Q: A rectangle is 2 meters longer than it is wide. If the area is $$24\ \text{m}^2$$, what are the dimensions?

$$4\ \text{m} \times 6\ \text{m}$$

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

Accepted Answer

$$-x^2y$$ + $$5xy^2$$

Question 4

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

Accepted Answer

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

Question 5

Solve for $$x$$: $$2x + 3 = 11.$$

Accepted Answer

$$x = 4$$

Question 6

Which of the following is the equation of the line passing through $$(1,2)$$ and $$(3,6)$$?

Accepted Answer

$$y = 2x$$

Question 7

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

Accepted Answer

$$x = \dfrac{3}{5}$$

Question 8

Simplify $$\dfrac{2x^2$y}{4xy^2$}.$$

Accepted Answer

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

Question 9

A rectangle is 2 meters longer than it is wide. If the area is $$24\ 	ext{m}^2$$, what are the dimensions?

Accepted Answer

$$4\ 	ext{m} 	imes 6\ 	ext{m}$$

Question 10

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

Accepted Answer

$$x = 13$$

Question 11

Which of the following is the solution to the system: $$x + y = 3$$, $$x - y = 1$$?

Accepted Answer

$$(2, 1)$$

Question 12

Tickets for an amusement park cost $$10 each$$ for adults and $$5$$ each for children. If $$90$$ tickets were sold for a total of $$700$$, how many adult tickets were sold?

Accepted Answer

$$40$$

Question 13

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 14

Simplify $$\dfrac{3x^2$ - 12}{6x}.$$

Accepted Answer

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

Question 15

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

Accepted Answer

Question 16

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

Accepted Answer

$$x = 5$$

Question 17

Write the equation of the line with slope $$m = 2$$ passing through $$(1, 3).$$

Accepted Answer

Question 18

If $$a^2b^3$ \cdot ab^2$ = ?$

Accepted Answer

$$a^3b^5$

Question 19

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

Accepted Answer

$$x = 8$$

Question 20

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

Accepted Answer

$$x = 2, 3$$

College Algebra Final Exam Review: Key Concepts and Practice Problems

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