CAIE IGCSE Mathematics Extended E6.6.1 In 3d Carry Out Calculations and Solve Problems in Three Dimensions Questions

Practise Extended CAIE IGCSE Mathematics by deriving face or cross-section diagonals, projecting lines onto planes, and applying Pythagoras or trigonometric ratios to three-dimensional problems.

Exam points

Calculate a face or cross-section diagonal with Pythagoras before using it in a second three-dimensional triangle.
Identify the projection of a line onto a plane when finding the angle between the line and that plane.
Use Pythagoras or a trigonometric ratio in the derived 3D triangle and keep intermediate values accurate.

[Maximum number: 6]

Figure for Question CAIE IGCSE Mathematics Extended E6.6.1 In 3d Carry Out Calculations and Solve Problems in Three Dimensions Questions 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

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CAIE IGCSE Mathematics Extended E6.6.1 In 3d Carry Out Calculations and Solve Problems in Three Dimensions Questions question 1

Question (a)

Question (b)