IB Maths AI SL 2.4 Key graph features

IB Mathematics: applications and interpretation guide, first assessment 2021

Students practise identifying and calculating key features—roots, vertex, axis of symmetry, maxima/minima—from real-world quadratic, trigonometric, and rational graphs.

How this is tested

solve h(d) = 0 or use symmetry d = −b/(2a) to find where a dolphin re-enters water in a quadratic model
read the x-coordinate of the vertex or apply dy/dx = 0 to find maximum height of an arch modelled by y(x)
extract amplitude and principal axis from a cosine tide model h(t) = −2.5 cos(30t) + 4.5

[Maximum number: 2]

At 12:05 pm, Navam starts draining water from a small reservoir into an empty pond.
He controls the rate the water is drained so that the volume of water remaining in the reservoir, $V \mathrm{~m}^{3}$ , varies inversely with the time, t, where t is the number of minutes after 12:00 pm.
At 12:05 pm, the volume of water in the reservoir is $300 \mathrm{~m}^{3}$ .

Find the value of t when the volume of water remaining in the reservoir equals the volume of water in the pond.

The following diagram shows part of the graph of y=V(t).

Figure for Question 10(b) — IB Maths AI SL

How this is tested

Question 10(b)