Basic Trigonometry: WJEC GCSE Higher November 2020 Unit 2 Q10

Higher November 2020 Unit 2 Q10

10. The diagram below shows a circle with centre at point O.
A, B, C and D are all points on the circumference of the circle.

AB = 7·5 cm and BC = 4·7 cm.

Diagram not drawn to scale

(a)

(i) Give the reason why \(A\hat{B}C\) is 90°. [1]

(ii) Calculate the size of angle \(x\). [3]

(b) Write down the size of angle \(y\).
State the circle theorem you have used to find your answer. [2]

\(y =\) …………

Circle theorem used: …………

Mark scheme (a)

Scheme	Marks	Comments
(a)(i) Correct reason given. e.g. ‘An angle at the circumference subtended by a diameter is a right angle’. ‘ line AC is a diameter’	E1	Accept any correct unambiguous wording. The key word is ‘diameter’. Allow eg ‘angle in a semicircle is 90°’, ‘line AC goes through the centre’. ‘opposite a diameter’ Do not accept ‘because it’s a right angle’.
(a)(ii) \(\tan x = \dfrac{7{\cdot}5}{4{\cdot}7}\)	M1
\(x = \tan^{-1}(7{\cdot}5 / 4{\cdot}7)\) or \(\tan^{-1} 1.6\) or \(\tan^{-1} 1.59(\ldots)\)	m1	Implies M1.
= 57·9(…)(°) or 57·8(…)(°) or 58(°)	A1	C.A.O.

Scheme	Marks	Comments
A correct and complete method (using Pythagoras’s theorem and a trigonometric relationship).	M2
x = 57·9(…)(°) or 57·8(…)(°) or 58(°) CAO	A1

Mark scheme (b)

Scheme	Marks	Comments
(y =) 58(°)	B1	Strict FT of ‘their x’.
Correct circle theorem given. e.g. ‘angles (at the circumference) subtended by the same chord (or arc) are equal’, ‘angles in the same segment (are equal)’.	E1	Accept any correct unambiguous wording. Allow eg ‘angles on the same chord (are equal)’ Do not accept e.g. ‘they are equal’ on its own.