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

1QuestionInterpret graphsConcept Practice
4 marks~6 minCriterion A
A car travels along a straight road. Its motion is shown on the distance–time graph below.

The graph passes through the points (0,0)(0, 0), (5,25)(5, 25), and (10,40)(10, 40), where time is in seconds and distance is in metres.
a
Calculate the speed of the car during the first 5 seconds. [1]
b
Calculate the speed of the car during the final 5 seconds. [1]
c
The road has a posted average-speed limit of 3.5 m/s for the full 10-second stretch. Calculate the car's average speed for the entire journey and justify whether the speed limit is exceeded. [2]
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Solutions

2QuestionRecognize shapesAssessment Practice
4 marks~6 minCriterion C
A landscape architect models two fountain jets as parabolas. The first jet follows the path y=x2y = x^2, where xx is horizontal distance (metres) and yy is height (metres). The second jet follows a path that is a vertical translation of the first jet upward by 3 metres.
a
Explain how a vertical translation upward by 3 metres affects the equation of y=x2y = x^2. [1]
b
Deduce the equation of the second jet and calculate its yy-intercept. [2]
c
The architect states: "The second jet always stays at least 3 metres above the first jet." Justify whether this statement is correct. [1]
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Solutions

3QuestionPlot 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

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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