Calculus and Absolute Value Quiz

Which of the following best describes the absolute value of a number?

The absolute value of a number can be negative.

What is the absolute value of -7?

The absolute value is denoted by the symbol | | which means ______.

Match the number with its absolute value:

According to the definition, if $a < 0$, then $|a|$ is equal to:

If $|x| = 0$, then $x$ must be equal to 0.

Absolute value describes the ______ of a number on the number line from the origin.

Which of the following topics are covered in the provided material?

The document includes information on advanced statistical analysis.

Who prepared the material in exam practice book?

Chapter 1 covers _________ /.

Match the chapter number with the corresponding topic:

Which of these topics is included in the 'Summery (sic) and the Formulas' section?

L'Hopital's Rule is covered in Chapter 10.

Name one application of calculus covered in the material.

Chapter 2 discusses 'The Relation between _________ and _________.

Which chapter discusses 'Rolle’s & Mean Theorem'?

What is the first step in solving the inequality $|4x - 3| \ge 5$?

When solving $|3x + 9| = |2x + 1|$, squaring both sides is a valid method to remove the modulus sign.

What are the critical values (CV) obtained when solving $|2x - 3| \ge |x + 3|$?

When solving $x + 6 > |3x + 2|$, the modulus sign can be addressed by ______ both sides.

Solve for $x$: $e^{2x+3} = 7$

What operation is performed to simplify $6 < 3 < 2$?

The solution to $ln(5-2x) = -3$ is approximately $x = 2.475$.

The solution to $|2x + 1| < 5$ is $x < 2$ or $x > -3$.

After rearranging the equation $(3x + 9)^2 = (2x + 1)^2$, what is the simplified quadratic equation before factoring?

Solve for $x$: $\frac{10}{1 + e^{-x}} = 2$

To solve $4 + 3^{x+1} = 8$, after transposing, you take the natural logarithm of both sides resulting in $(x+1)$ln(3) = ln(______).

Match each inequality with its corresponding solution:

Given $e^{2x} - 3e^x + 2 = 0$, which of the following are solutions for $x$?

The first step to solving $\log_3(7x + 3) = \log_3(5x + 9)$ is to exponentiate both sides using base 10.

Given $\log_2(5x + 7) = 5$, after exponentiating both sides with base 2 and simplifying, $x$ = ______

Match the logarithmic equation with the first step in solving for x:

The general solution for $\tan \theta = m$ is given by $\theta = RA + 2\pi k$, where $k \in \mathbb{Z}$ and $RA$ is the reference angle.

Which of the following should be added to the solution of $\theta$ when solving for $\sin \theta$?

When $\cos \theta = 0 $, the general solution can be written as $\theta = \frac{\pi}{2} + 2 \pi k$.

For $\tan \theta$, including $\tan \theta = 0$, add ________ to the solution.

If $\sin \theta = -m$, which of the following is a possible general solution for $\theta$?

Solve for $x$: $\sqrt{3} \tan x = 1$

For what values of $\sin \theta$ does the equation have NO solution?

If $\cos \theta = -m$, then $\theta = \cos^{-1}(-m) + 2\pi k = \pm RA + $ ______

Match the trigonometric function with what should be added to the solutions:

If $\tan \theta = -m$, then one possible solution can be $\theta = (\pi - RA) + \pi k$

Given the equation $\sin(3x + \frac{18}{5\pi}) = -\sin(\frac{9}{5\pi} - 2x)$, which of the following is a general solution for $x$?

The solutions $x = \frac{23\pi}{90}$, $x = \frac{59\pi}{90}$, $x = -\frac{13\pi}{90}$, $x = -\frac{49\pi}{90}$, $x = -\frac{17\pi}{18}$, and $x = -\frac{5\pi}{6}$ are valid solutions for the equation given.

What trigonometric identity is used to simplify the equation $4\cos^2 x + \sin 2x - 1 = 0$?

The equation $4\cos^2 x + \sin 2x - 1 = 0$ can be factorized into $(3\cos x - \sin x)(\sin x + \cos x) = $ ______.

What are the two general solutions obtained after simplification of $\sin(3x + \frac{18}{5\pi}) = \sin(2x - \frac{9}{5\pi})$?

Match the trigonometric expression with its equivalent form or result:

The only solutions to the equation $4\cos^2 x + \sin 2x - 1 = 0$ in the interval $0 \le x \le 2\pi$ can be found directly without any factorization or simplification.

If $x = -6 + 2\pi k$ is a solution to a trigonometric equation, what does $k$ represent?