Higher November 2020 Paper 6 Q16

16 The diagram shows a circle, centre O.

Points A, B and C lie on the circumference of the circle.
Line AOB is a diameter.
Line DAE is a tangent to the circle.
Angle CAE = 32°.

Not to scale

(a) Give a reason why angle ACB is a right angle. [1]

(b) The radius of the circle is 8 cm.

Calculate length BC. [4]

Answer	Marks	Part marks and guidance
[angle in a] semi-circle oe	1		Accept other reasoning if fully justified

Mark scheme (b)

Answer	Marks	Part marks and guidance
13.5 to 13.6	4	B1 for angle BAC = 58° or angle ABC = 32° M2 for 16sin(their 58) or 16cos(their 32) or M1 for \(\sin(\textit{their}\ 58) = \frac{BC}{\textit{their}\ 16}\) or \(\cos(\textit{their}\ 32) = \frac{BC}{\textit{their}\ 16}\) or better If 0 or B1 scored then instead award SC2 for 6.7 to 6.8 as final answer Grads or rads: If 0, 1 or 2 scored then instead award SC3 for 15.8[8…] to 15.9 or 12.6[4…] as final answer or If 0 scored award SC1 for 7.9[4…] or 6.3[2…]	May be seen on diagram or implied by use of sin58 or cos32 Only award M marks if their angle and trig ratio are consistent ie do not accept 16sin32 unless angle BAC previously seen as 32.