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Real-Life Problem Solving with Equations — Free MYP5 Mathematics (Standard) Practice Questions
1QuestionInterpreting and Validating SolutionsConcept Practice
2 marks~3 minCriterion C
A mobile data plan charges a monthly fee. Plan A costs dollars and Plan B costs dollars, where is the number of gigabytes used.
A customer claims that both plans cost the same when gigabytes.
Substitute into both expressions, show your working, and justify whether the customer's claim is correct. [2]
A customer claims that both plans cost the same when gigabytes.
Substitute into both expressions, show your working, and justify whether the customer's claim is correct. [2]
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
3QuestionMulti-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
4QuestionAge 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
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