Q: A population of bacteria triples every 4 hours. If the initial population is $$200$$, which function models the population $$P(t)$$ after $$t$$ hours?

$$P(t) = 200 \times 3$$^{t/4}$$

Q: Which of the following best describes the end behavior of the polynomial $$f(x) = -3x^5$ + 2x^3$ - x + 7$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Question 1

A chemical reaction requires a solution with a pH that is a function of the concentration $$C of $$hydrogen ions, given by $$pH(C) = -\log_{10}(C). If $$the concentration of hydrogen ions is $$C = 1 	imes 10$$^{-5}$$ mol/L, what is the pH of the solution?

Accepted Answer

$$5$$

Question 2

Which of the following equations represents a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 3

A population of bacteria triples every 4 hours. If the initial population is $$200$$, which function models the population $$P(t)$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 200 	imes 3$$^{t/4}$$

Question 4

Which of the following is the solution set to the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 5

A quadratic function models the height $$h (in $$meters) of a ball thrown upward from a bridge as $$h(t) = -4.9t^2$ + 19.6t + 30. $$What is the maximum height reached by the ball?

Accepted Answer

$$49.6$$ meters

Question 6

Which of the following is the inverse of the function $$f(x) = 2x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{2}$$

Question 7

A pharmaceutical company needs to mix two solutions: one with $$20\%$$ concentration and one with $$50\%$$ concentration to obtain $$10$$ liters of a $$32\%$$ solution. How many liters of the $$50\%$$ solution should be used?

Accepted Answer

$$4$$ liters

Question 8

Which of the following statements is true about the function $$f(x) = x^4$ - 2x^2$ + 1$$?

Accepted Answer

$$f(x) is an $$even function

Question 9

Given the system of equations:

$$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$

What is the solution $$(x, y)$$?

Accepted Answer

$$(2, 1)$$

Question 10

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 11

A rational function $$f(x) = \frac{x^2$ - 9}{x^2$ - 4}$$ has which of the following vertical asymptotes?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 12

If $$f(x) = \sqrt{x - 1}$$ and $$g(x) = x^2$ + 1$$, what is the domain of the composite function $$f \circ g$$?

Accepted Answer

$$x \leq -1 or$$ $$x \geq 1$$

Question 13

Which of the following is equivalent to $$\log_2$(8x)$$ using logarithm properties?

Accepted Answer

$$3 + \log_2$(x)$$

Question 14

A quadratic equation $$ax^2 + bx + c = 0$ has a discriminant D$$ = $$b^2 - 4ac$. If D$$ \u003c 0$$, what can be said about the solutions?

Accepted Answer

There are two complex conjugate solutions

Question 15

Which of the following is the result of dividing $$2x^3$$ - $$3x^2 + 4x - 5$ by x - 2$ using synthetic division?

Accepted Answer

$$2x^2 + x + 6$ with a remainder of 7$

Question 16

Which of the following is the solution to the equation $$\sqrt{2x + 3} = 5$$?

Accepted Answer

$$x = 11$$

Question 17

A car depreciates in value according to the function $$V(t) = 20000 	imes (0.85)^t$$, where $$t is $$the number of years after purchase. What is the value of the car after $$3$$ years?

Accepted Answer

$$12206.25$$

Question 18

Which of the following is the correct solution to the equation $$2^{x+1} = 16$?

Accepted Answer

$$x = 3$$

Question 19

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

Accepted Answer

$$5$$

Question 20

Which of the following best describes the end behavior of the polynomial $$f(x) = -3x^5$ + 2x^3$ - x + 7$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

College Algebra Syllabus and Core Topics Overview

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