Interpreting Real-Life Graphs
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Interpreting Real-Life Graphs — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionConnecting Graphs to Real SituationsConcept Practice
2 marks~3 minCriterion A
A cyclist's journey is shown on the distance–time graph.

Segment A: t=0t = 0 to t=10t = 10 s, distance increases from 00 m to 2020 m.
Segment B: t=10t = 10 s to t=20t = 20 s, distance remains constant at 2020 m.
Segment C: t=20t = 20 s to t=30t = 30 s, distance decreases from 2020 m to 00 m.
a
Calculate the gradient of Segment A. [1]
b
Interpret what the gradient of Segment B tells you about the cyclist's motion during that interval. [1]
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Solutions

2QuestionConnecting Graphs to Real SituationsAssessment Practice
6 marks~9 minCriterion C
A cyclist's speed vv (m/s) during a 20-second ride is modelled by

v(t)=−0.05t3+1.5t2,0≤t≤20,v(t) = -0.05t^3 + 1.5t^2, \quad 0 \leq t \leq 20,

and passes through A(0, 0)A(0,\,0), B(5, 8)B(5,\,8), C(10, 12)C(10,\,12), D(15, 10)D(15,\,10), and E(20, 0)E(20,\,0).

The derivative is v′(t)=−0.15t2+3tv'(t) = -0.15t^2 + 3t.
a
Calculate the average rate of change of speed between t=5t = 5 s and t=15t = 15 s. [2]
b
By drawing a tangent to the curve at C(10, 12)C(10,\,12), estimate the instantaneous rate of change of speed at t=10t = 10 s. State the coordinates of the two points used on your tangent line. [2]
c
Calculate v′(10)v'(10) and advise the cyclist's coach whether the rider should increase effort, maintain pace, or begin conserving energy at t=10t = 10 s. Justify your advice using the value obtained and the shape of the graph. [2]
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Solutions

3QuestionConnecting Graphs to Real SituationsConcept Practice
4 marks~6 minCriterion A
A car journey is shown on the distance–time graph.

- Segment A: (0,0)(0, 0) to (2,120)(2, 120)
- Segment B: (2,120)(2, 120) to (5,120)(5, 120)
- Segment C: (5,120)(5, 120) to (7,0)(7, 0)

Time is in hours; distance is in kilometres.
a
Calculate the speed of the car during Segment A. [1]
b
Calculate the total distance travelled during the entire journey. [1]
c
The legal speed limit on this road is 55 km/h. Advise the driver whether they broke the speed limit at any point during the journey, justifying your answer with the speeds from all three segments. [2]
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Solutions

4QuestionConnecting Graphs to Real SituationsAssessment Practice
6 marks~9 minCriterion D
A city is considering extending a bus route. The projected daily ridership (in thousands of passengers) as a function of route length xx km is

R(x)=0.5x+2R(x) = 0.5x + 2

and the daily operating cost (in thousands of dollars) is

C(x)=0.3x+5.C(x) = 0.3x + 5.

Each passenger pays a fare of 2.50 dollars. The current route length is 10 km, and the city plans to extend the route to 22 km.
a
Calculate the current daily profit, where profit = revenue −- operating cost and revenue = fare ×\times ridership. [2]
b
Determine the route length at which daily revenue equals daily operating cost. [2]
c
Advise the city whether the planned extension to 22 km is financially justified. In your response, identify one limitation of the linear model and explain how it could affect the reliability of your advice. [2]
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Solutions

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