Substitution into Expressions and Formulae
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Substitution into Expressions and Formulae — Free MYP2 Mathematics Practice Questions

1QuestionEvaluating Algebraic Formulas with Given ValuesConcept Practice
2 marks~3 minCriterion A
A rectangle has side lengths a=5a = 5 cm and b=3b = 3 cm. The perimeter of a rectangle is given by

P=2(a+b).P = 2(a + b).

Calculate the perimeter of this rectangle. [2]
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Solutions

2QuestionSubstituting Values into Simple ExpressionsAssessment Practice
4 marks~6 minCriterion C
A kayak rental company charges a flat fee of 25 dollars plus 10 dollars per half-hour (30-minute block). A student models the cost CC (in dollars) for hh hours as C=25+10hC = 25 + 10h.
a
Calculate the cost for a 3-hour booking using the student's formula. [1]
b
Calculate the actual cost for a 3-hour booking using the company's pricing structure. [1]
c
Compare the student's formula with the company's pricing structure for bookings of 2.5 hours and 3.5 hours. State which booking shows a difference and explain why. [2]
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Solutions

3QuestionSubstitution with Negative and Decimal ValuesAssessment Practice
6 marks~9 minCriterion D
A scientist uses the formula F=1.8C+32F = 1.8C + 32 to convert temperatures from Celsius to Fahrenheit. A thermometer has a systematic error (a fixed, consistent offset) of −2°C-2°\text{C}, meaning every reading is 2°C2°\text{C} lower than the true temperature. The scientist records −10°C-10°\text{C} in Antarctica.
a
Calculate the Fahrenheit value for the recorded temperature C=−10C = -10. Show your substitution clearly. [2]
b
The true temperature is −8°C-8°\text{C} after correcting for the error. Calculate the Fahrenheit value for the true temperature, then state the difference in Fahrenheit between your two results. [2]
c
The systematic error of −2°C-2°\text{C} was measured in a warm laboratory. Explain why this error value may not be reliable when the thermometer is used in Antarctica. [2]
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Solutions

4QuestionSubstituting Values into Simple ExpressionsAssessment Practice
4 marks~6 minCriterion B
Parity means whether a number is odd or even.
a
Complete the table by substituting n=1,2,3,4,5,6n = 1, 2, 3, 4, 5, 6 into 2n+12n + 1 and 3n3n. [1]

nn123456
2n+12n + 1\_\_\_\_\_\_\_\_\_\_\_\_
3n3n\_\_\_\_\_\_\_\_\_\_\_\_
b
Describe the parity pattern you see in each row of your table. [1]
c
n=10n = 10 is an even number. State whether 2(10)+12(10) + 1 and 3(10)3(10) are odd or even, then calculate both values to verify. [2]

Solutions

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