IB Maths AI HL AI 5.2 Integration and kinematics 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 2Medium6 marks

A pump transfers liquid into a container. For $t\geq 0$ its flow rate is modelled by

q(t)=2t e^{-t^2}\ \text{L min}^{-1},

where $t$ is the time in minutes since the pump starts. Let $V(t)$ litres be the total volume transferred by time $t$

(a)

Show that $V(t)=1-e^{-t^2}$

[2]

(b)

Calculate the volume transferred in the first $1.5$ minutes. Give your answer to three significant figures.

[1]

(c)

Determine the time at which $0.80$ L has been transferred. Explain why any other mathematical solution is not relevant.

[3]

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