Graphing Quadratic Cubic and Exponential Functions
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Graphing Quadratic Cubic and Exponential Functions — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionGraphing Simple Cubic FunctionsConcept Practice
2 marks~3 minCriterion A
An engineer models the vertical displacement of a suspension bridge cable using the cubic function y=x3−4xy = x^3 - 4x, where xx is the horizontal distance (in metres) from the centre of the bridge and yy is the vertical displacement (in metres) from the reference level.

The graph of y=x3−4xy = x^3 - 4x is provided.
a
Deduce the yy-intercept of the graph, showing your working. [1]
b
Interpret what the yy-intercept means in the context of the bridge model. [1]
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Solutions

2QuestionGraphing and Identifying Exponential Growth and DecayAssessment Practice
4 marks~6 minCriterion D
A wildlife reserve records the population of a rare beetle species over four consecutive years. The population is modelled by an exponential function. The graph shows population PP (in hundreds) against time tt (in years), with points (0,3)(0, 3), (1,6)(1, 6), (2,12)(2, 12), (3,24)(3, 24) labelled.
a
State the initial population and deduce the growth factor from the graph. [2]
b
Write the equation of the exponential model in the form P=a⋅btP = a \cdot b^t. [1]
c
The reserve can sustainably support a maximum of 5000 beetles. Advise the reserve manager whether intervention is required before year t=5t = 5, justifying your answer with a calculation. [1]
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3QuestionFinding Vertex and Axis of SymmetryAssessment Practice
8 marks~12 minCriterion D
A drone's height above the ground (in metres) is modelled by

h(t)=−5t2+40t+10h(t) = -5t^2 + 40t + 10

where tt is the time in seconds after launch.
a
Determine the time at which the drone reaches its maximum height and calculate that maximum height. [2]
b
The drone operates safely only when its height is at least 15 m. Deduce the time interval during which the drone maintains a safe height. [2]
c
A safety regulation states the drone must remain above 15 m for at least 7 seconds. Using your results, advise the drone operator whether this model provides sufficient assurance of compliance with the regulation, and justify your advice by identifying one reason why the real flight may not match the model's prediction. [4]
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4QuestionGraphing Simple Cubic FunctionsAssessment Practice
6 marks~9 minCriterion B
A packaging engineer models container volume using y=x3y = x^3, where xx is the side length in centimetres and yy is the volume in cm³. A second design scales volume by a factor of 2, modelled by y=2x3y = 2x^3.

xx: −3, −2, −1, 0, 1, 2, 3-3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3

y=x3y = x^3: −27, −8, −1, 0, 1, 8, 27-27,\ -8,\ -1,\ 0,\ 1,\ 8,\ 27

y=2x3y = 2x^3: −54, −16, −2, 0, 2, 16, 54-54,\ -16,\ -2,\ 0,\ 2,\ 16,\ 54
a
Explain how the yy-values of y=2x3y = 2x^3 relate to those of y=x3y = x^3, identifying the pattern shown in the table. [2]
b
Deduce the yy-values of y=3x3y = 3x^3 at x=−2x = -2 and x=4x = 4, using the pattern from part (a) rather than direct calculation. [2]
c
A third design requires a volume output of at least 150 cm³ when x=4x = 4. The engineer proposes y=ax3y = ax^3 with a=2a = 2. Advise the engineer whether a=2a = 2 is sufficient and state the minimum integer value of aa that meets the requirement. [2]

Solutions

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