Question 1

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

Accepted Answer

A function that can be expressed as the ratio of two polynomials, where the denominator is not zero.

Question 2

Given the polynomial $$f(x) = x^3$ - 4x^2$ + x + 6$$, which of the following is a possible rational root according to the Rational Root Theorem?

Accepted Answer

$$2$$

Question 3

Which of the following statements about the graph of $$y = \frac{1}{x} is $$true?

Accepted Answer

It has a vertical asymptote at $$x = 0$$ and a horizontal asymptote at $$y = 0.$$

Question 4

A hospital monitors the spread of a virus using the exponential function $$N(t) = N_0$ e$$^{kt}$$, where N_0$ is the initial number of cases. If the number of cases doubles every 3 days, what is the value of k$?

Accepted Answer

$$k = \frac{\ln 2}{3}$$

Question 5

Which of the following is the correct inverse of the function $$f(x) = 3x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 5}{3}$$

Question 6

A chemical reaction follows the law $$C(t) = C_0$ e$$^{-kt}$$, where C_0$ is the initial concentration. If after 10 minutes the concentration is half the original, what is the value of k$?

Accepted Answer

$$k = \frac{\ln 0.5}{10}$$

Question 7

Which of the following is NOT a property of logarithms?

Accepted Answer

$$\log_b(x + y) = \log_b x + \log_b y$$

Question 8

A ball is thrown upward and its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$24.4$$ meters

Question 9

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

Accepted Answer

$$x = 4$$

Question 10

Which of the following is the correct form of the Binomial Theorem for $$(a + b)^n$$?

Accepted Answer

$$(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a$$^{n-k}$$ b^k$$

Question 11

Which of the following is the correct solution to the trigonometric equation $$\sin x = \frac{1}{2}$$ for $$x in$$ $$[0, 2\pi]$$?

Accepted Answer

$$x = \frac{\pi}{6}, \frac{5\pi}{6}$$

Question 12

Which of the following is the correct equation for a circle with center $$(h, k)$$ and radius $$r$$?

Accepted Answer

$$(x - h)^2$ + (y - k)^2$ = r^2$

Question 13

A population of bacteria triples every 5 hours. If the initial population is $$100$$, what will the population be after $$10$$ hours?

Accepted Answer

$$900$$

Question 14

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

Accepted Answer

$$x = 3$$

Question 15

Which of the following is the correct expression for the sum of a geometric series with first term $$a$$ and common ratio $$r$$ ($$r 
eq 1) $$for $$n$$ terms?

Accepted Answer

$$S_n = a \frac{1 - r^n}{1 - r}$$

Question 16

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

Accepted Answer

$$x = 3, y = 2$$

Question 17

Which of the following is the correct domain of the function $$f(x) = \sqrt{x - 2}$$?

Accepted Answer

$$x \geq 2$$

Question 18

Which of the following is the correct value of $$\cos(\pi)$$?

Accepted Answer

$$-1$$

Question 19

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

Accepted Answer

$$x = 32$$

Precalculus Syllabus and Course Structure Overview

Guida di studio - Domande di pratica

Study guide - Flashcard