Algebraic Simplification and Expansion
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Algebraic Simplification and Expansion — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionSimplifying Like TermsConcept Practice
2 marks~3 minCriterion C
A landscape architect is designing a triangular garden bed. The three side lengths are 2x2x cm, 3x3x cm, and 4x4x cm, and the perimeter of the garden bed is 36 cm.
a
Calculate the value of xx. [1]
b
The architect states: "The longest side of this garden bed exceeds half the perimeter, so the design is impractical." Justify whether this statement is correct, supporting your answer with calculations. [1]
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Solutions

2QuestionExpanding Double Brackets BinomialsAssessment Practice
10 marks~15 minCriterion D
A concert venue has a maximum capacity of 4000 seats. When the ticket price is 50 dollars, 2000 people are expected to attend. Market research shows that for every 2 dollar decrease in ticket price, 120 more people are expected to attend.

Let xx represent the number of 2 dollar decreases in ticket price.

Revenue is modelled by R(x)=(50−2x)(2000+120x)R(x) = (50 - 2x)(2000 + 120x).
a
Expand and simplify R(x)R(x) into the form R(x)=ax2+bx+cR(x) = ax^2 + bx + c. [2]
b
Deduce the value of xx that maximises revenue, and hence find the corresponding ticket price. [3]
c
The venue manager claims that the model predicts a maximum revenue above 105 000 dollars. Assess whether this claim is correct, and explain one reason why the model may not reflect actual revenue at this ticket price. [5]
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Solutions

3QuestionExpanding Double Brackets BinomialsConcept Practice
2 marks~3 minCriterion A
A garden designer plans a rectangular patio with side lengths (x+3)(x + 3) m and (x+5)(x + 5) m, where x>0x > 0. The rectangle is divided into four smaller rectangles by splitting each side at the integer term.
a
Show that the total area of the patio can be written as x2+8x+15x^2 + 8x + 15. [1]
b
The designer has 40 m² of paving material available. Given that x=2x = 2, advise the designer whether the available material is sufficient to complete the patio. [1]
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Solutions

4QuestionSimplifying Expressions with Multiple TermsAssessment Practice
6 marks~9 minCriterion B
A sound engineer balances two audio channels using the expression a(x+y)+b(x−y)a(x+y)+b(x-y), where aa and bb are integer gain values and xx, yy represent signal inputs.
a
Expand and simplify each expression. State the coefficient of xx and the coefficient of yy. [2]

a=2, b=3a=2,\ b=3: 2(x+y)+3(x−y)\quad 2(x+y)+3(x-y)

a=4, b=1a=4,\ b=1: 4(x+y)+1(x−y)\quad 4(x+y)+1(x-y)

a=5, b=2a=5,\ b=2: 5(x+y)+2(x−y)\quad 5(x+y)+2(x-y)

a=3, b=5a=3,\ b=5: 3(x+y)+5(x−y)\quad 3(x+y)+5(x-y)
b
Deduce a general rule for the coefficient of xx and the coefficient of yy in the simplified form of a(x+y)+b(x−y)a(x+y)+b(x-y). Justify your rule using the distributive property. [2]
c
A new channel setting uses a=7a=7 and b=4b=4. The engineer needs the coefficient of yy to be positive to avoid phase cancellation. Use your rule to predict the simplified form of 7(x+y)+4(x−y)7(x+y)+4(x-y), then advise the engineer whether this setting should be approved for use. [2]

Solutions

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