Q: A chemist mixes two solutions: one with 30% acid and another with 50% acid. How many liters of each should be mixed to obtain 10 liters of a 42% acid solution?

4 liters of 30% solution and 6 liters of 50% solution

Q: A car’s value depreciates according to the function $V(t) = 20000(0.85)^t$, where $t$ is the number of years after purchase. What is the value of the car after 3 years?

$V(3) = 20000 \cdot (0.85)^3 = 20000 \cdot 0.6141 = 12282$

Question 1

Which of the following best describes the primary purpose of College Algebra as outlined in the course syllabus?

Accepted Answer

To foster mathematical modeling, problem-solving, and critical thinking skills with applications in real-world and non-STEM contexts.

Question 2

A biologist is modeling the population growth of a species using the function $P(t) = 500 \cdot 2^{0.3t}$, where $t$ is measured in years. What is the population after 5 years?

Accepted Answer

$P(5) = 500 \cdot 2^{1.5} = 500 \cdot 2.828 = 1414$

Question 3

Which of the following equations represents a line with a slope of $-3$ and a $y$-intercept of $4$?

Accepted Answer

$y = -3x + 4$

Question 4

A company’s profit $P$ (in thousands of dollars) is modeled by the quadratic function $P(x) = -2x^2 + 8x + 10$, where $x$ is the number of units (in thousands) produced. What is the maximum profit, and how many units should be produced to achieve it?

Accepted Answer

Maximum profit is $P(2) = -2(2)^2 + 8(2) + 10 = 18$ at $x = 2$ thousand units.

Question 5

Which of the following is the correct solution to the system of equations: $\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$?

Accepted Answer

$x = 2, y = 1$

Question 6

A radioactive substance decays according to the formula $A(t) = A_0 e^{-0.05t}$, where $A_0$ is the initial amount and $t$ is time in years. If $A_0 = 100$ grams, how much remains after 10 years? (Round to the nearest gram.)

Accepted Answer

$A(10) = 100 e^{-0.5} \approx 100 \cdot 0.6065 = 61$ grams

Question 7

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

Accepted Answer

It is a hyperbola with a vertical asymptote at $x = 2$ and a horizontal asymptote at $y = 0$.

Question 8

A student is analyzing the function $g(x) = 3x^2 - 12x + 7$. What are the coordinates of the vertex of this parabola?

Accepted Answer

$(2, -5)$

Question 9

If the probability of a machine failing on any given day is $0.02$, what is the probability that it will not fail over a 5-day work week?

Accepted Answer

$(1 - 0.02)^5 = 0.9039$

Question 10

Which of the following is the correct solution to the inequality $2x - 5 < 9$?

Accepted Answer

$x < 7$

Question 11

A chemist mixes two solutions: one with 30% acid and another with 50% acid. How many liters of each should be mixed to obtain 10 liters of a 42% acid solution?

Accepted Answer

4 liters of 30% solution and 6 liters of 50% solution

Question 12

Which of the following is the correct logarithmic form of the exponential equation $5^x = 125$?

Accepted Answer

$\log_5 125 = x$

Question 13

A car’s value depreciates according to the function $V(t) = 20000(0.85)^t$, where $t$ is the number of years after purchase. What is the value of the car after 3 years?

Accepted Answer

$V(3) = 20000 \cdot (0.85)^3 = 20000 \cdot 0.6141 = 12282$

Question 14

Which of the following is the correct solution set for the equation $|3x - 7| = 5$?

Accepted Answer

$x = 4, x = \frac{2}{3}$

Question 15

A student is using a graphing calculator to solve the equation $x^2 - 6x + 8 = 0$. What are the solutions?

Accepted Answer

$x = 2, x = 4$

Question 16

Which of the following best describes the end behavior of the function $f(x) = -2x^3 + 5x^2 - x + 7$ as $x 	o \infty$?

Accepted Answer

$f(x) 	o -\infty$

Question 17

A hospital administrator is scheduling nurses for shifts. If there are 6 nurses and 3 shifts to fill, how many different ways can the shifts be assigned if each nurse can work only one shift?

Accepted Answer

$6 	imes 5 	imes 4 = 120$

Question 18

Which of the following is the correct domain of the function $f(x) = \sqrt{x - 3}$?

Accepted Answer

$x \geq 3$

Question 19

A student is asked to solve the system of inequalities: $\begin{cases} y > 2x - 1 \ y \leq -x + 4 \end{cases}$. Which of the following points is in the solution set?

Accepted Answer

$(1, 3)$

College Algebra (Math 1710) – Course Structure, Topics, and Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards