CAIE A-Level Further Math A2 3.2.6 Toppling and Sliding Questions

Practise analysing toppling, sliding, friction and equilibrium limits for rigid bodies with Further Mathematics Paper 2 questions and mark schemes.

Exam points

Apply de Moivre's theorem to powers and roots of complex numbers.

[Maximum number: 3]

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A uniform square lamina ABCD has sides of length 10 cm. The point E is on BC with $E C=7.5 \mathrm{~cm}$ , and the point F is on DC with $C F=x \mathrm{~cm}$ . The triangle EFC is removed from ABCD (see diagram). The centre of mass of the resulting shape ABEFD is a distance $\bar{x} \mathrm{~cm}$ from CB and a distance $\bar{y} \mathrm{~cm}$ from CD.

Find the greatest possible value of x, giving your answer in the form $a+b \sqrt{2}$ , where a and b are constants to be determined.

Use condition: $\bar{x} \geqslant x$ $2 x^{2}-80 x+400 \geqslant 0$ $x=20-10 \sqrt{2}$
4b 3

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CAIE A-Level Further Math A2 3.2.6 Toppling and Sliding Questions question 1