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

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

Q: Given the matrix $$A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$$ and $$B = \begin{pmatrix} 2 & 0 \\ 1 & 2 \end{pmatrix}$$, what is $$A + B$$?

$$ \begin{pmatrix} 3 & 2 \\ 4 & 6 \end{pmatrix} $$

Question 1

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 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

$$ x = 5, y = 1 $$

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

$$ x = 1, x = 5 $$

Question 6

A company’s profit $$P (in $$dollars) from selling $$x$$ units is modeled by $$P(x) = -2x^2$ + 40x - 100. $$What is the maximum profit?

Accepted Answer

$$ 300 $$

Question 7

Which of the following is equivalent to $$\log_2$ 32$$?

Accepted Answer

$$ 5 $$

Question 8

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

Accepted Answer

$$ 9 $$

Question 9

Which of the following describes the transformation of $$f(x) = x^2$ to g(x) = (x$$ - $$3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 10

Solve the inequality $$2x - 5 \u003e 7.$$

Accepted Answer

$$ x \u003e 6 $$

Question 11

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

Accepted Answer

$$ x = 3, x = -\frac{5}{3} $$

Question 12

Which of the following is the correct formula for the distance between points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$ \sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$} $$

Question 13

Which of the following is the correct property of logarithms for $$\log_b(MN)$$?

Accepted Answer

$$ \log_b(M) + \log_b(N) $$

Question 14

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-0.03t}$$. If the initial amount is 100$ grams, how much remains after 10$ years? (Round to the nearest gram)

Accepted Answer

$$ 74 $$

Question 15

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

Accepted Answer

$$ x = 4 $$

Question 16

Given the matrix $$A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$ and $$B = \begin{pmatrix} 2 & 0 \ 1 & 2 \end{pmatrix}$$, what is $$A + B$$?

Accepted Answer

$$ \begin{pmatrix} 3 & 2 \ 4 & 6 \end{pmatrix} $$

Question 17

Which of the following is the correct midpoint formula for points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$ \left( \frac{x_1$ + x_2$}{2}, \frac{y_1$ + y_2$}{2} \right) $$

Question 18

Which of the following is the solution to the equation $$\sqrt{x + 5} = 4$$?

Accepted Answer

$$ x = 11 $$

Question 19

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

Accepted Answer

$$ 6 $$

College Algebra (Math 103) Syllabus and Course Structure – HACC

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