CAIE IGCSE Mathematics 6. Topic 6 Question Bank

Practise triangle geometry using Pythagoras, trigonometric ratios, exact values, graphs and non-right-angled triangle methods.

Covered syllabus points

C6.1 Pythagoras’ theorem C6.2 Right-angled triangles

[Maximum number: 5]

Figure for Question 6. Trigonometry question 1 — CAIE IGCSE Mathematics Core

NOT TO SCALE

An isosceles triangle has base 12 cm and sides 16 cm. Find the area of this triangle.
$\mathrm{cm}^2$

The height is
$\sqrt{16^2-\left(\frac{12}{2}\right)^2}=\sqrt{220}.$
Hence the area is
$\frac12\times12\times\sqrt{220}=6\sqrt{220}=89.0\ \mathrm{cm^2}\ \text{(approximately)}.$

[Maximum number: 6]

The diagram shows a circle, centre O, radius 11 cm. C, F, G and H are points on the circumference of the circle.
The line AD touches the circle at C and is parallel to the line EG. B is a point on AD and angle $A B O=140^{\circ}$ .

(a)

Show that $BC=13.11\text{ cm}$ , correct to 2 decimal places.

[ 3 ]

180-140 or 90- their (b)(ii)
$\tan(180-140)=\frac{11}{BC}$ oe
$[BC=]13.109\ldots$

(b)

Calculate BH.

BH= ___ cm

[ 3 ]

6.11 or 6.112 to 6.114
M1 for $OB^{2}=13.11^{2}+11^{2}$ .
A1 for 17.1 or 17.11 or 17.112 to 17.114.
OR
M1 for $\frac{11}{\sin40}$ oe.
A1 for 17.1 or 17.11... or 17.112 to 17.113.

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Covered syllabus points

6. Trigonometry question 1

6. Trigonometry question 2

Question (a)

Question (b)