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Exam 12: Review of Basic Concepts and Skills

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Question 21

Multiple Choice

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Simplify the expression.

A) 4
B) -4
C) -8
D) not a real number

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Question 22

Multiple Choice

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Use a descriptive variable and an inequality symbol (<, >, $\ge$ , $\le$ ) to write a model for the statement. The Smith family will spend at least $16,500 on home improvements.

A) Let a represent the amount. a < $16,500.
B) Let a represent the amount. a $\le$ $16,500.
C) Let a represent the amount. a > $16,500.
D) Let a represent the amount. a $\ge$ $16,500.

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Question 23

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Rationalize the expression by building a perfect square root factor for the denominator.

Translate the phrase into an algebraic expression. seven less than twice a number

Write the polynomial in standard form and name the lead coefficient. -8x² + 3x³ + 1 + (-3x)

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x³ - 4x² - 4x + 16

Reduce to lowest terms.

Simplify the expression. Assume all variables represent non-negative real numbers.

Use the following to answer questions : -List all the numbers in the set that are elements of R.

The time it takes an object to fall a certain distance is given by the formula , where t is the time in seconds and s is the distance the object has fallen. Find how long it takes an object to hit the ground, if it is dropped from the top of a building that is 140 ft in height. Round answer to 2 decimal places.

Simplify the compound rational expression. Use either method.

Compute as indicated. Write final results in lowest terms.

Create the indicated algebraic expression. Use descriptive variables. The length of a rectangular lawn is 8 ft more than three times the width of the lawn. Express the length of the lawn in terms of the width.

Perform the operation indicated mentally or using pencil/paper.

Simplify by combining like terms. -8z - z - 4z

Simplify the expression using the quotient to a power property.

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x² + 17x + 70

Simplify the expression by rationalizing the denominator. State results in exact form.

Compute as indicated. Write your answer in lowest terms.

Factor using u-substitution. 36 + x⁴ - 13x²