October 2021 Paper 1 Q2
2 Alex is comparing the cost of mobile phone contracts. Contract \(\boldsymbol{A}\) has a set-up cost of £40 and then costs 4p per minute. Contract \(\boldsymbol{B}\) has no set-up cost, does not charge for the first 100 minutes and then costs 6p per minute.
(a) Find an expression for the cost of each of the contracts in terms of \(m\), where \(m\) is the number of minutes for which the phone is used and \(m \gt 100\). [2]
(b) Hence find the value of \(m\) for which both contracts would cost the same. [2]
| Scheme | Marks | AO |
|---|---|---|
| \((C =)\ 4000 + 4m\) | B1 | 3.3 |
| \((C =)\ 6(m - 100)\) | B1 | 3.3 |
| [2] |
Notes
B1: Correct equation / expression for \(A\)
Or \(40 + 0.04m\)
B1: Correct equation / expression for \(B\)
Or \(0.06(m - 100)\)
B1B0 if units inconsistent in two equations
SC B1 for both \(44 + 0.04m\) and \(0.06m\) (or \(4400 + 4m\) and \(6m\)) – from using \(m = 0\) at 100 minutes
| Scheme | Marks | AO |
|---|---|---|
| \(4000 + 4m = 6(m - 100)\) \(2m = 4600\) | M1 | 1.1 |
| \(m = 2300\) | A1 | 3.4 |
| [2] |
Notes
M1: Attempt to solve simultaneously, from two linear equations in \(m\)
At least one equation must have constant term
Could be implied by final answer of 38hrs 20 mins
A1: Obtain 2300 (minutes)
isw once 2300 seen