Question 1

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

Accepted Answer

$x = 2$ and $x = 3$

Question 2

A biologist models the population of bacteria with the exponential function $P(t) = 500e^{0.2t}$. What is the population after 5 hours?

Accepted Answer

$P(5) = 500e^{1} \approx 1359.14$

Question 3

Which of the following is the vertex of the quadratic function $f(x) = 2x^2 - 8x + 3$?

Accepted Answer

$(2, -5)$

Question 4

A company’s revenue $R$ (in thousands of dollars) is modeled by $R(x) = -3x^2 + 24x + 60$, where $x$ is the number of items sold (in thousands). What is the maximum revenue?

Accepted Answer

$R(4) = 108$ thousand dollars

Question 5

Which of the following is the correct solution to $|2x - 5| = 7$?

Accepted Answer

$x = 6$ or $x = -1$

Question 6

Given the system of equations: $\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$, what is the solution?

Accepted Answer

$x = 2$, $y = 1$

Question 7

Which of the following is the correct equation for the line of best fit given points $(1, 2)$, $(2, 4)$, and $(3, 6)$?

Accepted Answer

$y = 2x$

Question 8

A radioactive substance decays according to $A(t) = 100e^{-0.3t}$. How much remains after 10 hours?

Accepted Answer

$A(10) = 100e^{-3} \approx 4.98$

Question 9

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

Accepted Answer

$x = 21$

Question 10

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

$h(2.04) \approx 21.9$ meters

Question 11

Which of the following is the correct solution to the logarithmic equation $\log_{2}(x) = 5$?

Accepted Answer

$x = 32$

Question 12

A scientist uses the regression equation $y = 0.8x + 2$ to predict the concentration of a chemical. What is the predicted concentration when $x = 10$?

Accepted Answer

$y = 10$

Question 13

Which of the following is the correct solution to the equation $x^2 = 49$?

Accepted Answer

$x = 7$ or $x = -7$

Question 14

Given the matrix equation $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 11 \end{bmatrix}$, what is the value of $x$?

Accepted Answer

$x = 1$

Question 15

Which of the following is the correct solution to the radical equation $\sqrt{2x - 1} = 3$?

Accepted Answer

$x = 5$

Question 16

A population grows according to $P(t) = 200e^{0.05t}$. How long will it take for the population to double?

Accepted Answer

$t \approx 13.86$ years

Question 17

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

Accepted Answer

$x = 4$

Question 18

A quadratic equation $ax^2 + bx + c = 0$ has complex roots. Which condition must be true?

Accepted Answer

$b^2 - 4ac < 0$

Question 19

Which of the following is the correct solution to the system $\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 3$, $y = 2$

Question 20

Which of the following is the correct solution to the equation $e^{x} = 7$?

Accepted Answer

$x = \ln 7$

College Algebra I: Final Exam Review (Chapters 1, 6, 12)

Study Guide - Practice Questions

Study Guide - Flashcards