Higher June 2019 Paper 1 Q14
14 Here is a quadrilateral.
Not drawn accurately
\(a = 90^\circ \quad\) and \(\quad a : b = 5 : 3\)
\(x : y = 1 : 3\)
Show that \(\quad b = x\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: work out the value of both angles | ||
| \((b =)\ 90 \div 5 \times 3\) or 54 | M1 | oe may be on diagram for \(b\) or \(x\) |
| \((x =)\ \dfrac{360 - 90 - \text{their } 54}{3 + 1}\) or \(\dfrac{216}{4}\) | M1dep | oe |
| \((b =)\ 54\) and \((x =)\ 54\) with M2 awarded | A1 | |
| Alternative method 2: assumes both angles are equal and uses sum of angles in a quadrilateral | ||
| \((b =)\ 90 \div 5 \times 3\) or 54 | M1 | oe may be on diagram for \(b\) or \(x\) |
| 90 + their 54 + their 54 + \(3 \times\) their 54 or 360 – 90 – their 54 – their 54 and either \(3 \times\) their 54 or their \(162 \div 3\) or their \(162 \div 54\) | M1dep | oe addition of the four angles in the quadrilateral or subtraction of 90 and the two equal angles from 360 and multiplication to work out the fourth angle or division of the fourth angle by 3 or 54 to act as a check |
| 90 + 54 + 54 + 162 = 360 and \(54 \times 3 = 162\) or 360 – 90 – 54 – 54 = 162 and \(162 \div 3 = 54\) or \(162 \div 54 = 3\) | A1 | oe |
| Alternative method 3: assumes both angles are equal and uses ratio to check 90° | ||
| 5 : 3 : 3 : 9 | M1 | |
| \(360 \div (5 + 3 + 3 + 9) \times 5\) or \(360 \div 20 \times 5\) | M1dep | oe |
| \(360 \div 20 \times 5 = 90\) with M2 awarded | A1 | |
Additional guidance
Any correct method to work out 54 scores M1 on alt 1 or alt 2