Real-Life Problem Solving with Equations
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Real-Life Problem Solving with Equations — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionMulti-Step Problems with VariablesConcept Practice
2 marks~3 minCriterion B
A community centre arranges daily volunteer shifts. The shift lengths (in hours) follow a pattern of consecutive integers:

Day 1: 1+2=31 + 2 = 3 hours
Day 2: 2+3+4=92 + 3 + 4 = 9 hours
Day 3: 3+4+5+6=183 + 4 + 5 + 6 = 18 hours
Day 4: 4+5+6+7+8=304 + 5 + 6 + 7 + 8 = 30 hours

On Day 5, shifts run for 6 consecutive integers starting at 5.
a
Deduce the pattern connecting the sum of each set to its terms. [1]
b
A volunteer coordinator claims Day 5 totals exactly 45 hours of coverage. Justify whether this claim is correct. [1]

Solutions

2QuestionAge Distance and Geometry-Based ProblemsAssessment Practice
2 marks~3 minCriterion A
A ladder leans against a vertical wall. The ladder is 8 m long and its base rests on horizontal ground 6 m from the wall. The angle θ\theta is formed between the ladder and the wall at the top.

Deduce the size of angle θ\theta, giving your answer in degrees to one decimal place. [2]
Question diagram

Solutions

3QuestionChoosing Appropriate MethodsAssessment Practice
4 marks~6 minCriterion D
A cyclist's journey is modelled by a straight-line graph of distance (km) against time (hours). The line passes through the points (1,15)(1, 15) and (3,45)(3, 45).
a
Calculate the cyclist's speed. [1]
b
Deduce the equation of the line in the form d=mtd = mt, where dd is distance in km and tt is time in hours. [1]
c
The cyclist's destination is 70 km away. Using your equation, advise whether the cyclist should plan to complete the journey within a 5-hour window. Justify your answer. [2]
Question diagram

Solutions

4QuestionChoosing Appropriate MethodsAssessment Practice
3 marks~5 minCriterion C
A car's distance from its starting point is recorded below.

Time (hours)01234
Distance (km)04090120200
a
Calculate the average speed of the car during the interval t=2t = 2 hours to t=4t = 4 hours, using

average speed=total distancetotal time\text{average speed} = \frac{\text{total distance}}{\text{total time}}

Show your working and give your answer in km/h. [1]
b
The car travels the same total distance of 200 km in 4 hours on a second journey, but at a constant speed throughout. Calculate this constant speed. [1]
c
The road used for the first journey has a speed limit of 60 km/h. Justify whether your answer from part (a) alone is sufficient evidence to conclude that the speed limit was exceeded during the interval t=2t = 2 to t=4t = 4 hours. [1]

Solutions

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