Formulas in Real-World Contexts

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Formulas in Real-World Contexts — Free MYP2 Mathematics Practice Questions

1QuestionApplying the Speed Distance Time FormulaConcept Practice

2 marks~3 minCriterion A

A car travels from City P to City Q, a distance of 240 km, in 3 hours.

The speed formula is:

\text{speed} = \frac{\text{distance}}{\text{time}}

Identify the values of distance and time given in the question. [1]

Calculate the speed of the car in km/h. [1]

Solutions

2QuestionApplying the Speed Distance Time FormulaAssessment Practice

4 marks~6 minCriterion D

A car travels through a city for 30 minutes at a constant speed of 40 km/h. Using the formula

\text{distance} = \text{speed} \times \text{time}

a student calculates the car travels 20 km.

Identify one reason why the actual distance travelled may differ from 20 km. [1]

Explain how using average speed instead of constant speed would improve this estimate. [2]

A second city journey lasts 45 minutes at an average speed of 30 km/h. Compare the two journeys in terms of distance travelled. [1]

Solutions

3QuestionUsing the Formula for Area of ShapesAssessment Practice

5 marks~8 minCriterion B

A shear transforms a rectangle into a parallelogram by sliding the top side horizontally while keeping the base and height the same.

Use the three rectangles below to investigate the conjecture: a rectangle and a parallelogram with the same base and height have equal area.

Rectangle 1	base $= 5$ cm	height $= 3$ cm
Rectangle 2	base $= 7$ cm	height $= 4$ cm
Rectangle 3	base $= 6$ cm	height $= 5$ cm

Calculate the area of each rectangle. Record your results as labelled rows with the headings: Rectangle, Base (cm), Height (cm), Area (cm

^2

). [2]

Each rectangle is sheared into a parallelogram with the same base and height. Calculate the area of each parallelogram using

A = \text{base} \times \text{height}

, and add an "Area of parallelogram (cm

^2

)" row to your table. [1]

Compare the two sets of areas in your table. State the pattern you observe and explain why the formula gives the same result for both shapes. [2]

Solutions

4QuestionSolving Finance-Related Formula ProblemsAssessment Practice

5 marks~8 minCriterion C

A student claims: "If I deposit 500 dollars in a savings account at 4% annual compound interest (interest calculated on the growing total each year), after 3 years I will have exactly 562.43 dollars."

Using the formula

A = P(1 + r)^t

Identify the values of

P

r

, and

t

. [1]

Calculate the actual amount

A

after 3 years. Show all steps. [2]

Compare your answer with the student's claim and explain whether the claim is accurate. [2]

Solutions

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