Analysis and Approaches for IBDP Maths Ebook 1 | Page 308

Your Practice Set – Analysis and Approaches for IBDP Mathematics
100
Paper 2 Section B – Miscellaneous Problems
Example
The insurance cost of a van depends partly on the distance it has travelled. The following
table shows the distance and the insurance cost for six vans on 1 July 2019.
Travelling distance ( x km) 10000 12500 17500 20000 27500 35000
Insurance cost ($ y ) 9000 8800 8700 8600 8400 7800
The relationship between x and y can be modelled by the regression equation
y �ax � b .
(a) (i) Find the correlation coefficient.
(ii) Write down the value of a and of b .
On 1 July 2019, Jae Lim buys a van which has travelled 25000 km.
(b)
Use the regression equation to estimate the insurance cost of Jae Lim’s van,
giving your answer to the nearest 100 dollars.
The insurance cost of a van decreased by 3% each year.
(c)
Calculate the insurance cost of Jae Lim’s van after 8 years.
Jae Lim will stop using his van when its insurance cost reaches 5000 dollars.
[4]
[3]
[4]
(d)
Find the year when Jae Lim stops using his van.
[4]
Solution
(a) (i) r �� 0.9717142437
(M1) for valid approach
r �� 0.972
A1 N2
(b)
(ii) a �� 0.0432
A1 N1
b � 9432
A1 N1
The estimated insurance cost
� �0.0432(25000) � 9432
(A1) for substitution
� 8352
(A1) for correct value
� $8400
A1 N3
[4]
[3]
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