

c

Compare how quickly the area grows for small side lengths versus large side lengths, using values from the graph. [1]

Solutions

7QuestionArea of Rectangles Triangles and ParallelogramsConcept Practice

3 marks~5 minCriterion A

The diagram shows a rectangle divided into triangle A, parallelogram P, and triangle B. The rectangle has length 10 cm and height 6 cm. Triangles A and B each have base 5 cm and height 6 cm. Parallelogram P has base 5 cm and height 6 cm.

a

Calculate the areas of triangle A and triangle B. [1]

b

Calculate the area of parallelogram P. [1]

c

Describe the relationship between the area of the rectangle and the areas of triangle A, parallelogram P, and triangle B combined. [1]

Solutions

8QuestionSurface Area of a Rectangular PrismAssessment Practice

6 marks~9 minCriterion C

A student calculates the surface area of a rectangular prism (

l = 8

cm,

w = 5

cm,

h = 3

cm) as shown:

SA = 2(8 \times 5) + 2(5 \times 3) = 80 + 30 = 110 \text{ cm}^2

a

Identify the missing term in the student's calculation. [1]

b

Explain why the formula

SA = 2lw + 2lh + 2wh

accounts for all six faces of the prism. Use the net diagram provided to support your answer. [2]

c

Calculate the correct surface area. Show each step clearly. [3]

Solutions

9QuestionUnderstanding Surface Area ConceptuallyAssessment Practice

3 marks~5 minCriterion B

The graph shows the surface area of a cube with side length

s

(cm), using the formula

SA = 6s^2

.

a

Identify the shape of the graph. [1]

b

Explain why the surface area increases faster than the side length. [1]

c

Compare the surface area when

s = 2

cm and when

s = 4

cm. What does this tell you about how surface area grows? [1]

Solutions

10QuestionSolving Surface Area Problems in ContextAssessment Practice

4 marks~6 minCriterion D

A student wants to wrap a gift box shaped like a rectangular prism with these dimensions:

Length

(l)

: 20 cm, Width

(w)

: 15 cm, Height

(h)

: 10 cm

The surface area formula is:

S = 2(lw + lh + wh)

a

Calculate the surface area of the box. Show all working. [2]

b

Identify and explain two limitations of using this formula to estimate the amount of wrapping paper needed. In your answer, state one assumption the formula makes about the shape of the box. [2]

Solutions

11QuestionVolume of a CubeAssessment Practice

3 marks~5 minCriterion B

The table shows the volume of cubes with different edge lengths.

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

a

Identify the relationship between the edge length

s

and the volume

V

of a cube. [1]

b

Calculate the volume of a cube with an edge length of 5 cm. [1]

c

A second cube has a volume of 64 cm³ and a third cube has a volume of 125 cm³. Compare the edge lengths of these two cubes. [1]

Solutions

12QuestionIntroduction to Volume of CylindersAssessment Practice

3 marks~5 minCriterion C

A cylinder has a fixed height of 5 cm. Its volume is given by

V = \pi r^2 h

where

r

is the radius and

h

is the height.

a

Identify the part of the formula that shows volume is not directly proportional to the radius. [1]

b

Explain why the graph of

V

against

r

is a curve rather than a straight line. [1]

c

Two cylinders both have height 5 cm. Cylinder A has radius 2 cm and Cylinder B has radius 4 cm. The radius of B is twice the radius of A. Compare the volumes and explain why the volume of B is not simply twice the volume of A. [1]

Solutions

13QuestionIntroduction to Volume of CylindersAssessment Practice

4 marks~6 minCriterion D

A paint factory fills cylindrical cans using the formula

V = \pi r^2 h

Each can has a radius of 7 cm and a height of 20 cm. Use

\pi \approx \dfrac{22}{7}

.

a

Calculate the volume of one can. [1]

b

Each can is filled to only 90% of its full capacity. Calculate the volume of paint in one can. [1]

c

Explain whether the formula overestimates or underestimates the actual volume of paint in the can, and identify one real-world reason why leaving an air gap is necessary. [2]

Solutions

14QuestionArea and Perimeter of Compound ShapesAssessment Practice

6 marks~9 minCriterion B

The table shows the perimeters of L-shaped figures made from unit squares.

Figure number	1	2	3
Arm length (units)	2	3	4
Perimeter (units)	8	12	16

a

State the perimeter of Figure 4. [1]

b

Calculate the perimeter of Figure 10. Show your working. [2]

c

Write a formula for the perimeter

P

of Figure

n

. Use your formula to find

P

when the arm length is 15 units, and explain why your answer is correct by breaking the L-shape into two rectangles and accounting for any shared sides. [3]

Solutions

15QuestionDrawing and Interpreting Nets of 3D ShapesAssessment Practice

6 marks~9 minCriterion C

A cereal company makes a cardboard box that is a cuboid measuring 30 cm × 20 cm × 10 cm. When the flat net is folded and glued, each joined edge has a flap (a narrow strip used for gluing) that is 1 cm wide.

a

Calculate the total surface area of the cuboid. [2]

b

A cuboid net has 7 flaps. Calculate the total area of the flaps in cm². [2]

c

The company claims the net's total area (surface area + flap area) equals the exact amount of cardboard used. Compare this claim with what actually happens when the box is assembled. [2]

Solutions

16QuestionArea and Perimeter of Compound ShapesAssessment Practice

6 marks~9 minCriterion D

A gardener plans a flower bed made of a rectangle (length 8 m, width 5 m) with a semicircle (radius 2.5 m) attached to one shorter side.

a

Calculate the total area of the flower bed. [2]

b

Describe two ways the real garden soil could make the gardener's calculated area inaccurate. [2]

c

The gardener also needs to fence the entire boundary of the flower bed. Calculate the total length of fencing required. [2]

Solutions

17QuestionReading Bearings and Compass DirectionsAssessment Practice

4 marks~6 minCriterion C

A bearing is an angle measured clockwise from north, written as a three-digit number from

000°

to

360°

.

