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Real-Life Problem Solving with Equations — Free MYP5 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: hours
Day 2: hours
Day 3: hours
Day 4: hours
On Day 5, shifts run for 6 consecutive integers starting at 5.
Day 1: hours
Day 2: hours
Day 3: hours
Day 4: 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
2QuestionChoosing Appropriate MethodsAssessment Practice
2 marks~3 minCriterion D
A small business pays a monthly electricity bill structured as follows: a fixed base charge of 50 dollars, a rate of 0.10 dollars per kWh for the first 500 kWh, and 0.15 dollars per kWh for any usage beyond 500 kWh.
A single linear equation has been proposed to model the total monthly cost (in dollars) for kWh consumed.
Calculate the cost predicted by the linear model and the actual cost when kWh, then justify whether the single linear equation is a suitable model for this billing structure. [2]
A single linear equation has been proposed to model the total monthly cost (in dollars) for kWh consumed.
Calculate the cost predicted by the linear model and the actual cost when kWh, then justify whether the single linear equation is a suitable model for this billing structure. [2]
Solutions
3QuestionAge Distance and Geometry-Based ProblemsAssessment Practice
5 marks~8 minCriterion A
A rectangular park has length m and width m, where represents the age in years of a student. The perimeter of the park is 124 m. A straight diagonal path connects two opposite corners of the park.
a
Show that the perimeter of the park gives the equation , and hence deduce the value of . [2]
b
Using your value of , calculate the length and width of the park. [1]
c
The park's management states that any diagonal path longer than 45 m requires safety lighting. Using Pythagoras' theorem, calculate the length of the diagonal path correct to 2 decimal places, and hence justify whether safety lighting is required. [2]
Solutions
4QuestionChoosing Appropriate MethodsAssessment Practice
3 marks~5 minCriterion C
A car's distance from its starting point is recorded below.
| Time (hours) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Distance (km) | 0 | 40 | 90 | 120 | 200 |
a
Calculate the average speed of the car during the interval hours to hours, using
Show your working and give your answer in km/h. [1]
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 to hours. [1]
Solutions
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