Enlarge triangle A with scale factor \(\frac{1}{3}\) and centre of enlargement (−1, 5). [3]
(b) Prism P and prism Q are similar.
The ratio of the surface area of prism P to the surface area of prism Q is 1 : 3.
(i) Jay says
The height of prism P is one third of the height of prism Q.
Explain why he is wrong. [1]
(ii) The volume of prism Q is 86 cm\(^3\).
Calculate the volume of prism P. [3]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Triangle with vertices at (1, 6), (2, 6), (2, 4)
3
B2 for triangle correct size and orientation in wrong position
OR
B1 for enlargement centre (−1, 5) incorrect scale factor < 1 or for triangle with two vertices correct or for three rays from (−1, 5) to vertices of triangle A or for triangle correct size but wrong orientation
Mark scheme (b)
Answer
Marks
Part marks and guidance
(i) Height factor is square root of area factor oe in words or figures
1
Mark the best bit so long as no contradiction
Must include correct reference to square or square root
(ii) 16.5 to 16.6
3
B2 for \(\left(\sqrt{3}\right)^3\) oe or \(\dfrac{1}{\left(\sqrt{3}\right)^3}\) oe soi by 5.19 to 5.20 or 0.192 to 0.193
OR B1 for \(\sqrt{3}\) or \(\dfrac{1}{\sqrt{3}}\) oe soi by 1.73[…] or 0.577[…]
Accept \(\dfrac{86\sqrt{3}}{9}\) oe Note that \(\left(\sqrt{3}\right)^3 = 3\sqrt{3}\) and \(\dfrac{1}{\left(\sqrt{3}\right)^3} = \dfrac{\sqrt{3}}{9}\)
