Foundation November 2018 Paper 2 Q15
15 A company uses this formula to work out the cost, £\(A\), of a taxi ride.
\[A = 4 + 1.8m + b\]£4 is a fixed charge
\(m\) is the number of miles travelled
£\(b\) is a charge for booking online
(a) Clare books a taxi online and travels 8 miles.
She pays £20 altogether.
How much is the charge for booking online? [3 marks]
(b) A different company
has a fixed charge of £3
charges £1.90 per mile
has no charge for booking online.
Write a formula for the cost, £\(C\), of a taxi ride with this company. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(1.8(0) \times 8\) or 14.4(0) | M1 | implied by 5.6(0) or 18.4(0) |
| \(20 -\) their \(14.4(0) - 4\) or \(20 - 18.4(0)\) or 1.6 | M1dep | |
| 1.60 | A1 | condone £1.60p |
| Alternative method 2 | ||
| \(b = A - 4 - 1.8m\) | M1 | oe correct formula with \(b\) as the subject |
| \(20 - 4 - 1.8(0) \times 8\) or 1.6 | M1dep | |
| 1.60 | A1 | condone £1.60p |
Additional guidance
| \(1.8(0) \times 8\) may be within an incorrect calculation eg \(4 + 1.8(0) \times 8 + 20\) | M1 |
| Answer | Mark | Comments |
|---|---|---|
| \(C = 3 + 1.9(0)m\) | B1 | oe formula with \(C\) as subject accept \(C = 3 + 1.9(0) \times m\) condone \(+ 0\) or \(+ 0b\) |
Additional guidance
| \(3 + 1.9m\) | B0 |
| Do not accept eg \(A = \ldots\) for \(C = \ldots\) | B0 |
| Allow \(m\) to be \(\times\) mile(s) but not a different letter unless defined eg1 \(C = 3 + 1.9(0) \times\) miles eg2 \(C = 3 + 1.9(0)\) miles eg3 \(C = 3 + 1.9(0)\) per mile or \(C = 3 + 1.9(0)\)pm eg4 \(C = 3 + 1.9(0)x\) | B1 B0 B0 B0 |
| Ignore £ inserted in part or all of equation eg \(C = 3 + £1.90m\) | B1 |
| Correct formula followed by substitution (and evaluation) | B1 |