Q: Which of the following describes the end behavior of the polynomial $f(x) = -2x^4 + 5x^2 - 3$?

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

Q: A medical test result is modeled by the function $T(x) = \frac{100}{1 + e^{-0.5x}}$, where $x$ is the number of hours after administration. What is $T(0)$?

$T(0) = \frac{100}{1 + 1} = 50$

Q: Which of the following is the sum of the first 5 terms of the arithmetic sequence where $a_1 = 3$ and $d = 4$?

$a_1 + a_2 + a_3 + a_4 + a_5 = 3 + 7 + 11 + 15 + 19 = 55$

Q: A radioactive substance decays according to $N(t) = N_0 e^{-kt}$. If $N_0 = 200$ and $k = 0.1$, what is $N(10)$?

$N(10) = 200e^{-1} \approx 73.58$

Q: A quadratic function models the height $h$ (in meters) of a ball thrown upward as $h(t) = -4.9t^2 + 20t + 1.5$. What is the maximum height reached by the ball?

Maximum at $t = \frac{-b}{2a} = \frac{-20}{2 \times -4.9} \approx 2.04$; $h(2.04) \approx 21.98$ meters

Q: Which of the following is the sum of the infinite geometric series $\sum_{n=0}^{\infty} 5 \left(\frac{1}{3}\right)^n$?

$S = \frac{5}{1 - \frac{1}{3}} = \frac{5}{\frac{2}{3}} = 7.5$

Q: Which of the following is the correct expression for the sum of the first $n$ terms of an arithmetic sequence with first term $a_1$ and common difference $d$?

$S_n = \frac{n}{2}[2a_1 + (n-1)d]$

Question 1

Which of the following is the correct definition of the domain of a function $f(x)$?

Accepted Answer

The set of all possible input values $x$ for which $f(x)$ is defined.

Question 2

A pharmaceutical company models the concentration $C$ of a drug in the bloodstream over time $t$ (in hours) by the function $C(t) = 5e^{-0.3t}$. What is the concentration after 4 hours?

Accepted Answer

$C(4) = 5e^{-1.2} \approx 1.51$

Question 3

Which of the following is the inverse of the function $f(x) = 2x + 5$?

Accepted Answer

$f^{-1}(x) = \frac{x-5}{2}$

Question 4

A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population $P$ after $t$ hours?

Accepted Answer

$P(t) = 500 	imes 2^{t/3}$

Question 5

Which of the following is a solution to the quadratic equation $x^2 - 6x + 8 = 0$?

Accepted Answer

$x = 2$

Question 6

A car rental company charges a flat fee of $\$30$ plus $\$0.20$ per mile driven. Which function models the total cost $C$ for driving $m$ miles?

Accepted Answer

$C(m) = 30 + 0.20m$

Question 7

Which of the following describes the end behavior of the polynomial $f(x) = -2x^4 + 5x^2 - 3$?

Accepted Answer

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

Question 8

A chemical reaction follows the equation $A(t) = 100 - 20\ln(t+1)$, where $A$ is the amount of reactant left after $t$ minutes. How much reactant remains after 2 minutes?

Accepted Answer

$A(2) = 100 - 20\ln(3) \approx 78.03$

Question 9

Which of the following is the correct solution set for the inequality $x^2 - 4x < 0$?

Accepted Answer

$0 < x < 4$

Question 10

A medical test result is modeled by the function $T(x) = \frac{100}{1 + e^{-0.5x}}$, where $x$ is the number of hours after administration. What is $T(0)$?

Accepted Answer

$T(0) = \frac{100}{1 + 1} = 50$

Question 11

Which of the following is the sum of the first 5 terms of the arithmetic sequence where $a_1 = 3$ and $d = 4$?

Accepted Answer

$a_1 + a_2 + a_3 + a_4 + a_5 = 3 + 7 + 11 + 15 + 19 = 55$

Question 12

A system of equations is given by $\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$. What is the solution $(x, y)$?

Accepted Answer

$(x, y) = (2, 1)$

Question 13

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

Accepted Answer

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

Question 14

A radioactive substance decays according to $N(t) = N_0 e^{-kt}$. If $N_0 = 200$ and $k = 0.1$, what is $N(10)$?

Accepted Answer

$N(10) = 200e^{-1} \approx 73.58$

Question 15

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

Accepted Answer

$x = 32$

Question 16

A quadratic function models the height $h$ (in meters) of a ball thrown upward as $h(t) = -4.9t^2 + 20t + 1.5$. What is the maximum height reached by the ball?

Accepted Answer

Maximum at $t = \frac{-b}{2a} = \frac{-20}{2 	imes -4.9} \approx 2.04$; $h(2.04) \approx 21.98$ meters

Question 17

Which of the following is the sum of the infinite geometric series $\sum_{n=0}^{\infty} 5 \left(\frac{1}{3}\right)^n$?

Accepted Answer

$S = \frac{5}{1 - \frac{1}{3}} = \frac{5}{\frac{2}{3}} = 7.5$

Question 18

A matrix equation is given by $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 11 \end{bmatrix}$. What is the value of $x$?

Accepted Answer

$x = 1$

Question 19

Which of the following is the correct expression for the sum of the first $n$ terms of an arithmetic sequence with first term $a_1$ and common difference $d$?

Accepted Answer

$S_n = \frac{n}{2}[2a_1 + (n-1)d]$

College Algebra (MATH-1314) Course Overview and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards