| Date | May 2011 | Marks available | 3 | Reference code | 11M.1.sl.TZ1.8 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Calculate | Question number | 8 | Adapted from | N/A |
Question
A teacher earns an annual salary of \(45 000\) USD for the first year of her employment. Her annual salary increases by \(1750\) USD each year.
Calculate the annual salary for the fifth year of her employment.
She remains in this employment for 10 years. Calculate the total salary she earns in this employment during these 10 years.
Markscheme
\(45000 + (5 - 1)1750\) (M1)(A1)
Note: Award (M1) for substituted AP formula, (A1) for correct substitutions.
\( = 52000\) USD (A1) (C3)
Notes: If a list is used, award (M1) for recognizing AP, award (A1) for seeing 52000 in their list, (A1) for final answer.
[3 marks]
\(\frac{{10}}{2}(2(45000) + (10 - 1)(1750))\) (M1)(A1)
Notes: Award (M1) for substituted AP formula, (A1)(ft) for correct substitutions. Follow through from their common difference used in part (a).
\( = 528750\) USD (A1)(ft) (C3)
Notes: Accept \(529 000\). If a list is used, award (M1) for recognizing sum of AP, (A1) for seeing \(60 750\) included in the sum or \(528 750\) in a cumulative list.
[3 marks]
Examiners report
Although part a was very well done, a large number of candidates multiplied the difference by \(n\) rather than \(n - 1\).
Although part a was very well done, a large number of candidates multiplied the difference by \(n\) rather than \(n - 1\). Many candidates misread, or misinterpreted, part b and found the \({10^{{\text{th}}}}\) term rather than the sum of the first \(10\) terms.
