Edexcel IGCSE Math A 4 geometry and trigonometry

Use this Geometry and Trigonometry hub to move from angle reasoning and shape properties into area, volume, similarity, vectors and trigonometry.

Covered syllabus points

4.1 Angles, lines and triangles 4.2 Polygons 4.3 Symmetry 4.4 Measures 4.5 Construction 4.6 Circle properties 4.7 Geometrical reasoning 4.8 Trigonometry and Pythagoras’ theorem 4.9 Mensuration of 2D shapes 4.10 3D shapes and volume 4.11 Similarity

[Maximum number: 3]

Two circles, $C_{1}$ and $C_{2}$ , are drawn on a centimetre grid, with a scale of 1 cm for 1 unit on each axis.

The centre of circle $C_{1}$ is at the point with coordinates (-1,3) and the radius of $C_{1}$ is 13 cm.

The centre of circle $C_{2}$ is at the point with coordinates (7,18) and the radius of $C_{2}$ is 6 cm.

Work out the distance between the centre of $C_{1}$ and the centre of $C_{2}$

$(18-3)^2+(7-(-1))^2=15^2+8^2=289$ $\sqrt{289}=17$
Final answer:
17

[Maximum number: 4]

4 A B C and DEF are similar triangles.

Figure for Question 4 Geometry and trigonometry question 2 — Edexcel IGCSE Math A Higher

Diagram NOT accurately drawn

(a)

Work out the length of DE. cm

The area of triangle DEF is $525 \mathrm{~cm}^{2}$

[ 2 ]

$40\div16\times12=30$

Final answer:
30

(b)

Find the area of triangle DEF in $\mathrm{m}^{2}$ $\mathrm{m}^{2}$

[ 2 ]

$525\div100^2=0.0525$

Final answer:
0.0525

Accept:
$5.25\times10^{-2}$

[Maximum number: 3]

Figure for Question 4 Geometry and trigonometry question 3 — Edexcel IGCSE Math A Higher

Diagram NOT accurately drawn
ACE and BCD are straight lines.
AB is parallel to DE
Work out the value of x

Scale factor:
$6\div1.2=5$

Corresponding sides:
5(2x)=2x+910x=2x+98x=9

Final answer:
$x=\frac98$

Accept 1.125, 1.12, or 1.13.

[Maximum number: 6]

Figure for Question 4 Geometry and trigonometry question 4 — Edexcel IGCSE Math A Higher

L, M, N and P are points on a circle, centre O
Angle $M N P=58^{\circ}$

(a)

Find the size of angle MLP

[ 2 ]

(b)

Give a reason for your answer.

[ 2 ]

Reason:

Opposite angles in a cyclic quadrilateral sum to $180^\circ$ .

B1, dep on a correct answer or correct method seen for part (a)(i).

(c)

Find the size of the reflex angle MOP

[ 2 ]

$360-2\times58$
OR
$2\times122$

Final answer:
244

Marking guidance:
- M1 ft from part (a)
- A1 for 244

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Covered syllabus points

4 Geometry and trigonometry question 1

4 Geometry and trigonometry question 2

Question (a)

Question (b)

4 Geometry and trigonometry question 3

4 Geometry and trigonometry question 4

Question (a)

Question (b)

Question (c)