| Date | November 2014 | Marks available | 2 | Reference code | 14N.1.sl.TZ0.7 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 7 | Adapted from | N/A |
Question
The number of apartments in a housing development has been increasing by a constant amount every year.
At the end of the first year the number of apartments was 150, and at the end of the sixth year the number of apartments was 600.
The number of apartments, \(y\), can be determined by the equation \(y = mt + n\), where \(t\) is the time, in years.
Find the value of \(m\).
State what \(m\) represents in this context.
Find the value of \(n\).
State what \(n\) represents in this context.
Markscheme
\(\frac{{600 - 150}}{{6 - 1}}\) (M1)
OR
\(600 = 150 + (6 - 1)m\) (M1)
Note: Award (M1) for correct substitution into gradient formula or arithmetic sequence formula.
\( = 90\) (A1) (C2)
the annual rate of growth of the number of apartments (A1) (C1)
Note: Do not accept common difference.
\(150 = 90 \times (1) + n\) (M1)
Note: Award (M1) for correct substitution of their gradient and one of the given points into the equation of a straight line.
\(n = 60\) (A1)(ft) (C2)
Note: Follow through from part (a).
the initial number of apartments (A1) (C1)
Note: Do not accept “first number in the sequence”.
