Foundation November 2017 Paper 1 Q9
9. Laura rides her bicycle along a course.
She starts at point \(A\), marked on the scale diagram below.
The scale of the diagram is 1 cm represents 0·8 km.
On screen this diagram may not be shown at actual size. To measure it, use the question paper (PDF) printed at 100%.
(a) Write down the coordinates of point \(A\). [1]
(b)
Laura rides to point \(B\) at (1, 3), then to point \(C\) at (4, –2) and then to point \(D\).
Mark the positions of point \(B\) and point \(C\) on the grid. [2]
(c)
Laura takes 20 minutes to ride from point \(D\) directly back to point \(A\).
Her target speed for this part of the journey is 24 km/h.
The scale of the diagram is 1 cm represents 0·8 km.
Does Laura meet her target speed?
Yes ☐ No ☐
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| (−4, 3) | B1 | Do not allow a column vector. |
| Scheme | Marks | Comments |
|---|---|---|
| Points correctly plotted at (1, 3) and (4, −2) | B2 | B1 for each, ignoring mis-labelling or missing labels |
| Scheme | Marks | Comments |
|---|---|---|
| Line \(AD\) measured as 10 cm | B1 | Seen or implied; allow ±0·2 cm |
| 8 km (in 20 mins) or equivalent seen | B1 | FT ‘their 10’ × 0.8 |
| Justified conclusion e.g. 24 km in 60 mins or equivalent and ‘yes’ or \((\text{Time} =)\ \dfrac{8}{24} = \dfrac{1}{3}\) hours = 20 mins and ‘yes’ or \((\text{Distance} =)\ 24 \times \dfrac{1}{3} = 8\) km and ‘yes’ | B1 | FT ‘their 10’ × 0.8 × 3 correctly interpreted or \(\dfrac{\text{‘their 10’} \times 0.8}{24}\) correctly interpreted or \(24 \times \dfrac{1}{3} = 8\) km correctly compared to ‘their 10’ × 0.8 |
| (6) |