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

$x = 3$

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