Graphs of Functions
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Graphs of Functions — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionPlot linear functionsConcept Practice
4 marks~6 minCriterion A
A student tests a remote-controlled car on a straight track, recording the following data.

Time (s)012345
Distance (m)0246810
a
Construct a graph of distance against time, plotting all six points on a fully labelled coordinate grid. Describe the pattern shown by the points. [2]
b
Deduce the equation that models the relationship between distance dd (m) and time tt (s), showing your reasoning. [1]
c
The track available for testing is 13 m long. Advise the student whether it is safe to run the car for 7 seconds without reaching the end of the track. Justify your answer with a calculation. [1]
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Solutions

2QuestionPlot quadratic functionsAssessment Practice
4 marks~6 minCriterion D
A landscape architect models the cross-section of a decorative arch using the function y=(x−3)2+2y = (x - 3)^2 + 2, where xx and yy are measured in metres. The parent function is y=x2y = x^2.
a
State the coordinates of the vertex of y=(x−3)2+2y = (x - 3)^2 + 2 and write down the equation of its axis of symmetry. [2]
b
Explain the two transformations that map the graph of y=x2y = x^2 onto the graph of y=(x−3)2+2y = (x - 3)^2 + 2. [1]
c
The arch must clear a pathway centred at x=3x = 3 that is 4 metres wide and 2.5 metres tall. Advise the architect whether the arch satisfies both clearance requirements, supporting your advice with calculations. [1]
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Solutions

3QuestionPlot linear functionsAssessment Practice
6 marks~9 minCriterion C
A student investigates the cooling of a hot liquid by recording its temperature (TT, in °C) every 5 minutes (tt, in minutes):

tt (min): 0, 5, 10, 15, 20, 25

TT (°C): 85, 72, 61, 52, 44, 38

The student proposes the linear model T=−1.8t+85T = -1.8t + 85 to describe the cooling.
a
Calculate the predicted temperature at each time value using the model T=−1.8t+85T = -1.8t + 85. Show all working. [2]
b
Deduce the residual (actual minus predicted) for each data point and describe the pattern you observe. [2]
c
Critique the student's decision to use the linear model T=−1.8t+85T = -1.8t + 85 for this cooling process, with reference to the residuals from part (b) and the real-world behaviour of cooling liquids. [2]
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Solutions

4QuestionPlot quadratic functionsAssessment Practice
6 marks~9 minCriterion B
A structural engineer models the vertical cross-section of a concrete arch using the quadratic function y=ax2+bx+cy = ax^2 + bx + c, where yy is the height (in metres) at horizontal position xx (in metres). Measurements taken at five positions are recorded below.

xx (m): −2, −1, 0, 1, 2-2,\ -1,\ 0,\ 1,\ 2

yy (m): 11, 6, 3, 2, 311,\ 6,\ 3,\ 2,\ 3
a
Calculate the first differences and second differences of the yy-values. [2]
b
Deduce the value of aa, given that the second difference of a quadratic y=ax2+bx+cy = ax^2 + bx + c with unit steps equals 2a2a. Hence state the equation of the arch. [1]
c
The arch must clear a minimum height of 1.51.5 m at x=3x = 3 m to allow vehicles to pass beneath it. Substituting x=3x = 3 into your equation from part (b), advise the engineer whether the arch is safe for vehicles at that position. [3]

Solutions

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