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.

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Question 1

Paper 2Easy5 marks

A technician records the water depth hh in a tank as it is filled. The measurements, recorded to the nearest 0.1 cm0.1\text{ cm} are shown in Figure 1.

0123456780246810121416182022Time, t (min)Water depth, h (cm)(0, 4.0)(2, 8.1)(4, 12.0)(6, 16.2)(8, 20.1)
(a)

State a suitable type of model for the relationship between hh and tt 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+bh=at+b Give aa and bb to three significant figures.

[2]
(c)(i)

Use your model to estimate the water depth after 55 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]

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