4MA0 Higher June 2016 Paper 4 Q12
12
Diagram NOT accurately drawn
The diagram shows triangle \(ACD\).
\(B\) is a point on \(AC\) and \(E\) is a point on \(AD\) so that \(BE\) is parallel to \(CD\).
\(AE\) = 4 cm
\(AC\) = 11.7 cm
\(BE\) = 6 cm
\(CD\) = 13.5 cm
(a) Calculate the length of \(AB\). (2)
(b) Calculate the length of \(ED\). (2)
| Scheme | Marks |
|---|---|
Eg \(\dfrac{13.5}{6}\) or \(\dfrac{9}{4}\) or 2.25 or \(\dfrac{6}{13.5}\) or \(\dfrac{4}{9}\) or 0.444(444…) or (\(AB\) =) \(11.7 \div \dfrac{9}{4}\) or (\(AB\) =) \(11.7 \times \dfrac{4}{9}\) or (\(AB\) =) \(6 \times \dfrac{11.7}{13.5}\) oe \(\dfrac{AB}{11.7} = \dfrac{4}{9}\) or \(\dfrac{AB}{6} = \dfrac{11.7}{13.5}\) oe | M1 |
| 5.2 | A1 |
| (2) |
Notes
M1: For correct scale factor or correct equation involving \(AB\) or correct expression for \(AB\)
Accept 0.444(444…) rounded to at least 3SF
| Scheme | Marks |
|---|---|
Eg (\(AD\) =) \(\dfrac{9}{4} \times 4\) or (\(AD\) =) \(\dfrac{4}{\text{"5.2"}} \times 11.7\) or (\(ED\)) = \(\left[\dfrac{9}{4} \times 4\right] - 4\) or (\(ED\)) = \(\dfrac{4}{\text{"5.2"}} \times (11.7 - \text{“5.2”})\) or \(\dfrac{AD}{4} = \dfrac{9}{4}\) or \(\dfrac{AD}{11.7} = \dfrac{4}{\text{"5.2"}}\) or \(ED + 4 = \dfrac{9}{4} \times 4\) or \(\dfrac{ED}{11.7 - \text{"5.2"}} = \dfrac{4}{\text{"5.2"}}\) or \(AD = 9\) | M1 |
| 5 | A1 |
| (2) |
Notes
M1: For a correct expression for \(ED\) or \(AD\) or
For a correct equation involving \(ED\) or \(AD\)