IB DP Math MAI HL : IB Style Mock Exams – Set 3 Paper 1

Question

Roger buys a new laptop for himself at a cost of £495. At the same time, he buys his daughter Chloe a higher specification laptop at a cost of £2200.

It is anticipated that Roger’s laptop will depreciate at a rate of 10 % per year, whereas Chloe’s laptop will depreciate at a rate of 15 % per year.

a. Estimate the value of Roger’s laptop after 5 years. [2]

Roger and Chloe’s laptops will have the same value k years after they were purchased.

b. Find the value of k . [2]

c.  Comment on the validity of your answer to part (b). [1]

Answer/Explanation

(a) £495 × 0.9k= 2200 × 0.85k 

(b) k = 26,1 (26.0968..)

(c) depreciation rates unlikely to be constant (especially over a long time period) 

Question

A slope field for the differential equation \(\frac{dy}{dx}=x^2 + \frac{y}{2}\) is shown.

Some of the solutions to the differential equation have a local maximum point and a local
minimum point.
(a) (i) Write down the equation of the curve on which all these maximum and minimum points lie.
(ii) Sketch this curve on the slope field.
The solution to the differential equation that passes through the point (0 , −2) has both a
local maximum point and a local minimum point.
(b) On the slope field, sketch the solution to the differential equation that passes
through (0, −2).

Answer/Explanation

Ans:

(a) (i) \(x^2+\frac{y}{2}=0 (y=-2x^2)\)
(ii) \(y=-2x^2\) drawn on diagram (correct shape with a maximum at (0, 0))

(b)


correct shape with a local maximum and minimum, passing through (0, 2)
local maximum and minimum on the graph of \(y=-2x^2\)

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