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Date November Example questions Marks available 4 Reference code EXN.2.SL.TZ0.7
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number 7 Adapted from N/A

Question

Helen and Jane both commence new jobs each starting on an annual salary of $70,000. At the start of each new year, Helen receives an annual salary increase of $2400.

Let $Hn represent Helen’s annual salary at the start of her nth year of employment.

At the start of each new year, Jane receives an annual salary increase of 3% of her previous year’s annual salary.

Jane’s annual salary, $Jn, at the start of her nth year of employment is given by Jn=700001.03n-1.

At the start of year N, Jane’s annual salary exceeds Helen’s annual salary for the first time.

Show that Hn=2400n+67600.

[2]
a.

Given that Jn follows a geometric sequence, state the value of the common ratio, r.

[1]
b.

Find the value of N.

[3]
c.i.

For the value of N found in part (c) (i), state Helen’s annual salary and Jane’s annual salary, correct to the nearest dollar.

[2]
c.ii.

Find Jane’s total earnings at the start of her 10th year of employment. Give your answer correct to the nearest dollar.

[4]
d.

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

uses Hn=H1+n-1d with H1=70000 and d=2400       (M1)

Hn=70000+2400n-1        A1

so  Hn=2400n+67600         AG

 

[2 marks]

a.

r=1.03        A1

 

[1 mark]

b.

evidence of use of an appropriate table or graph or GDC numerical solve feature to find the value of N such that Jn>Hn         (M1)

 

EITHER

for example, an excerpt from an appropriate table

        (A1)

 

OR

for example, use of a GDC numerical solve feature to obtain N=10.800         (A1)

 

Note: Award A1 for an appropriate graph. Condone use of a continuous graph.

 

THEN

N=11        A1

 

[3 marks]

c.i.

H11=94000$        A1

J11=94074$        A1

Helen’s annual salary is $94000 and Jane’s annual salary is $94074

 

Note: Award A1 for a correct H11 value and A1 for a correct J11 value seen in part (c) (i).

 

[2 marks]

c.ii.

at the start of the 10th year, Jane will have worked for 9 years so the value of S9 is required         R1

 

Note: Award R1 if S9 is seen anywhere.

 

uses Sn=J1rn-1r-1 with J1=70000r=1.03 and n=9        (M1)

 

Note: Award M1 if n=10 is used.

 

S9=700001.039-11.03-1=711137.42        (A1)

=711137$

Jane’s total earnings are $711137 (correct to the nearest dollar)

 

[4 marks]

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.i.
[N/A]
c.ii.
[N/A]
d.

Syllabus sections

Topic 1—Number and algebra » SL 1.2—Arithmetic sequences and series
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Topic 1—Number and algebra » SL 1.3—Geometric sequences and series
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