Podcast
Questions and Answers
What are natural numbers?
What are natural numbers?
What are whole numbers?
What are whole numbers?
What are integers?
What are integers?
What is absolute value?
What is absolute value?
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Is absolute value always positive?
Is absolute value always positive?
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|X| represents a _______ line.
|X| represents a _______ line.
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The symbol '=' represents a _______ line.
The symbol '=' represents a _______ line.
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What is the process when graphing an inequality?
What is the process when graphing an inequality?
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What is the elimination method in solving equations?
What is the elimination method in solving equations?
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What is the sum of cubes formula?
What is the sum of cubes formula?
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What is the difference of cubes formula?
What is the difference of cubes formula?
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What is the domain of a rational function?
What is the domain of a rational function?
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What is the process of dividing rational expressions?
What is the process of dividing rational expressions?
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What should you do before adding or subtracting rational expressions?
What should you do before adding or subtracting rational expressions?
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What is the method for simplifying a complex fraction?
What is the method for simplifying a complex fraction?
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What is long division of polynomials?
What is long division of polynomials?
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What does synthetic division of polynomials involve?
What does synthetic division of polynomials involve?
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What is the time word equation format?
What is the time word equation format?
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How do you express a fraction in radical notation?
How do you express a fraction in radical notation?
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What does it mean to rationalize the denominator?
What does it mean to rationalize the denominator?
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How can you eliminate a radical in an equation?
How can you eliminate a radical in an equation?
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What is the square root property?
What is the square root property?
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What does a negative radical number represent?
What does a negative radical number represent?
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What is the quadratic formula?
What is the quadratic formula?
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What do negative exponents indicate?
What do negative exponents indicate?
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Study Notes
Number Types
- Natural Numbers: Counting numbers starting from 1 (e.g., 1, 2, 3, ...).
- Whole Numbers: Non-negative integers including zero (e.g., 0, 1, 2, 3, ...).
- Integers: Whole numbers including their negatives (e.g., -3, -2, -1, 0, 1, 2, 3, ...).
Absolute Value
- Represents the distance from zero on a number line; always non-negative.
- Can be negative if preceded by a negative sign outside (e.g., |-1| is -1).
Inequalities
- When graphing inequalities, find the boundary line using the y-intercept and slope (rise/run).
- Perform a test using a point (usually (0,0)); if true, shade that side; if not, shade the opposite.
Elimination Method
- Used to solve systems of equations by removing one variable through addition or subtraction.
- Multiply equations if necessary to facilitate elimination.
Algebraic Identities
- Sum of Cubes: ( a^3 + b^3 = (a + b)(a^2 - ab + b^2) ).
- Difference of Cubes: ( a^3 - b^3 = (a - b)(a^2 + ab + b^2) ).
Rational Functions
- Domain: All real numbers except where the denominator is zero (e.g., ( { x | x \text{ is real, } x \not= 14, x \not= 2 } )).
- Dividing Expressions: Factor expressions, identify restricted values, convert to multiplication using the reciprocal.
Operations on Rational Expressions
- Adding/Subtracting: Factor first, find the Least Common Denominator (LCD), and adjust equations accordingly.
- Simplifying Complex Fractions: Multiply numerator and denominator by the least common multiple of all denominators.
Polynomial Division
- Long Division: Present problem as long division, ensuring all exponents are accounted for and solve akin to numerical division.
- Synthetic Division: Use the constant from the divisor; bring down the exponent and multiply until complete.
Time Word Problems
- Combine parts of two individuals to find the total, with time calculated based on the context of the question.
Radical Expressions
- Radical Notation: Understand the relationship between fractional exponents and radical notation (inside over outside).
- Rationalizing Denominators: Multiply fraction by another fraction equivalent to 1 to eliminate radicals in the denominator.
Solving Radicals
- Eliminate radicals by multiplying by the index, ensuring radicals are isolated before proceeding. Always remember to check solutions.
Square Root Property
- If ( a^2 = b ), then ( a = \pm \sqrt{b} ).
Quadratic Formula
- The solution of ( ax^2 + bx + c = 0 ) can be found using ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ).
Negative Exponents
- Move bases with negative exponents to the opposite part of the fraction, rewriting accordingly.
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Description
Test your knowledge of basic number types with these MAT-1033 flashcards. Covering natural numbers, whole numbers, integers, and absolute value definitions, this quiz is perfect for reinforcing foundational mathematical concepts. Perfect for students looking to solidify their understanding in mathematics.