Practice Test on Algebra and Powers
Chapter
Chapter 2
Section
Practice Test on Algebra and Powers
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Solutions 26 Videos

Sketch and label a representation for each of the following algebraic terms. Explain how your sketches are both alike and different.

a) y^2

b) m

c) m^3

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Q1

Jacqueline is making a quilt using finished squares like the one shown. Each square has an area of 310 cm^2.

a) Write an expression that represents the length of the side of the square in terms of its area.

b) Estimate the length. Describe the process you used.

c) Use a calculator to determine the correct length to two decimal places.

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Q2

Determine the approximate length of the roadway bordering the adjacent square properties.

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Q3

Simplify

\displaystyle 3^43^6

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Q4a

Simplify

\displaystyle \frac{(\frac{4}{5})^6}{(\frac{4}{5})^5}

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Q4b

Simplify

\displaystyle \frac{x^3x^6}{x}

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Q4c

Simplify

\displaystyle 6.1 (6.1^6)(6.1^5)(5^2)

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Q4d

Simplify

\displaystyle (-7)^4(-7^6)

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Q5

Simplify

a) \displaystyle (6^3)^2

b) \displaystyle (x^2)^5

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Q7ab

Simplify

\displaystyle (5x^4)^5

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Q7c

Simplify

\displaystyle [(\frac{2}{5})^4]^5

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Q7d

Simplify

\displaystyle (y^3)^2(y^5)^2

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Q7e

Simplify

\displaystyle (\frac{2}{x^2})^2

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Q7f

What is meant by “like terms”? Explain how algebra tiles or diagram? can help you to identify like terms.

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Q8

Simplify.

\displaystyle 5x - 2x

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Q9a

Simplify.

\displaystyle 7xy + 2xy

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Q9b

Simplify.

\displaystyle (3x^2 -5a) + (4x^2 -a)

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Q9c

Which expression below is equivalent to \displaystyle (y^2 + 5y) -(3y^2 -y) ?

A -2y^2 + 6y

B 4y^2 + 4y

C 2y^2 + 6y

D -2y^2 + 6y

E none of the above

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Q10

Expand.

\displaystyle 2)(x -3)

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Q11a

Expand.

\displaystyle 3x(4x^2 -5x)

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Q11b

Expand.

\displaystyle y^5(5y^4 + 3y^3 -y^2)

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Q11c

Expand and simplify.

\displaystyle 2(x -3) + 3(x + 2)

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Q12a

Expand and simplify.

\displaystyle 3(y^2 + y -2) - (y^2 + 2y + 4)

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Q12b

Expand and simplify.

\displaystyle 2x(3x -2) + x^2 + 0.2(x^2 + 3)

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Q12c

Mary and Bill are setting up a summer concession stand at the park. They need these jobs filled:

a) Determine a simplified algebraic expression to represent the weekly payroll for all 11 employees. Assume that they will always work at least 30 h per week.

b) Use your expression to determine the weekly payroll if each employee works 32 h per week.

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Q13

Determine an expression that simplifies to 3x^2 if the expression contains:

  • exactly two binomials
  • the distributive property used once
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Q14