Question 1

Which of the following is the correct set notation for the union of sets $$A = \{1, 2, 3\}$$ and $$B = \{3, 4, 5\}$$?

Accepted Answer

$$A \cup B = \{1, 2, 3, 4, 5\}$$

Question 2

A chemical reaction requires the temperature $$T (in $$degrees Celsius) to satisfy the inequality $$2T - 10 \u003e 30. $$What is the minimum temperature required for the reaction to occur?

Accepted Answer

$$T \u003e 20$$

Question 3

Which of the following is the solution to the absolute value equation $$|x - 4| = 7$$?

Accepted Answer

$$x = 11 or$$ $$x = -3$$

Question 4

A business tracks its profit $$P$$ using the linear equation $$P = 500x - 2000$$, where $$x is $$the number of units sold. What is the break-even point?

Accepted Answer

$$x = 4$$

Question 5

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

Accepted Answer

$$x = 2, y = 3$$

Question 6

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

Accepted Answer

$$h = 22.4$$ meters

Question 7

Which of the following is the correct factorization of the polynomial $$x^2 - 5x + 6$?

Accepted Answer

$$(x - 2)(x - 3)$$

Question 8

A medical dosage is calculated using the formula $$D = \frac{mg}{kg}. If a $$patient weighs $$70 kg $$and the prescribed dosage is $$2 mg/kg$$, what is the total dosage?

Accepted Answer

$$140 mg$$

Question 9

Simplify the radical expression $$\sqrt{50} + \sqrt{18}.$$

Accepted Answer

$$5\sqrt{2} + 3\sqrt{2} = 8\sqrt{2}$$

Question 10

Which of the following is the correct solution to the quadratic equation $$x^2 - 4x - 5 = 0$?

Accepted Answer

$$x = 5 or$$ $$x = -1$$

Question 11

A population grows exponentially according to $$P(t) = 1000e$$^{0.05t}$$, where t$ is in years. What is the population after 10$ years?

Accepted Answer

$$P(10) = 1000e$$^{0.5}$$ \approx 1649$$

Question 12

Which of the following is the correct logarithmic form of the exponential equation $$2^x = 10$$?

Accepted Answer

$$x = \log_2$ 10$$

Question 13

A quadratic function $$f(x) = ax^2$ + bx + c$$ opens upward and has its vertex at $$(2, -3). $$Which statement is true?

Accepted Answer

$$a \u003e 0$$ and the minimum value is $$-3$$

Question 14

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

Accepted Answer

$$x = 32$$

Question 15

A car depreciates in value according to $$V = 20000(0.85)^t$$, where $$t is $$the number of years. What is the value of the car after $$3$$ years?

Accepted Answer

$$V = 20000(0.85)^3$ \approx 12251$$

Question 16

Which of the following is the correct solution to the rational equation $$\frac{2}{x} = 4$$?

Accepted Answer

$$x = 0.5$$

Question 17

A scientist mixes two solutions: one with $$30\%$$ salt and another with $$10\%$$ salt. How many liters of each should be mixed to obtain $$20$$ liters of a $$20\%$$ salt solution?

Accepted Answer

$$10$$ liters of each solution

Question 18

Which of the following is the correct simplification of the rational expression $$\frac{x^2$ - 9}{x + 3}$$?

Accepted Answer

$$x - 3$$

Question 19

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-0.1t}$$. If the initial amount is 100$ grams, how much remains after 20$ years?

Accepted Answer

$$N(20) = 100e$$^{-2}$$ \approx 13.53$$ grams

Question 20

Which of the following is the correct solution to the logarithmic equation $$\ln(x) = 2$$?

Accepted Answer

$$x = e^2$

College Algebra: Comprehensive Study Notes by Module

Study Guide - Practice Questions

Study Guide - Flashcards