CAIE IGCSE Mathematics Extended E6.6 Pythag…metry

Covered syllabus points

E6.6.1 in 3D Carry out calculations and solve problems in three dimensions

[Maximum number: 6]

Figure for Question 1 — CAIE IGCSE Mathematics Extended

\section*{NOT TO SCALE}

The diagram shows a cuboid ABCDEFGH. $A E=6.4 \mathrm{~cm}, E H=5.1 \mathrm{~cm}$ and $A G=13 \mathrm{~cm}$ .

(a)

Calculate EF.

E F=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . . . c m ~[3]

[ 3 ]

10.1 or 10.10...

M2 for $E F^{2}+6.4^{2}+5.1^{2}=13^{2}$ or better
or M1 for $6.4^{2}+5.1^{2}$ or $13^{2}-6.4^{2}$ or $13^{2}$
- $5.1^{2}$

(b)

Calculate the angle between the line AG and the base EFGH of the cuboid.

[ 3 ]

29.5 or $29.49 \ldots$ to $29.54 \ldots$

M2 for $\sin [\ldots=] \frac{6.4}{13}$ oe
or M1 for identifying angle A G E

[Maximum number: 4]

\section*{NOT TO SCALE}

The diagram shows a solid cuboid with sides of length $4.5 \mathrm{~cm}, 8 \mathrm{~cm}$ and 13.2 cm .

Figure for Question 2 — CAIE IGCSE Mathematics Extended

NOT TO SCALE

Calculate the angle between AB and the horizontal base of the cuboid.

29.8 or 29.83 to $29.84 \ldots$

M3 for $\tan =\frac{8}{\sqrt{13.2^{2}+4.5^{2}}}$ oe

or $\mathbf{M 2}$ for $13.2^{2}+4.5^{2}$

or for $13.2^{2}+4.5^{2}+8^{2}$

or M1 for identifying correct angle

[Maximum number: 4]

NOT TO SCALE

The diagram shows a cuboid with a diagonal PB.
Calculate the angle between the diagonal PB and the base ABCD.

$17.1^\circ$ , or $17.10\ldots^\circ$ .

M3 for $\tan\theta=\frac{4}{\sqrt{12^2+5^2}}$ oe.
M2 for $12^2+5^2$ oe, or $12^2+5^2+4^2$ oe.
M1 for recognising angle PBD.

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

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question 3