IB Maths AI HL AI 2.2 Modelling questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1 Paper 2

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Question 1

Paper 1Easy5 marks

A technician records the volume of water in a reservoir during a filling test.

Time, $t$ (min)	0	5	10	15
Volume, $V$ (L)	18	31	43	56

The technician proposes a linear model $V=mt+c$

(a)

State one feature of the measurements that supports the use of a linear model.

[1]

(b)

Using the measurements at $t=0$ and $t=15$ show that the fitted model is

V=18+\frac{38}{15}t.

[2]

(c)

Hence estimate the volume of water after 12 minutes.

[1]

(d)

State whether using the model to predict the volume after 24 minutes is interpolation or extrapolation.

[1]

Question 2

Paper 1Medium7 marks

A website records the number of visits per day during the first five days after its launch.

$t$ number of days after launch	1	2	3	4	5
$V$ visits per day	320 000	470 000	760 000	1 040 000	1 700 000

To work with more manageable values, let $W=V/100\,000$ The manager considers an exponential model $W=A b^{t-1}$ and a power model $W=Ct^p$

(a)

For the exponential model, determine the fitted values of $A$ and $b$ and the Pearson’s product moment correlation coefficient for the linearized data. Give your answers to three significant figures.

[3]

(b)

For the power model, determine the fitted values of $C$ and $p$ and the Pearson’s product moment correlation coefficient for the linearized data. Give your answers to three significant figures.

[3]

(c)

State which model is better supported by these data, giving a reason based on the correlation coefficients.

[1]

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