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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 45000 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.

[3]
a.

She remains in this employment for 10 years. Calculate the total salary she earns in this employment during these 10 years.

[3]
b.

Markscheme

45000+(51)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]

a.

102(2(45000)+(101)(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 529000. If a list is used, award (M1) for recognizing sum of AP, (A1) for seeing 60750 included in the sum or 528750 in a cumulative list.

[3 marks]

b.

Examiners report

Although part a was very well done, a large number of candidates multiplied the difference by n rather than n1.

a.

Although part a was very well done, a large number of candidates multiplied the difference by n rather than n1. Many candidates misread, or misinterpreted, part b and found the 10th term rather than the sum of the first 10 terms.

b.

Syllabus sections

Topic 1 - Number and algebra » 1.7 » Arithmetic sequences and series, and their applications.
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