Question 1

Evaluate $$4^2 - 2(3) + (8 - 7$$)$$. What is the result?

Accepted Answer

$$9$$

Question 2

Convert $$0.00032 to $$scientific notation.

Accepted Answer

$$3.2 	imes 10$$^{-4}$$

Question 3

Simplify the expression: $$2x^2y$$ - $$3x^2y$$ + $$4xy^2$$

Accepted Answer

$$-x^2y$$ + $$4xy^2$$

Question 4

Factor the expression: $$x^2 - 9$

Accepted Answer

$$(x + 3)(x - 3)$$

Question 5

Solve for $$x$$: $$2x + 5 = 13$$

Accepted Answer

$$x = 4$$

Question 6

Which of the following is the solution to $$3x - 2 = 7$$?

Accepted Answer

$$x = 3$$

Question 7

A rectangle has a length that is $$2$$ meters more than its width. If the area is $$48 m$^2$$, what are the length and width?

Accepted Answer

Width $$= 6 m$$, Length $$= 8 m$$

Question 8

Simplify the expression: $$\dfrac{2x^3$y^2$$}{$$4x^2y$$}$

Accepted Answer

$$\dfrac{x y}{2}$$

Question 9

Solve for $$x$$: $$\sqrt{x + 1} = 3$$

Accepted Answer

$$x = 8$$

Question 10

Write the equation of the line passing through $$(1, 4)$$ and $$(3, 8).$$

Accepted Answer

$$y = 2x + 2$$

Question 11

Which of the following is the solution to the system of equations: $$x + y = 5$$ and $$x - y = 1$$?

Accepted Answer

$$(3, 2)$$

Question 12

A ticket for an amusement park costs $$10 for children and 15 $$for adults. If 100 tickets were sold for a total of $1300, how many tickets were sold for children?

Accepted Answer

$$70$$

Question 13

Simplify: $$\dfrac{3x^2$y}{6xy^2$}$$

Accepted Answer

$$\dfrac{x}{2y}$$

Question 14

If $$f(x) = 2x - 5$$, what is $$f^{-1}(x$$)$$, the inverse function?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x + 5}{2}$$

Question 15

Which of the following is the solution to $$2(x - 3) = x + 4$$?

Accepted Answer

$$x = 10$$

Question 16

If $$y$$ varies directly as $$x$$ and $$y = 12$$ when $$x = 3$$, what is $$y$$ when $$x = 5$$?

Accepted Answer

$$20$$

Question 17

Which of the following is the solution to $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 18

A painter uses 45 paintbrushes, one kind at $$8.50$$ each and another at $$7.25$$ each. If $$358.75$$ was spent in total, how many of the $$8.50$$ brushes were bought?

Accepted Answer

$$25$$

Question 19

Simplify: $$\dfrac{(2x^2$y^3)^2$}{4x^3$y}$$

Accepted Answer

$$x y^5$

College Algebra Final Exam Review: Key Concepts and Practice

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