4MA0 Higher January 2013 Paper 4 Q17
17
Diagram NOT accurately drawn
\(AB\) is parallel to \(DE\).
The lines \(AE\) and \(BD\) intersect at \(C\).
\(AB\) = 7.5 cm, \(AC\) = 7 cm, \(CD\) = 5.2 cm, \(CE\) = 5.6 cm.
Calculate the area of triangle \(EDC\). (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{BC}{5.2} = \dfrac{7}{5.6}\) oe or \(\dfrac{BC}{7} = \dfrac{5.2}{5.6}\) oe | M1 |
| 6.5 | A1 |
| (2) |
Notes
M1: for correct, relevant proportionality statement with 3 values substituted
A1: cao
| Scheme | Marks |
|---|---|
\(\dfrac{DE}{7.5} = \dfrac{5.6}{7}\) oe or \(\dfrac{DE}{5.6} = \dfrac{7.5}{7}\) oe or \(\dfrac{DE}{5.2} = \dfrac{7.5}{\text{“}6.5\text{”}}\) oe or \(\dfrac{DE}{7.5} = \dfrac{5.2}{\text{“}6.5\text{”}}\) | M1 |
| 6 | A1 |
| (2) |
Notes
M1: for correct, relevant proportionality statement with 3 values substituted
A1: cao
| Scheme | Marks |
|---|---|
(scale factor) eg \(\dfrac{7}{5.6}\) or \(\dfrac{5.6}{7}\) or \(\dfrac{4}{5}\) oe or \(\dfrac{5}{4}\) oe (May be implied by second M1) allow ratio notation | M1 |
(scale factor)2 eg \(\left(\dfrac{4}{5}\right)^2\) oe or 0.64 or \(\left(\dfrac{5}{4}\right)^2\) oe 1.5625 allow ratio notation | M1 |
| 13.44 | A1 |
| (3) |
Notes
M1: Also award M1 for ht of \(\triangle CDE = \dfrac{4}{5} \times \dfrac{21}{\tfrac{1}{2} \times 7.5}\) (= 4.48)
M1: Also award M1 for \(\tfrac{1}{2} \times \text{“}6\text{”} \times \text{“}4.48\text{”}\)
A1: Also accept 13.4 if both method marks scored
M2 for eg (Area \(\triangle ABC\) =) \(\tfrac{1}{2} \times 7 \times \text{“}6.5\text{”} \sin C = 21\) and (Area \(\triangle CDE\) =) \(\tfrac{1}{2} \times 5.2 \times 5.6 \sin C\)
Also award M2 for \(s = \dfrac{5.2 + 5.6 + \text{“}6\text{”}}{2}\) (= 8.4) and Area = \(\sqrt{\text{“}8.4\text{”}(\text{“}8.4\text{”} - 5.2)(\text{“}8.4\text{”} - 5.6)(\text{“}8.4\text{”} - \text{“}6\text{”})}\)