Interpreting Real-Life Graphs
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Interpreting Real-Life Graphs — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionEstimating Values and Trends from GraphsAssessment Practice
4 marks~6 minCriterion A
A car journey is represented by a distance–time graph with three straight-line segments.

Segment 1 (00 h to 22 h): speed =30= 30 km/h
Segment 2 (22 h to 3.53.5 h): speed =60= 60 km/h
Segment 3 (3.53.5 h to 55 h): speed =45= 45 km/h

The car starts at d=0d = 0 km.
a
Construct a table of values showing the distance at 0.50.5-hour intervals from t=0t = 0 h to t=5t = 5 h. [2]
b
Deduce a linear equation of the form d=mt+cd = mt + c for the distance during Segment 2. [1]
c
The driver claims the car reached 100100 km before t=2.7t = 2.7 h. Justify whether this claim is correct. [1]
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Solutions

2QuestionEstimating Values and Trends from GraphsAssessment Practice
5 marks~8 minCriterion C
The graph shows the rate of change of a function f(x)f(x) over 0≤x≤80 \le x \le 8. The gradient graph is piecewise linear, passing through (0, 4)(0,\ 4), (2, 0)(2,\ 0), (4, −2)(4,\ -2), (6, 0)(6,\ 0), and (8, 3)(8,\ 3). It is given that f(0)=5f(0) = 5, and that the area between the gradient graph and the xx-axis from x=0x = 0 to any value xx equals the change in f(x)f(x) over that interval.
a
Deduce the xx-coordinates where f(x)f(x) has stationary points. [1]
b
Justify the classification of each stationary point as a local maximum or local minimum, using the sign of the gradient on either side. [2]
c
A designer claims that f(x)f(x) never falls below its starting value on 0≤x≤80 \le x \le 8. Assess whether this claim is correct, supporting your answer with estimated values of f(x)f(x) at the stationary points. [2]
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Solutions

3QuestionReading Distance-Time GraphsAssessment Practice
6 marks~9 minCriterion D
A distance–time graph shows a delivery journey from point AA to point DD with three segments:

- Segment ABAB: A(0, 0)A(0,\ 0) to B(2, 60)B(2,\ 60)
- Segment BCBC: B(2, 60)B(2,\ 60) to C(5, 60)C(5,\ 60)
- Segment CDCD: C(5, 60)C(5,\ 60) to D(t, 0)D(t,\ 0), completed in 33 hours

Distance is in kilometres; time is in hours.
a
Calculate the gradient of segment ABAB and the coordinates of point DD. [2]
b
Deduce the gradient of segment CDCD and explain what it represents in the context of this journey. [2]
c
A logistics company requires the return speed to be at least 23\dfrac{2}{3} of the outbound speed. Evaluate whether this journey meets the requirement and justify your advice to the company. [2]
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Solutions

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