Syllabus Edition

First teaching 2021

Last exams 2024

|

Geometry Toolkit (CIE IGCSE Maths: Core)

Exam Questions

2 hours56 questions
1
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1 mark

qp3-0580-12-paper-1-nov-2020-cie-igcse-maths

Write down the order of rotational symmetry of this regular octagon.

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2
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2 marks

Write down the mathematical name for this

i)
quadrilateral,
qp3ai-0580-32-paper-3-nov-2020-cie-igcse-maths
[1]
ii)
solid.
qp3aii-0580-32-paper-3-nov-2020-cie-igcse-maths
[1]

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3a
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3 marks

qp4a-0580-11-paper-1-may-2020-cie-igcse-maths

On each shape draw all the lines of symmetry.

3b
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1 mark

qp4b-0580-11-paper-1-may-2020-cie-igcse-maths

Write down the order of rotational symmetry of this shape.

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4
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1 mark

qp9-0580-12-paper-1-may-2020-cie-igcse-maths

Write down the order of rotational symmetry of the diagram.

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5
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2 marks

The diagram shows a regular polygon.

qp7a-0580-33-paper-3-may-2020-cie-igcse-maths

i)
Write down the mathematical name for this shape.
[1]
ii)
Write down the order of rotational symmetry of this shape.
[1]

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6
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2 marks

qp3a-0580-32-paper-3-march-2020-cie-igcse-maths

i)
Write down the mathematical name for this type of angle.
[1]

ii)
Measure this angle.
[1]

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7
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1 mark

qp2-0580-11-paper-1-oct-nov-2019-cie-igcse-maths

Write down the order of rotational symmetry of this regular pentagon.

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8a
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1 mark

qp21-0580-12-paper-1-oct-nov-2019-cie-igcse-maths

The diagram shows some quadrilaterals.

Complete the statements.

Quadrilateral ................. is a rhombus.

8b
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1 mark

Quadrilateral A is a ..........................................

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9
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2 marks

The diagram shows the nets of two solids.

Write down, under each net, the mathematical name for the solid.

q14b-058012-mayjune2019-cie-igcse-maths-core

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10
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1 mark

q3-058012-march2019-cie-igcse-maths-core

Complete the statement.

Angle ...................... is a reflex angle.

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11
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1 mark

q5b-058011-octnov2018-cie-igcse-maths-core

Write down the mathematical name of this polygon.

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12
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1 mark

q1-058012-octnov2018-cie-igcse-maths-core

Write down the type of angle shown in the diagram.

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13
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2 marks

Draw all the lines of symmetry on the rectangle below.

q5a-058032-octnov2018-cie-igcse-maths-core

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14
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2 marks

q7-058013-octnov2018-cie-igcse-maths-core

On the shape, draw all the lines of symmetry.

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15
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1 mark

Shapes A comma space B and C are shown on the 1cm2 grid.

q2a-058033-octnov2018-cie-igcse-maths-core

Shape A is a special type of quadrilateral.

Write down the mathematical name for shape A.

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16
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1 mark

q2-058032-mayjune2018-cie-igcse-maths-core

Write down the mathematical name of the shaded quadrilateral shown on the grid.

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17a
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1 mark

Write down the mathematical name of the type of angle marked.

q6a-058013-mayjune2018-cie-igcse-maths-core

17b
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1 mark

A and B are points on the circumference of a circle, centre O.

q6b-058013-mayjune2018-cie-igcse-maths-core

Write down the mathematical name of the line A B.

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18a
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1 mark

q7-058012-march2018-cie-igcse-maths-core

The diagram shows a regular pentagon and a kite.

Complete the following statements.

The regular pentagon has ................................... lines of symmetry.

18b
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1 mark

The kite has rotational symmetry of order ................................... .

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19
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1 mark

Three quadrilaterals are shown on a 1 cm2 grid.

q2-058033-mayjune2019-cie-igcse-maths-core

Write down the mathematical name of the shaded quadrilateral.

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20
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1 mark

q5a-058011-octnov2018-cie-igcse-maths-core

Measure the radius of the circle, centre O.
Give your answer in centimetres.

............................... cm

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21a
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1 mark

In the space below, draw a circle with diameter 7cm.

21b
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1 mark

On your diagram, draw a chord.

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1a
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1 mark

Write down the mathematical name for

an angle which is less than 90°.

