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Date May 2017 Marks available 1 Reference code 17M.1.SL.TZ2.T_14
Level Standard Level Paper Paper 1 Time zone Time zone 2
Command term Write down Question number T_14 Adapted from N/A

Question

Jashanti is saving money to buy a car. The price of the car, in US Dollars (USD), can be modelled by the equation

P = 8500   ( 0.95 ) t .

Jashanti’s savings, in USD, can be modelled by the equation

S = 400 t + 2000.

In both equations t is the time in months since Jashanti started saving for the car.

Jashanti does not want to wait too long and wants to buy the car two months after she started saving. She decides to ask her parents for the extra money that she needs.

Write down the amount of money Jashanti saves per month.

[1]
a.

Use your graphic display calculator to find how long it will take for Jashanti to have saved enough money to buy the car.

[2]
b.

Calculate how much extra money Jashanti needs.

[3]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

400 (USD)     (A1)     (C1)

[1 mark]

a.

8500   ( 0.95 ) t = 400 × t + 2000     (M1)

 

Note:     Award (M1) for equating 8500 ( 0.95 ) t to 400 × t + 2000 or for comparing the difference between the two expressions to zero or for showing a sketch of both functions.

 

( t = )   8.64  (months)  ( 8.6414  (months) )     (A1)     (C2)

 

Note:     Accept 9 months.

 

[2 marks]

b.

8500 ( 0.95 ) 2 ( 400 × 2 + 2000 )     (M1)(M1)

 

Note:     Award (M1) for correct substitution of t = 2 into equation for P , (M1) for finding the difference between a value/expression for P and a value/expression for S . The first (M1) is implied if 7671.25 seen.

 

4870 (USD) (4871.25)     (A1)     (C3)

 

Note:     Accept 4871.3.

 

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 2—Functions » SL 2.2—Functions, notation domain, range and inverse as reflection
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