EduNinja

[Maximum number: 5]

NOT TO SCALE

The diagram shows triangle ABC on horizontal ground.
$A C=15 \mathrm{~m}, B C=8 \mathrm{~m}$ and $A B=20 \mathrm{~m}$ .
BP and CQ are vertical poles of different heights.
$B P=3 \mathrm{~m}$ and $C Q=4 \mathrm{~m}$ .
AQ and PQ are straight wires.

Another straight wire connects A to the midpoint of PQ.

Calculate the angle between this wire and the horizontal ground.

11.5 nfww or 11.48 to 11.49...
B1 for height 3.5
M2 for $15^2+4^2-2\times15\times4\cos117.5^\circ$
M1 for $\tan=\frac{3.5}{\text{their }17.216...}$ oe

[Maximum number: 4]

The diagram shows a prism, ABCDEF.
$A B=13 \mathrm{~cm}, A C=20 \mathrm{~cm}, C F=24 \mathrm{~cm}$ and angle $A B C=90^{\circ}$ .

Calculate the angle that AF makes with the base BCFE.

24.6 or 24.58 to 24.59

4

M3 for $\sin [\ldots]=\frac{13}{\sqrt{20^{2}+24^{2}}}$ oe

or M2 for $\sqrt{20^{2}+24^{2}}$ or $\sqrt{24^{2}+20^{2}-13^{2}}$

or M1 for $A F^{2}=20^{2}+24^{2}$ or $24^{2}+20^{2}-13^{2}$

or M1 for correct angle identified

[Maximum number: 3]

Figure for Question 3 — CAIE IGCSE Mathematics Extended

The diagram shows a prism with a rectangular base, ABFE. The cross-section, ABCD, is a trapezium with A D=B C. $A B=8 \mathrm{~cm}, G H=5 \mathrm{~cm}, B F=12 \mathrm{~cm}$ and angle $A B C=70^{\circ}$ .

(a)

The perpendicular from G onto EF meets EF at X.

[ 3 ]

(i)

Show that $E X=6.5 \mathrm{~cm}$ .

[ 1 ]

$8-\frac12(8-5)$ or $5+\frac12(8-5)$

(ii)

Calculate the angle between the diagonal AG and the base ABFE.

[ 2 ]

CAIE IGCSE Mathematics Extended E6.6 Pythagoras Theorem and Trigonometry Topic Practice

Question 1

Question 2

Question 3

Question (a)

Question (i)

Question (ii)