1b
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1 mark

a polygon with 5 sides

1c
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1 mark

a quadrilateral with exactly one pair of parallel sides

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2a
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1 mark

qp2a-0580-32-paper-3-nov-2020-cie-igcse-maths

Measure the length of this line in millimetres.

........................................... mm

2b
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2 marks

qp2b-0580-32-paper-3-nov-2020-cie-igcse-maths

i)
Measure the size of angle x.

[1]

ii)
Write down the mathematical name of this type of angle.
[1]

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3
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2 marks

Write down the order of rotational symmetry of each shape.

qp4-0580-13-paper-1-nov-2020-cie-igcse-maths

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4
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1 mark

The grid shows a point E and four quadrilaterals, A comma space B comma space C and D.

qp2-0580-31-paper-3-may-2020-cie-igcse-maths

Write down the mathematical name of shape A.

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5a
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1 mark

qp2a-0580-12-paper-1-may-2020-cie-igcse-maths

Write down the mathematical name for this type of angle.

5b
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2 marks

qp2b-0580-12-paper-1-may-2020-cie-igcse-maths

A spaceand B lie on a circle, centre O.

i)
Write down the mathematical name for line A B.
[1]
ii)
O A space equals space 8 space cm
Write down the length of the diameter of this circle.
............................................ cm [1]

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6
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3 marks

qp6a-0580-32-paper-3-may-2020-cie-igcse-maths

The diagram shows a cuboid.

On the 1 cm2 grid, complete the net of the cuboid.
One face has been drawn for you.

qp6a-1-0580-32-paper-3-may-2020-cie-igcse-maths

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7
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1 mark

Write down the mathematical name of a quadrilateral that has

  • rotational symmetry of order 1

and

  • only one line of symmetry.

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8a
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1 mark

qp2-0580-12-paper-1-march-2020-cie-igcse-maths

Measure the length of the line A B in millimetres.

.......................................... mm 

8b
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2 marks

A B is the diameter of a circle.

Draw this circle.

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9a
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1 mark

qp6-0580-01-paper-1-specimen-2020-cie-igcse-maths

Write down the order of rotational symmetry of the shape.

9b
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1 mark

Draw all the lines of symmetry on the shape.

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10
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1 mark

The diagram shows the net of a triangular prism on a 1cm2 grid.

qp3-0580-31-paper-3-may-2020-cie-igcse-maths

Write down the mathematical name for the type of triangle shown on the grid.

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11
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2 marks

qp14b-0580-12-paper-1-oct-nov-2019-cie-igcse-maths

Complete the description of this pattern.

The pattern has ................ lines of symmetry

and order of rotational symmetry ................

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12a
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3 marks

On each shape, draw all the lines of symmetry.

i)
q19i-058011-mayjune2019-cie-igcse-maths-core
[1]

ii)

q19ii-058011-mayjune2019-cie-igcse-maths-core

[2]

12b
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1 mark

Write down the name of a quadrilateral that has

  • rotational symmetry of order 2

and

  •  exactly two lines of symmetry.

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13a
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1 mark

Complete each statement.

A quadrilateral with only one pair of parallel sides is called a ...............................................

13b
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1 mark

An angle greater than 90° but less than 180° is called ...............................................

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14
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2 marks

On the 1cm2 grid, complete the net of this box.

q22b-058013-mayjune2019-cie-igcse-maths-core

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15
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1 mark

The diagram shows a net of a solid.

q7-058012-march2019-cie-igcse-maths-core

Write down the mathematical name of the solid.

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16
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1 mark

q23-058012-march2019-cie-igcse-maths-core

The diagram shows a quadrilateral on a 1 cm2 grid.

Write down the mathematical name of this quadrilateral.

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17a
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1 mark

Draw the line of symmetry on the shape below.

q7a-058011-octnov2018-cie-igcse-maths-core

17b
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1 mark

Shade one more square so that this pattern has rotational symmetry of order 2.

q7b-058011-octnov2018-cie-igcse-maths-core

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18
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2 marks

An open box in the shape of a cuboid is 7cm long, 5 cm wide and 4cm high.

Complete the net of the box.
The base of the box has been drawn for you.

q1e-058032-octnov2018-cie-igcse-maths-core

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19a
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1 mark

q9-058033-octnov2018-cie-igcse-maths-core

A comma space B and C are points on the circumference of the circle, centre O.
The straight line D E touches the circle at B.

Write down the mathematical name for the line D E.

19b
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1 mark

On the circle, draw a radius.

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20a
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1 mark

Here is a description of a quadrilateral.

