Question 1

A car is listed at $18,500. If a dealership offers a 15% discount, what is the final price of the car after the discount?

Accepted Answer

$ \$15,725 $

Question 2

Solve the equation $ 2(x+3) = 4x - 2 $ for $ x $.

Accepted Answer

$ x = 3 $

Question 3

Find the slope of the line that passes through the points $ (4, 5) $ and $ (8, 1) $.

Accepted Answer

$ m = -2 $

Question 4

A solution contains 20% copper. How much of this solution should be mixed with 300 ounces of an alloy that is 50% copper to get an alloy that is 30% copper?

Accepted Answer

$ 150 $ ounces

Question 5

Given the function $ f(x) = x^2 - 4x + 5 $, what is the vertex of the parabola?

Accepted Answer

$ (2, 1) $

Question 6

If $ y $ varies inversely as $ x $, and $ y = 10 $ when $ x = 4 $, what is the inverse variation equation?

Accepted Answer

$ y = \frac{40}{x} $

Question 7

A ball with a radius of $ 2 $ inches weighs $ 2.4 $ pounds. If the weight of a similar ball varies directly with the cube of its radius, what is the weight of a ball with a $ 3 $ inch radius?

Accepted Answer

$ 8.1 $ pounds

Question 8

Solve the system of equations using any method:
$ \begin{cases} 2x + y = 4 \ 3x - y = 7 \end{cases} $

Question 9

Simplify the expression $ (2x + 3)(x - 5) $.

Question 10

A city with a population of $ 500,000 $ is growing at a rate of $ 3\% $ per year. What will the population be in $ 12 $ years? (Round to the nearest person.)

Accepted Answer

$ 712,986 $

Question 11

Find the domain of the rational function $ f(x) = \frac{x+2}{x^2-9} $.

Accepted Answer

$ x 
eq -3, x 
eq 3 $

Question 12

Solve the quadratic equation $ x^2 - 4x + 4 = 0 $ using the square root property.

Accepted Answer

$ x = 2 $

Question 13

If the eighth term of an arithmetic sequence is $ 26 $ and the first term is $ 12 $, what is the common difference?

Accepted Answer

$ 2 $

Question 14

Simplify the expression $ \sqrt{50} $.

Accepted Answer

$ 5\sqrt{2} $

Question 15

Write the exponential equation for $ \log_2 x = 5 $.

Accepted Answer

$ x = 2^5 $

Question 16

A manufacturer needs to mix a solution that is $ 30\% $ acid. How many liters of $ 20\% $ acid solution must be mixed with $ 600 $ liters of $ 40\% $ acid solution to get the desired concentration?

Accepted Answer

$ 600 $ liters

Question 17

Find the inverse of the function $ f(x) = \frac{2x-2}{5} $.

Question 18

Solve the exponential equation $ 64^x = 16 $.

Accepted Answer

$ x = \frac{1}{3} $

Question 19

If $ y $ varies directly as $ x $, and $ y = 12 $ when $ x = 3 $, what is the constant of variation?

Accepted Answer

$ 4 $

Question 20

Find the sixth term of the geometric sequence whose first term is $ 5 $ and whose common ratio is $ 2 $.

Accepted Answer

$ 160 $

College Algebra Final Exam Review: Comprehensive Study Notes

Study Guide - Practice Questions

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