4MA0 Higher June 2012 Paper 3 Q18
18
Diagram NOT accurately drawn
\(A\), \(B\), \(C\) and \(D\) are points on a circle, centre \(O\).
\(AOBE\) and \(DCE\) are straight lines.
\(CO = CE\).
Angle \(AOD = 69^\circ\)
Angle \(CEO = x^\circ\)
Calculate the value of \(x\).
Show your working clearly.
(6)
NB The mark scheme for Q18 covers the majority of methods but there are other possible approaches.
If you encounter a mathematically correct method which is not covered and
(i) the answer is correct – award full marks
or
(ii) the answer is not correct – send the response, appropriately annotated, to Review.
| Scheme | Marks |
|---|---|
| \(\angle COE = x\) | B1 |
| \(\angle OCD = 2x\) or \(69 - x\) or \(34\frac{1}{2} + \frac{1}{2}x\) | B1 |
| \(\angle ODC = 2x\) or \(69 - x\) or \(34\frac{1}{2} + \frac{1}{2}x\) \(\angle COD = 180 - 4x\) or \(111 - x\) Accept \(x + y = 69\) or \(y - \frac{1}{2}x = 34\frac{1}{2}\) (where \(\angle OCD = \angle ODC = y\)) | B1 |
| \(3x = 69\) | M2 |
| 23 | A1 |
| (Total 6 marks) |
Notes
M2: M1 for a correct unsimplified equation in \(x\) eg
\(69 + 180 - 4x + x = 180\)
\(69 = 2x + x\)
\(69 - x = 2x\)
\(55.5 + 55.5 + 2x + x = 180\)
\(111 - x + 2x + 2x = 180\)
\(34\frac{1}{2} + \frac{1}{2}x = 2x\)
A1: cao
Award 6 marks for an answer of 23 if M1 or M2 scored
B1 B1 B1: May be stated, marked on diagram or part of an equation. B1 for each correct expression for an angle up to a max of 2. Award all 3 B marks if M1 or M2 scored.