Q: A lottery has 5 winning tickets out of 1000. If you buy 2 tickets, what is the probability that both are winners (without replacement)?

$$\dfrac{5}{1000} \times \dfrac{4}{999}$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{2x - 8}$$?

Accepted Answer

$$x \geq 4$$

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

Given the function $$f(x) = 2x^2$ - 5x + 3$$, what is the $$y-$$intercept of its graph?

Accepted Answer

$$(0, 3)$$

Question 4

Which of the following is the inverse of the function $$f(x) = 5x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x + 7}{5}$$

Question 5

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = -2x^2$ + 12x + 20$$, where $$x is $$the number of units sold (in thousands). What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $$52$$ thousand dollars at $$x = 3$$ thousand units.

Question 6

Solve the system of equations using matrices:

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

Accepted Answer

$$x = 2,\ y = 1$$

Question 7

Which of the following is the sum of the first $$5$$ terms of the geometric sequence with $$a_1 = 2$ and r = 3$?

Accepted Answer

$$242$$

Question 8

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height $$h (in $$feet) after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t. At $$what time does the ball reach its maximum height?

Accepted Answer

$$t = 1$$ second

Question 9

Which of the following is equivalent to $$\log_2$(32) - \log_2$(4)$$?

Accepted Answer

$$3$$

Question 10

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

Accepted Answer

$$9$$

Question 11

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 12

A radioactive substance decays according to the formula $$A(t) = A_0$ e$$^{-0.03t}$$, where A_0$ is the initial amount and t$ is in years. What is the half-life of the substance (to the nearest year)?

Accepted Answer

$$23$$ years

Question 13

Which of the following is the solution set for the equation $$|2x - 5| = 9$$?

Accepted Answer

$$\left\{7, -2\right\}$$

Question 14

A quadratic equation has roots $$4$$ and $$-3. $$Which of the following is its equation?

Accepted Answer

$$x^2 - x - 12 = 0$

Question 15

Which of the following best describes the range of the function $$f(x) = \dfrac{1}{x - 2}$$?

Accepted Answer

$$(-\infty, \infty)$$ except $$0$$

Question 16

A lottery has 5 winning tickets out of 1000. If you buy 2 tickets, what is the probability that both are winners (without replacement)?

Accepted Answer

$$\dfrac{5}{1000} 	imes \dfrac{4}{999}$$

Question 17

Which of the following is the sum of the infinite geometric series $$3 + 1.5 + 0.75 + \ldots$$?

Accepted Answer

$$6$$

Question 18

If $$f(x) = \dfrac{2x + 1}{x - 3}$$, what is the vertical asymptote of $$f(x)$$?

Accepted Answer

$$x = 3$$

Question 19

A parabola opens upward and passes through the points $$(0, 2)$$, $$(1, 5)$$, and $$(2, 10). $$Which of the following is its equation?

Accepted Answer

$$y = x^2$ + 2x + 2$$

Question 20

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

Accepted Answer

$$x = 3$$

College Algebra (MATH-1314) Syllabus and Course Structure Study Guide

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