Question 1

Evaluate $$4^2 - 2(3) + (6$$ \div 2)$$.

Accepted Answer

$$16 - 6 + 3 = 13$$

Question 2

Convert $$0.00053 to $$scientific notation.

Accepted Answer

$$5.3 	imes 10$$^{-4}$$

Question 3

Simplify $$3x^2y$$ - $$4x^2y$$ + $$5xy^2$$ - $$2xy^2.$$

Accepted Answer

$$-x^2y$$ + $$3xy^2$$

Question 4

Factor $$12x^2 - 15x$ completely.

Accepted Answer

$$3x(4x - 5)$$

Question 5

Solve for $$x$$: $$2(x + 1) + 12x = 5x + 23.$$

Accepted Answer

$$x = 2$$

Question 6

Simplify $$\dfrac{24x^5$}{18x^2$}.$$

Accepted Answer

$$\dfrac{4x^3$}{3}$$

Question 7

The length of a rectangle is 12 more than the width. The area of the rectangle is $$64 ft$^2. $$Find the length and the width.

Accepted Answer

Width = $$4 ft$$, Length = $$16 ft$$

Question 8

Solve for $$x$$: $$\dfrac{3}{x} = \dfrac{1}{2}.$$

Accepted Answer

$$x = 6$$

Question 9

Write the equation of the line passing through $$(1,2)$$ and $$(3,6).$$

Accepted Answer

$$y = 2x$$

Question 10

Solve the system of equations: $$x + y = 3$$, $$x - y = 1.$$

Accepted Answer

$$x = 2, y = 1$$

Question 11

Tickets for an amusement park cost $$10$$ each for adults and $$5$$ each for children. If $$90$$ tickets were sold and the total sales were $$720$$, how many adult tickets were sold?

Accepted Answer

$$48$$

Question 12

Simplify $$\dfrac{x^2$ - 9}{x^2$ - 6x + 9}.$$

Accepted Answer

$$\dfrac{x + 3}{x - 3}$$

Question 13

Solve for $$x$$: $$\dfrac{2x - 1}{3} = 5.$$

Accepted Answer

$$x = 7$$

Question 14

Paint town sold $$45$$ paintbrushes, one kind at $$8.50$$ each and another at $$7.25$$ each. In all, $$378.75$$ was taken in for the brushes. How many of each kind were sold?

Accepted Answer

$$25 at$$ $$8.50$$, $$20 at$$ $$7.25$$

Question 15

Which of the following is the solution to $$3x - 2y = 6$$ and $$x + y = 4$$?

Accepted Answer

$$(2,2)$$

Question 16

Simplify $$\dfrac{2x^2$ - 8}{4x}.$$

Accepted Answer

$$\dfrac{x - 2}{2}$$

Question 17

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$15$$

Question 18

Which of the following is the equation of a line with slope $$-\dfrac{3}{2}$$ passing through $$(0,4)$$?

Accepted Answer

$$y = -\dfrac{3}{2}x + 4$$

Question 19

Solve for $$x$$: $$\dfrac{5}{x} = 2.$$

Accepted Answer

$$x = 2.5$$

Question 20

Which of the following is the correct solution for $$x in$$ $$\dfrac{2x + 1}{3} = 5$$?

Accepted Answer

$$x = 7$$

College Algebra Final Exam Review: Key Concepts and Practice

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