CAIE IGCSE Mathematics Extended 6 Trigonometry

Covered syllabus points

E6.1 Pythagoras’ theorem E6.2 Right-angled triangles E6.3 Exact trigonometric values E6.4 Trigonometric functions E6.5 Non-right-angled triangles E6.6 Pythagoras’ theorem and trigonometry

[Maximum number: 9]

The quadrilateral ACDE is formed by two right-angled triangles ABE and BCD. $A C=17 \mathrm{~cm}, A E=18 \mathrm{~cm}$ and $B D=6 \mathrm{~cm}$ .

(a)

Show that $C D=10 \mathrm{~cm}$ .

[ 5 ]

$\frac{AB}{18}=\cos60^\circ$ or $AB=18\cos60^\circ$ $\cos60^\circ=\frac{1}{2}$ and AB=9
Correct use of Pythagoras' theorem, i.e. $CD^2=6^2+(17-\text{their }AB)^2$ oe
Correct evaluation for their AB: $CD^2=36+64$ or $CD=\sqrt{36+64}$ 100=10

(b)

Find the perimeter of the quadrilateral ACDE.

Give your answer in the form $p+k \sqrt{q}$ .

[ 4 ]

$39+9\sqrt{3}$
B3 for $BE=9\sqrt{3}$ or for answer equivalent to $39+9\sqrt{3}$ but not in required form
OR M2 for $\frac{BE}{18}=\frac{\sqrt3}{2}$ oe or better
or M1 for $\frac{BE}{18}=\sin60^\circ$ oe or better
M1 for 18+17+10+ their BE-6 oe
M2 for $\sqrt{18^2-\text{their }9^2}$ oe
or M1 for $BE^2+(\text{their }9)^2=18^2$ oe

[Maximum number: 16]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Extended

NOT TO
SCALE

The diagram shows a right-angled triangle PQR on horizontal ground. X is vertically above R and the angle of elevation of X from P is $21^{\circ}$ . $X R=2.8 \mathrm{~m}$ and $R Q=7.1 \mathrm{~m}$ .

[ 5 ]

(i)

Calculate the angle of elevation of X from Q.

[ 2 ]

21.5 or 21.52...
M1 for $\tan(\ldots)=\frac{2.8}{7.1}$ oe

(ii)

Calculate PQ.

[ 3 ]

10.2 or 10.17 to 10.18
M2 for $\left(\frac{2.8}{\tan21}\right)^2+7.1^2$ oe
or M1 for $\frac{2.8}{PR}=\tan21$ oe

(b)

Calculate the acute angle KML.

[ 3 ]

76.5 or 76.52 to 76.53
M2 for $\sin M=\frac{16.7\sin32}{9.1}$ oe
or M1 for $\frac{9.1}{\sin32}=\frac{16.7}{\sin M}$ oe

(c)

Figure for Question (c) — CAIE IGCSE Mathematics Extended

The area of triangle ABC is $62.89 \mathrm{~cm}^{2}$ .

[ 8 ]

(i)

Show that angle B A C=28.4^, correct to 1 decimal place.

[ 2 ]

$\frac12\times12.3\times21.5\times\sin(\ldots)=62.89$ or better
28.40 to 28.41...

(ii)

Calculate BC.
cm

[ 3 ]

12.2 or 12.17 to 12.18
M2 for $\sqrt{12.3^2+21.5^2-2\times12.3\times21.5\times\cos28.4}$
OR M1 for $12.3^2+21.5^2-2\times12.3\times21.5\times\cos28.4$
A1 for 148 or 148.2 to 148.3

(iii)

AB is extended to a point D such that angle B D C=90^.

Calculate BD.
cm

[ 3 ]

6.6[0] to 6.62
M2 for $21.5\cos28.4-12.3$
or M1 for $21.5\cos28.4$

[Maximum number: 4]

(a)

On the axes, sketch the graph of $y=\cos x$ , for $0^\circ\leqslant x\leqslant360^\circ$ .

[ 2 ]

(b)

Solve the equation $\cos x=0.294$ for $0^\circ\leqslant x\leqslant360^\circ$ .
$x=\quad\text{or}\quad x=$

[ 2 ]

All question bank results loaded

CAIE IGCSE Mathematics Extended 6 Trigonometry Topic Practice

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question (c)

Question (i)

Question (ii)

Question (iii)

Question 3

Question (a)

Question (b)