Q: Which of the following is the correct graph for the function $y = \log_{10}(x)$?

A curve passing through $(1, 0)$ and increasing slowly for $x > 1$.

Question 1

Which of the following best describes the union of two sets $A$ and $B$?

Accepted Answer

The set of all elements that are in $A$, in $B$, or in both.

Question 2

Simplify the expression $\sqrt{50} + 2\sqrt{8}$.

Accepted Answer

$5\sqrt{2} + 4\sqrt{2} = 7\sqrt{2}$

Question 3

Which of the following is the correct solution to the equation $2x - 5 = 11$?

Accepted Answer

$x = 8$

Question 4

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

Accepted Answer

$1.5$ meters

Question 5

Which of the following is the correct definition of a function?

Accepted Answer

A relation where each input has exactly one output.

Question 6

Solve the system of equations: $\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$

Accepted Answer

$x = 3, y = 1$

Question 7

Which of the following is the correct solution to the inequality $3x - 4 > 8$?

Accepted Answer

$x > 4$

Question 8

If $f(x) = 2x^2 - 3x + 1$, what is $f(-2)$?

Accepted Answer

$f(-2) = 15$

Question 9

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

Accepted Answer

$x = 32$

Question 10

A chemical reaction follows the exponential decay model $N(t) = N_0 e^{-0.03t}$, where $N_0$ is the initial amount. What is $N(0)$?

Accepted Answer

$N_0$

Question 11

Which of the following is the correct simplification of $\frac{2x^2y}{4xy^2}$?

Accepted Answer

$\frac{x}{2y}$

Question 12

Solve for $x$: $|2x - 5| = 9$

Accepted Answer

$x = 7$ or $x = -2$

Question 13

Which of the following is the correct solution to the quadratic equation $x^2 - 6x + 9 = 0$?

Accepted Answer

$x = 3$

Question 14

A company’s profit $P$ (in dollars) is modeled by $P = 5x - 200$, where $x$ is the number of units sold. What is the break-even point?

Accepted Answer

$x = 40$

Question 15

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

Accepted Answer

$x = 4$

Question 16

If $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$, what is $A \cap B$?

Accepted Answer

$\{3, 4\}$

Question 17

Which of the following is the correct solution to the rational inequality $\frac{x-2}{x+1} > 0$?

Accepted Answer

$x > 2$ or $x < -1$

Question 18

Which of the following is the correct result of multiplying $(2 + 3i)(1 - 4i)$?

Accepted Answer

$14 - 5i$

Question 19

Which of the following is the correct graph for the function $y = \log_{10}(x)$?

Accepted Answer

A curve passing through $(1, 0)$ and increasing slowly for $x > 1$.

Question 20

A hospital tracks the number of bacteria in a sample using $N(t) = 500e^{0.2t}$. How many bacteria are present after $t = 5$ hours? (Round to the nearest whole number.)

Accepted Answer

$500e^{1}$, \approx 1359$

College Algebra Syllabus and Course Overview – Math 1111

Study Guide - Practice Questions

Study Guide - Flashcards