Podcast
Questions and Answers
Given $x > 0$, simplify the expression $\frac{\sqrt{9x^2 - 4\sqrt{x^3}}}{3 - 4\sqrt{x}}$.
Given $x > 0$, simplify the expression $\frac{\sqrt{9x^2 - 4\sqrt{x^3}}}{3 - 4\sqrt{x}}$.
- $2x$
- $x$ (correct)
- $x\sqrt{x}$
- $-x$
Rationalize the denominator of the expression $\frac{3 - \sqrt{3}}{2 + \sqrt{3}} - 9$.
Rationalize the denominator of the expression $\frac{3 - \sqrt{3}}{2 + \sqrt{3}} - 9$.
- $-5\sqrt{3}$ (correct)
- $-2\sqrt{3}$
- $9\sqrt{3}$
- $5\sqrt{3}$
Determine the domain of the function $f(x) = \frac{2}{\sqrt{x - 5}} - 4$.
Determine the domain of the function $f(x) = \frac{2}{\sqrt{x - 5}} - 4$.
- $x > 5$ (correct)
- $x \le 5$
- $x < 5$
- $x \ge 5$
What is the derivative of the function $f(x) = x^{-2}$?
What is the derivative of the function $f(x) = x^{-2}$?
Solve for $x$ in the equation $\frac{1}{x-6} = \frac{3}{5x+1}$.
Solve for $x$ in the equation $\frac{1}{x-6} = \frac{3}{5x+1}$.
Find $\lim_{x \to 1} \frac{x-1}{\sqrt{x^2 - 1}}$.
Find $\lim_{x \to 1} \frac{x-1}{\sqrt{x^2 - 1}}$.
Solve for $x$ in the inequality $\frac{x}{3} + \frac{1}{6} \ge \frac{x}{2} + \frac{2}{3}$.
Solve for $x$ in the inequality $\frac{x}{3} + \frac{1}{6} \ge \frac{x}{2} + \frac{2}{3}$.
Solve for $x$ in the inequality $x^2 - 3x < 4$.
Solve for $x$ in the inequality $x^2 - 3x < 4$.
Amy charged $500 on her credit card, paid $100, then charged an additional $70. She was then charged 2% interest on her entire balance. How much interest was she charged?
Amy charged $500 on her credit card, paid $100, then charged an additional $70. She was then charged 2% interest on her entire balance. How much interest was she charged?
What is the average of the following numbers: 2, 4, 6, 8?
What is the average of the following numbers: 2, 4, 6, 8?
Flashcards
Simplifying Radical Expressions
Simplifying Radical Expressions
Simplify algebraic expressions involving radicals by factoring and applying the properties of radicals to combine like terms.
Rationalizing Denominators
Rationalizing Denominators
Rationalizing the denominator involves eliminating any radicals from the denominator of a fraction. This is typically done by multiplying the numerator and denominator by the conjugate of the denominator.
Domain of a Function
Domain of a Function
The domain of a function is the set of all possible input values (x-values) for which the function is defined. With square roots, ensure the expression inside the square root is non-negative.
Power Rule (Derivatives)
Power Rule (Derivatives)
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Solving Inequalities
Solving Inequalities
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Midpoint Formula
Midpoint Formula
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Number of Subsets
Number of Subsets
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Fraction of Work Remaining
Fraction of Work Remaining
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Average (Mean)
Average (Mean)
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Derivative of a constant
Derivative of a constant
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Study Notes
- The test duration is 60 minutes.
- Calculators are not allowed for use during the test.
- The test consists of twenty multiple-choice questions.
Question 1
- Requires simplification of the radical expression (√(9x²-4√x³))/(3-4√x), where x > 0.
- The answer is x.
Question 2
- Asks to rationalize the denominator of (3-√3)/(2+√3)-9.
- Yields -5√3.
Question 3
- Inquires about the domain of the function f(x) = 2/√(x-5)-4 .
- The domain is x > 5.
Question 4
- Asks for the derivative of f(x) = x⁻².
- -2x⁻¹ is the answer.
Question 5
- Requires solving for x in the equation 1/(x-6) = 3/(5x+1).
- The answer is 19/2.
Question 6
- Requires finding the limit as x approaches 1 of (x-1)/√(x²-1).
- The answer is 0.
Question 7
- Asks to solve for x in the inequality x/3 >= 1/3 + 2/3.
- x ≥ 3 is the answer.
Question 8
- Solve for x the inequality x² - 3x < 4.
- The range for x is -1 < x < 4.
Question 9
- Amy's initial balance was $500, paid $100. Later, she charged an additionall $70 and was charged 2% interest in total balance.
- The amount of interest charged as $9.40.
Question 10
- Asks for the average of the numbers 2, 4, 6, 8.
- The average is 5.
Question 11
- Jack's daily earnings varied: $50, $40, $30 (Wed), $30 (Thurs), and $100 on Friday.
- The variance of Jack's daily income is 850.
Question 12
- Given that A and B are independent events with P(A) = P(B) = 0.5, finds P(A ∪ B).
- P(A ∪ B) is 0.75.
Question 13
- The equation of the line with a slope of -5, passing through (0,8).
- y = -5x + 8 is the correct equation.
Question 14
- A lawn service operates within a 30-mile radius; the equation representing the service area with the office at (0,0).
- x² + y² = 900 is the equation.
Question 15
- Finding the midpoint of the segment connecting points A(-a, -b) and B(7a, -7b).
- The midpoint is (3a, -4b).
Question 16
- Finds the length of [TV] given the image.
- The length of [TV] is 11.
Question 17
- Finding the number of subsets for the set {a, b, c, d}.
- There are 16.
Question 18
- A contractor completes 2/9 of a job, another completes 1/3, find the unfinished fraction.
- The unfinished fraction of the job is 4/9.
Question 19
- A worker earns $4/hour for 40 hours, overtime is double. A $200 payment means finding overtime hours.
- He worked 5 hours of overtime.
Question 20
- Eric's bank statement details: $724.12 previous balance; $123.18 and $85.26 deposits, checks for $38.12 and $117.98, and a $15 service charge.
- The present balance is $761.46.
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