It has 4 right angles.
It has 2 lines of symmetry.
It has rotational symmetry of order 2.

Write down the mathematical name of this quadrilateral.

20b
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2 marks

Write down two geometrical properties of a parallelogram.

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21a
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1 mark

The net of a solid is drawn on a 1cm2 grid.

q21-058011-mayjune2018-cie-igcse-maths-core

Write down the name of the solid made from this net.

21b
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2 marks

Work out the volume of this solid.

............................cm3 

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22a
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1 mark

q4-058031-mayjune2018-cie-igcse-maths-core

The diagram shows a quadrilateral P Q R S which is made from four congruent triangles A, B, C and D.

Write down the mathematical name for the quadrilateral P Q R S

22b
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2 marks
i)
Write down the co-ordinates of S.

[1]

ii)
Measure the obtuse angle P S R.

[1]

22c
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2 marks
i)
Measure the length of the line P Q.

.............................. cm [1]

ii)
Work out the perimeter of the quadrilateral P Q R S.
................................ cm [1]

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23
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2 marks

q9-058031-mayjune2018-cie-igcse-maths-core

A comma space B and C are points on the circumference of a circle, centre O.

Write down the mathematical name for

i)
the straight line A C,
[1]
ii)
the straight line A B.

[1]

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24
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4 marks

Draw all the lines of symmetry on each shape.

q2a-058033-mayjune2018-cie-igcse-maths-core

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1a
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2 marks

qp-5a-0580-0980-w20-oct-nov-2020-cie-igcse-maths

The diagram shows a rhombus

On the diagram, draw all the lines of symmetry

1b
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1 mark

q5b-0580-0980-w20-oct-nov-2020-cie-igcse-maths

Shade two squares so that the diagram has rotational symmetry of order 2.

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2
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3 marks

A cuboid measures 6 cm by 3 cm by 1 cm.

i)
On the 1 cm2 grid, draw an accurate net of this cuboid.
One face has been drawn for you.
qp3di-0580-32-paper-3-nov-2020-cie-igcse-maths
[3]
ii)
Calculate the surface area of the cuboid.
.......................................... cm2 [2]

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3a
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3 marks

A cuboid has length 5 cm, width 4 cm and height 3 cm.

On the 1 cm2 grid, complete the net of the cuboid.
One face has been drawn for you.

qp12a-0580-13-paper-1-nov-2020-cie-igcse-maths

3b
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2 marks

Find the volume of the cuboid.

.......................................... cm3 

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4
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3 marks

The diagram shows the net of a solid on a 1cm2 grid.

qp3b-0580-33-paper-3-may-2020-cie-igcse-maths

i)
Write down the mathematical name for the solid.
[1]
ii)
Work out the volume of the solid.
.......................................... cm3 [2]

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5
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3 marks

A cuboid has length 3 cm, width 2 cm and height 1cm.

On the 1 cm2 grid, draw a net of the cuboid.

qp7-0580-12-paper-1-march-2020-cie-igcse-maths

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6
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3 marks

A cuboid measures 6cm by 3cm by 2 cm.
On this 1cm2 grid, draw a net of the cuboid.

qp5-0580-01-paper-1-specimen-2020-cie-igcse-maths

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7
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1 mark

qp14a-0580-12-paper-1-oct-nov-2019-cie-igcse-maths

Shade two more small squares to give a pattern with exactly one line of symmetry.

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8a
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1 mark

qp20-0580-13-paper-1-oct-nov-2019-cie-igcse-maths

Write down the co-ordinates of point B.

8b
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1 mark

The quadrilateral A B C D hasspace x space equals space 4 as a line of symmetry.

On the grid, plot point D.

8c
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1 mark

Write down the mathematical name of quadrilateral A B C D.

8d
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1 mark

Write down the order of rotational symmetry of quadrilateral A B C D.

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9
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1 mark

Shade two more squares so that this grid has rotational symmetry of order 4.

q7b-058012-mayjune2019-cie-igcse-maths-core

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10a
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1 mark

q8-058012-mayjune2018-cie-igcse-maths-core

For this diagram, write down

the number of lines of symmetry,

10b
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1 mark

the order of rotational symmetry.

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11
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2 marks

q1b-058032-march2018-cie-igcse-maths-core

The diagram shows a net of a cube.

i)
The square labelled B is the base.

Write the letter T in the square that is the top of the cube.

[1]

ii)
On the grid, draw a different net of this cube.
[1]

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