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 2Easy5 marks

A technician records the water depth $h$ in a tank as it is filled. The measurements, recorded to the nearest $0.1\text{ cm}$ are shown in Figure 1.

(a)

State a suitable type of model for the relationship between $h$ and $t$ based on the pattern of the data.

[1]

(b)

Use linear regression on the data in Figure 1 to determine a model in the form $h=at+b$ Give $a$ and $b$ to three significant figures.

[2]

(c)(i)

Use your model to estimate the water depth after $5$ minutes. Give your answer to three significant figures.

[1]

(c)(ii)

State whether this estimate is an interpolation or an extrapolation, and give a reason why using the model for this estimate is appropriate.

[1]

Question 2

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]

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