A student says a ship is at a bearing of

135°

from a lighthouse. The angle measured clockwise from the north line to the ship is

45°

.

a

State the correct three-digit bearing for an angle of

45°

clockwise from north. [1]

b

On the diagram, mark and label the north line, the

45°

angle, and the direction of the ship from the lighthouse. Use your diagram to explain why the student's bearing is incorrect. [2]

c

A bearing of

135°

places a ship in the southeast direction. Compare this position with the actual position of the ship, and explain the difference. [1]

Solutions

18QuestionUnderstanding Scale in Maps and BlueprintsAssessment Practice

4 marks~6 minCriterion D

A student measures a classroom floor: length

6.2

m, width

4.8

m. She draws a floor plan at a scale of

1:50

using a ruler with a precision of

\pm 0.5

mm (

\pm 0.05

cm).

a

Calculate the scale dimensions (in cm) of the floor plan. [1]

b

Explain how the ruler's precision creates a range of possible areas for the floor plan. Use the minimum and maximum possible scale dimensions in your answer. [2]

c

Identify one limitation of using this floor plan to order carpet for the classroom. [1]

Solutions

19QuestionMeasuring Bearings with a ProtractorAssessment Practice

8 marks~12 minCriterion B

The diagram shows five rays from point O to towns A, B, C, D, and E. Town A has a bearing of

0°

from O (due north). Town E has a bearing of

180°

from O (due south).

A (°):

0

(given) — B (°): ___ — C (°): ___ — D (°): ___ — E (°):

180

(given)

a

Measure and record the bearings of towns B, C, and D from point O. [3]

b

Describe the pattern in the bearings of towns A, B, C, D, and E. Use the pattern to calculate the bearing of town C without measuring. [3]

c

Compare your measured bearing of town C with your calculated value. Explain one reason why the two values might differ. [2]

Solutions

20QuestionCommon Mistakes in Unit ConversionAssessment Practice

3 marks~5 minCriterion C

The graph shows the area of a square,

A = s^2

, where

s

is the side length in metres and

A

is the area in square metres.

A student claims that to convert an area from square metres to square centimetres, you multiply by 100. (Recall:

1 \text{ m} = 100 \text{ cm}

.)

a

State the correct number of square centimetres in

1 \text{ m}^2

. [1]

b

Explain why multiplying by 100 works for length but not for area. [1]

c

Using the graph, compare the student's answer with the correct area in square centimetres for a square with side length

1 \text{ m}

. [1]

Solutions

21QuestionConverting Area UnitsAssessment Practice

4 marks~6 minCriterion D

A homeowner uses a 1:100 scale drawing of a rectangular floor. On the plan, the floor measures 8.5 cm by 6.2 cm. The actual floor has a small outward bulge (a curved section that pushes beyond the straight wall) along one of the longer walls.

a

Calculate the area of the floor shown on the plan in cm². [1]

b

Calculate the real floor area in m², using the scale 1:100. [2]

c

Explain why using the rectangular model may lead to the homeowner ordering too few tiles. [1]

Solutions

22QuestionFinding Perimeter of Irregular ShapesAssessment Practice

5 marks~8 minCriterion C

An L-shaped figure is formed by joining a vertical rectangle (width

3

cm, height

8

cm) to a horizontal rectangle (width

6

cm, height

3

cm), as shown.

A student calculates the perimeter by adding all sides of both rectangles separately:

3 + 8 + 6 + 3 + 3 + 8 + 6 + 3 = 38

cm.

a

Identify the six outer side lengths of the L-shaped figure. [1]

b

Calculate the correct perimeter of the L-shaped figure. Show your working. [2]

c

Explain why the student's method gives the wrong answer. [2]

Solutions

23QuestionFinding Perimeter of Irregular ShapesAssessment Practice

12 marks~18 minCriterion B

The perimeters of the first three L-shaped polygons in a sequence are 12 cm, 16 cm, and 20 cm. Each grid square has a side length of 1 cm.

a

Identify the pattern in the perimeters and state the perimeter of the 4th and 5th shapes. [2]

b

On the grid provided, draw the 5th shape. Explain how your drawing follows the same pattern as the first three shapes. [4]

c

Calculate the perimeter of your 5th shape by adding each side length. Compare this value with your prediction from part (a). [6]

Solutions

24QuestionArea of Trapeziums and Compound ShapesAssessment Practice

4 marks~6 minCriterion D

A farmer has a field shaped like a trapezium (a quadrilateral with one pair of parallel sides). The parallel sides measure 80 m and 120 m, and the perpendicular height is 50 m. One non-parallel side curves slightly outward, making the true area larger than the trapezium model suggests.

\text{Area of trapezium} = \frac{1}{2} \times (b_1 + b_2) \times h

where

b_1

and

b_2

are the parallel sides and

h

is the perpendicular height.

a

Calculate the area of the field using the formula above. Show your working. [2]

b

Explain whether the trapezium formula overestimates or underestimates the true area of this field, and identify one real-world limitation of using a straight-sided shape to model a field with a curved boundary. [2]

Solutions

Geometry – Measurement & Calculation — Free MYP2 Mathematics Practice Questions