Question 1

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

Accepted Answer

A function that can be written as $$f(x) = a_nx^n + a$$_{n-1}$$x^{n-1}$$ + \ldots + a_1x + $$a_0$$, where $$n is a $$positive integer and $$a_n 
eq 0$.

Question 2

A chemical reaction's rate $$R is $$modeled by the quadratic equation $$R = -2t^2$ + 8t + 5$$, where $$t is $$time in seconds. What is the maximum rate, and at what time does it occur?

Accepted Answer

Maximum rate is $$13 at$$ $$t = 2$$ seconds.

Question 3

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

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 4

A hospital tracks the number of patients $$P$$ admitted each day using the linear equation $$P = 12d + 30$$, where $$d is $$the number of days since the start of the month. How many patients are admitted on day 5?

Accepted Answer

$$P = 90$$

Question 5

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x + 3)(x - 3)$$

Question 6

A company’s profit $$P in $$thousands of dollars is modeled by $$P(x) = -4x^2$ + 40x - 36$$, where $$x is $$the number of units sold (in thousands). What is the number of units sold that maximizes profit?

Accepted Answer

$$x = 5$$

Question 7

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

Accepted Answer

$$x = 2$$, $$y = 3$$

Question 8

A ball is thrown upward and its height $$h in $$meters after $$t$$ seconds is given by $$h = -5t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22$$ meters

Question 9

Which of the following is the correct solution for $$\frac{2x}{x-1} = 4$$?

Accepted Answer

Question 10

A biologist models the population of bacteria by $$N(t) = 500e$$^{0.2t}$$, where t$ is time in hours. What is the population after 5$ hours?

Accepted Answer

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

Question 11

Which of the following is the correct solution to the quadratic equation $$3x^2 - 12x + 9 = 0$?

Accepted Answer

Question 12

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 25 + 0.20m$$

Question 13

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

Accepted Answer

$$x - 2$$

Question 14

A student invests $$\1000$ in an account that earns 5$$\%$$ annual interest, compounded yearly. What is the amount after 3$ years?

Accepted Answer

$$1000(1.05)^3$$ \approx \$$1157.63$

Question 15

Which of the following is the correct solution to $$|2x - 3| = 7$$?

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 16

A rectangular garden has a length that is $$3$$ meters longer than its width. If the area is $$40$$ square meters, what are the dimensions of the garden?

Accepted Answer

Width $$= 5 m$$, Length $$= 8 m$$

Question 17

Which of the following is the correct solution to $$x^2 + 4x + 4 = 0$?

Accepted Answer

$$x = -2 ($$double root)

Question 18

A pharmacist needs to mix a $$10\%$$ saline solution with a $$30\%$$ saline solution to get $$100 mL of a$$ $$25\%$$ solution. How much of the $$10\%$$ solution should be used?

Accepted Answer

$$25 mL$$

Question 19

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

Accepted Answer

$$x = 32$$

College Algebra Syllabus and Study Guide Overview

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드