Higher January 2019 Paper 1 Q5
5
Diagram NOT accurately drawn
\(BCD\) and \(AFE\) are straight lines.
Show that \(BCD\) is parallel to \(AFE\).
Give reasons for your working.
(5)
| Scheme | Marks |
|---|---|
| E.g. \(4x + 15 + 30x - 5 = 180\) OR \(20x + 45 + 4x + 15 = 180\) OR \(4x + 15 + 20x + 45 = 180\) OR \(30x - 5 = 20x + 45\) | M1 |
| \(x = 5\) | A1 |
| E.g. \(20 \times \text{``}{5}\text{''} + 45\) (=145) or \(4 \times \text{``}{5}\text{''} + 15\) (=35) or \(30 \times \text{``}{5}\text{''} - 5\) (=145) OR E.g. \(4x + 15 + 30x - 5 = 180\) AND \(30x - 5 = 20x + 45\) | M1 |
| E.g. \(AFC = 145\) and \(FCD = 145\) OR \(AFC = 145\) and \(BCF = 35\) OR \(x = 5\) from the solution of two equations | A1 |
| Working required Answer: Shown correctly with reasons | B1 |
| (5) | |
| (5 marks) |
Notes
M1: for forming an appropriate equation
A1: dep on previous M1
M1: for substituting their value for \(x\) into the expression NOT used to form the equation solved
OR
forms a second equation in \(x\)
A1: dep on previous M1
NB : It must be clear which angles are being found
B1: For full reasons:
Alternate angles are equal and angles in a straight line add to 180º OR
Allied angles (or co-interior) add to 180º and angles in a straight line add to 180º