Question 1

Which of the following is the correct solution to the equation $$2x - 5 = 9$$?

Accepted Answer

$$x = 7$$

Question 2

A chemist mixes a solution that is 30% acid with another that is 50% acid to make 10 liters of a 40% acid solution. How many liters of the 30% solution should be used?

Accepted Answer

$$4$$ liters

Question 3

Which of the following is the graph of the equation $$y = -2x + 3$$?

Accepted Answer

A line with slope $$-2$$ and $$y-$$intercept $$3$$

Question 4

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

Accepted Answer

Question 5

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. If a customer is charged $$\65$, how many miles did they drive?

Accepted Answer

$$200$$ miles

Question 6

Which of the following is the solution set for the inequality $$3x - 7 \u003c 2x + 5$$?

Accepted Answer

$$x \u003c 12$$

Question 7

If the quadratic equation $$x^2 - 6x + 8 = 0$ models the height of a ball thrown upward, at what times does the ball reach the ground?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 8

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

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

Question 9

A population of bacteria triples every 4 hours. If the initial population is $$500$$, what will the population be after $$8$$ hours?

Accepted Answer

Question 10

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 3, y = 1$$

Question 11

A rectangle has a length that is 3 meters more than twice its width. If the perimeter is 36 meters, what is the width?

Accepted Answer

$$5$$ meters

Question 12

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x-4}$$?

Accepted Answer

All real numbers except $$x = 4$$

Question 13

If $$g(x) = \sqrt{x+2}$$, what is the range of $$g(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 14

A medical researcher is studying the decay of a drug in the bloodstream, modeled by $$C(t) = 100e$$^{-0.2t}$$, where C$ is the concentration in mg/L and t$ is time in hours. What is the concentration after 5 hours?

Accepted Answer

$$C(5) \approx 36.79 mg/L$$

Question 15

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

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 16

A quadratic function models the height $$h (in $$meters) of a projectile: $$h(t) = -4.9t^2$ + 20t + 1.5. $$After how many seconds does the projectile reach its maximum height?

Accepted Answer

$$t = 2.04$$ seconds

Question 17

Which of the following is the inverse of the function $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x - 7}{3}$$

Question 18

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit?

Accepted Answer

$$P = 20$$ thousand dollars

Question 19

Which of the following is the solution to the equation $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Math 120 College Algebra: 16-Week Course Structure and Key Topics

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