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: 4]

NOT TO SCALE

ABCDEFGH is a cuboid with a square base of side $x \mathrm{~cm}$ . $C G=20 \mathrm{~cm}$ and $A G=28 \mathrm{~cm}$ .

Calculate the value of x.

13.9 or 13.85 to 13.86
M3 for $2x^2=28^2-20^2$ or better, or M2 for $x^2+x^2+20^2=28^2$ , or M1 for any correct Pythagoras in 2D or their $AC\times\sin45^\circ$

[Maximum number: 4]

Figure for Question 2 — CAIE IGCSE Mathematics Extended

The diagram shows a triangular prism ABCDQP of length 7 cm.
The cross-section is triangle PAB with PA=4 cm, AB=5 cm and angle $PAB=90^\circ$ .
Calculate the angle between the line PC and the base ABCD.

24.9 or 24.93 to 24.94
M3 for $\tan=\frac4{\sqrt{5^2+7^2}}$ oe
or lower Pythagoras/angle recognition marks as in markscheme

[Maximum number: 6]

Figure for Question 3 — 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

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

Covered syllabus points

Question 1

Question 2

Question 3

Question (a)

Question (b)