Practice IB Mathematics Applications & Interpretation (AI) Topic SL 2.4—features of a Graph with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 2.4—features of a Graph and mirrors Paper 1, 2, 3 style where relevant.
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The side profile of a vase is modelled by the curve for .
Determine the -coordinate of the point where the graph of intersects the -axis.
The area bounded by the curve , the -axis, and the -axis is revolved around the -axis. Calculate the volume of the resulting solid of revolution.
The height of a ball launched upward is represented by the function , where denotes time in seconds and denotes height in meters.
Find the vertex of the quadratic model and explain its meaning, including whether it gives a maximum or minimum height.
Identify the equation of the function's axis of symmetry.
Determine the range of and sketch its graph, clearly labeling the vertex and the -intercept.
Consider the function .
Draw a sketch, clearly indicating its domain, the equations of any asymptotes and any points where the graph intersects the coordinate axes.
Utilizing your graph or an analytical method, find the solution to the inequality .
A water tank initially contains 5 litres of water. Water is being drained from the tank at a constant rate of 1 litre per minute. The function represents the amount of water (in litres) left in the tank after minutes.
Determine the domain and range of in the context of this problem.
Identify any intercepts on the graph and interpret their meaning in the context of the problem.
A phone battery is initially charged to 80%. The battery level decreases at a constant rate of 10 percentage points per hour. The function represents the battery charge (in percent) after hours.
Determine the domain and range of in the context of this problem.
Identify any intercepts on the graph and interpret their meaning in the context of the problem.