Question 1

Simplify the expression $$\frac{3x^2$y^{-5}$$}{$$6x^{-3}y^2$}$$ using only positive exponents. Leave the answer in exponential notation.

Accepted Answer

$$\frac{x^5$}{2y^7$}$$

Question 2

Divide and simplify: $$\frac{m^8$n^7$$}{$$m^5n^4$}.$$

Accepted Answer

$$m^3n^3$

Question 3

A laptop originally costs $971. This is 30% off the original price. What was the original price?

Accepted Answer

$$1387.14$$

Question 4

Solve the system graphically: $$\begin{cases} x - y = 6 \ x + y = 10 \end{cases}$$

Accepted Answer

$$(8, 2)$$

Question 5

Solve the system using the elimination (addition) method: $$\begin{cases} x - 2y = 6 \ -4x - 2y = -26 \end{cases}$$

Accepted Answer

$$(2, -2)$$

Question 6

Solve the system using the substitution method: $$\begin{cases} y = -3x + 13 \ 2x + 9y = -8 \end{cases}$$

Accepted Answer

$$(2, 7)$$

Question 7

Find the $$y-$$intercept and slope for the function $$f(x) = -5 - 7x. $$Which of the following is correct?

Accepted Answer

Slope: $$-7$$, $$y-$$intercept: $$-5$$

Question 8

Which of the following graphs represents a function?

Accepted Answer

A graph where each $$x-$$value has only one $$y-$$value.

Question 9

Find a linear function whose graph has slope $$-3$$ and $$y-$$intercept $$(0, 7). $$Which equation is correct?

Accepted Answer

$$y = -3x + 7$$

Question 10

Solve the inequality $$4x + 3 \u003e 7. $$Write the solution in interval notation.

Accepted Answer

$$(1, \infty)$$

Question 11

A mixture contains peanuts at $$5 per pound and cashews at 8 $$per pound. If the mixture weighs 20 pounds and costs $6.50 per pound, how many pounds of peanuts should be used?

Accepted Answer

10 pounds

Question 12

Find the domain of the function $$f(x) = \sqrt{x-2}.$$

Accepted Answer

$$[2, \infty)$$

Question 13

Find the range of the function $$f(x) = x^2$ - 4.$$

Accepted Answer

$$[-4, \infty)$$

Question 14

If $$f(x) = -4x$$, find $$f(4).$$

Accepted Answer

$$-16$$

Question 15

Solve for $$x$$: $$2(x - 3) = 4x + 8.$$

Accepted Answer

$$x = -7$$

Question 16

Which of the following is the solution to $$|x - 2| = 5$$?

Accepted Answer

$$x = 7 or$$ $$x = -3$$

Question 17

Find the $$y-$$intercept for the equation $$y = 2x - 3.$$

Accepted Answer

$$(0, -3)$$

Question 18

Which of the following intervals represents all real numbers greater than or equal to $$-2$$?

Accepted Answer

$$[-2, \infty)$$

Question 19

If $$A = \{1, 2, 3, 4\}$$ and $$B = \{3, 4, 5, 6\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{3, 4\}$$

Question 20

Which of the following best describes the solution set for $$x^2 = 9$?

Accepted Answer

$$x = 3 or$$ $$x = -3$$

College Algebra Test Review Guidance

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