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Algebraic Fractions and Rational Expressions — Free MYP4 Mathematics (Extended) Practice Questions
1QuestionAlgebraic Fraction Word ProblemsConcept Practice
4 marks~6 minCriterion A
A water treatment plant monitors chemical concentration using the rational function
where is the concentration in milligrams per litre and is the time in hours after treatment begins. The safe upper limit for the chemical is .
where is the concentration in milligrams per litre and is the time in hours after treatment begins. The safe upper limit for the chemical is .
a
Calculate , simplifying your answer fully. [2]
b
Advise the plant operator whether the concentration at hours requires immediate action, justifying your answer with reference to the safe limit. [2]
Solutions
2QuestionAdding and Subtracting with Common DenominatorsAssessment Practice
4 marks~6 minCriterion D
A bakery models its average cost per batch of cupcakes (in dollars) using the expression
where 1200 dollars represents ingredient costs, 800 dollars represents labour costs, and is the number of batches produced.
where 1200 dollars represents ingredient costs, 800 dollars represents labour costs, and is the number of batches produced.
a
Simplify to a single rational expression. [1]
b
The bakery owner uses to decide how many batches to produce each week. Interpret this expression in the context of the bakery: explain what it reveals about cost behaviour, and advise the owner whether this model alone is sufficient to support production decisions. [3]
Solutions
3QuestionMultiplying and Dividing Algebraic FractionsAssessment Practice
4 marks~6 minCriterion C
A two-stage water filtration system removes contaminants at each stage. The fraction of contaminants removed by stage one is and by stage two is , where represents the initial contaminant level. The combined removal fraction is the product of the two stage fractions.
a
Deduce a simplified expression for the combined removal fraction after both stages. [1]
b
The initial contaminant level is . Calculate the combined removal fraction and interpret what this value means for the filtration system. [2]
c
A filtration engineer claims that this two-stage system is sufficient to meet a safety standard requiring a combined removal fraction greater than for all . Justify whether the engineer's claim is correct. [1]
Solutions
4QuestionAdding and Subtracting with Common DenominatorsAssessment Practice
6 marks~9 minCriterion B
A chemical engineer models the net concentration of a reagent in a reactor using the expression
where is temperature in °C and .
where is temperature in °C and .
a
Deduce the general rule for adding and subtracting algebraic fractions that share a common denominator . [2]
b
Apply your rule to simplify the expression above, showing all working. [3]
c
The reactor operates safely only when the net concentration expression yields a value greater than 30 for integer temperatures in the range . Justify whether the reactor operates safely across this entire range. [1]
Solutions
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