CAIE IGCSE Mathematics Core 6 Trigonometry

Covered syllabus points

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

[Maximum number: 3]

Figure for Question 1 — CAIE IGCSE Mathematics Core

The diagram shows a circle, centre O, with diameter PQ. R is a point on the circumference.

Calculate the length of PQ.

P Q=

cm [3]

7.31 or 7.310 to 7.311

M2 for $\frac{6.2}{\cos32^\circ}$ oe.
M1 for $\frac{6.2}{PQ}$ oe.

[Maximum number: 7]

(a)

NOT TO SCALE

ABC is a right-angled triangle.

Calculate BC.
$BC=\quad\mathrm{cm}$

[ 3 ]

8.4
M2 for $9.1^2-3.5^2$ oe or better
or M1 for $BC^2+3.5^2=9.1^2$ oe or better

(b)

$\triangle E F$ is a right-angled triangle.

Calculate EF.

E F=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . . c m ~[2]

[ 2 ]

6.88 to 6.881

2

M1 for $\cos 35=\frac{[\ldots]}{8.4}$ oe or better
or $\sin 55=\frac{[\ldots]}{8.4}$ oe or better

(c)

JKL is a right-angled triangle.

NOT TO SCALE

Calculate angle JKL.

[ 2 ]

$51.3[4 \ldots]$

2

M1 for $\tan [\ldots=] \frac{10}{8}$ oe or better

[Maximum number: 4]

Figure for Question 3 — CAIE IGCSE Mathematics Core

The diagram shows two right-angled triangles, ABC and ACD.
Work out the value of x.

60 cao
M3 for $39^2+52^2-25^2=x^2$ oe
or M2 for $39^2+52^2=25^2+x^2$ oe
or M1 for a correct Pythagoras expression

[Maximum number: 3]

Figure for Question 4 — CAIE IGCSE Mathematics Core

A ladder of length 5.6 m rests against a vertical wall.
The bottom of the ladder is 1.5 m from the bottom of the wall, on horizontal ground.
Calculate the distance from the top of the ladder to the base of the wall.
m [3]

5.4[0] or 5.395...

M2 for $5.6^2-1.5^2$ oe.
M1 for $5.6^2=(\ldots)^2+1.5^2$ oe.

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CAIE IGCSE Mathematics Core 6 Trigonometry Topic Practice

Covered syllabus points

Question 1

Question 2

Question (a)

Question (b)

Question (c)

Question 3

Question 4