IB Maths AI HL AI 2.1 Functions and graphs 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 1Medium6 marks

During an 8-hour monitoring period, the water depths in two tanks are modelled by

f(t)=-0.25(t-4)^2+10,\qquad g(t)=t+2,

where $f(t)$ is the depth in Tank A, $g(t)$ is the depth in Tank B, and $t$ is the time in hours since monitoring began. Depths are in centimetres, and $0\leq t\leq 8$

(a)

Construct a function $D(t)$ such that $D(t)>0$ means Tank A is deeper than Tank B. Give $D(t)$ in expanded form.

[2]

(b)

Use a GDC to graph $y=D(t)$ then sketch the graph for $0\leq t\leq 8$ in your answer booklet. Label both axes with units and indicate the $y$ -intercept, turning point, $t$ -intercept and value at $t=8$

[3]

(c)

Use your sketch to state which tank has the greater depth at $t=7$

[1]

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