Substitution and Evaluation of Expressions
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Substitution and Evaluation of Expressions — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionMultiple Substitutions in Complex ExpressionsConcept Practice
2 marks~3 minCriterion A
A landscape architect is designing a triangular flower bed. The base of the triangle is b=(2x+3)b = (2x + 3) cm and the height is h=4yh = 4y cm, where xx and yy are positive integers determined by the available space.

The area of a triangle is A=12bhA = \dfrac{1}{2}bh.

When x=2x = 2 and y=1y = 1, calculate the area of the flower bed, in cm², showing all substitution steps. [2]
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Solutions

2QuestionSolving Word Problems with SubstitutionAssessment Practice
2 marks~3 minCriterion D
A local bakery calculates delivery cost using C=2n+5C = 2n + 5, where CC is the total delivery cost in dollars and nn is the number of items ordered. The fixed fee is 5 dollars; each item costs an additional 2 dollars.

Advise the bakery owner whether the formula C=2n+5C = 2n + 5 is fair for customers placing small orders. Support your advice with at least one calculation and justify a specific modification to the formula that would address any identified problem. [2]
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Solutions

3QuestionEvaluating with Negative Numbers and FractionsAssessment Practice
6 marks~9 minCriterion B
A signal-processing engineer models the attenuation (reduction in strength) of a radio signal at stage nn of a transmission network using the expression (n+1n)−1\left(n + \dfrac{1}{n}\right)^{-1}.

The first five values are:

(1+11)−1=12,(2+12)−1=25,(3+13)−1=310,(4+14)−1=417,(5+15)−1=526\left(1 + \frac{1}{1}\right)^{-1} = \frac{1}{2}, \quad \left(2 + \frac{1}{2}\right)^{-1} = \frac{2}{5}, \quad \left(3 + \frac{1}{3}\right)^{-1} = \frac{3}{10}, \quad \left(4 + \frac{1}{4}\right)^{-1} = \frac{4}{17}, \quad \left(5 + \frac{1}{5}\right)^{-1} = \frac{5}{26}
a
Deduce a general formula for the attenuation at stage nn, expressing your answer in the form nf(n)\dfrac{n}{f(n)}. [2]
b
Calculate the attenuation at stage 1010 using your formula. [2]
c
The engineer claims that the attenuation will never fall below 0.090.09 for any stage in this network (n≤12n \leq 12). Justify whether this claim is correct. [2]

Solutions

4QuestionMultiple Substitutions in Complex ExpressionsAssessment Practice
12 marks~18 minCriterion C
A structural engineer uses the following values to model load-bearing stress in a beam:

a=2,b=−3,c=12a = 2, \quad b = -3, \quad c = \tfrac{1}{2}
a
Evaluate 2a2−3b+4c2a^2 - 3b + 4c. [2]
b
Evaluate a3+b2c\dfrac{a^3 + b^2}{c}. [2]
c
The two expressions give different results. Justify which expression produces the greater stress value and explain how the structure of each expression — including the effect of negative values and division by a fraction — leads to that outcome. [8]

Solutions

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