Podcast
Questions and Answers
What are comparison symbols?
What are comparison symbols?
Symbols used to compare values
What is a set?
What is a set?
A collection of things, usually numbers when used in a mathematical way.
What does an open circle (○) on a graph mean?
What does an open circle (○) on a graph mean?
Don't include this value.
What does a closed circle (●) on a graph mean?
What does a closed circle (●) on a graph mean?
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What does it mean to find the absolute value of a number?
What does it mean to find the absolute value of a number?
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What is the notation used for absolute value?
What is the notation used for absolute value?
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What is a descriptive variable?
What is a descriptive variable?
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What are real numbers divided into?
What are real numbers divided into?
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What is a rational number?
What is a rational number?
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What is an irrational number?
What is an irrational number?
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In algebra, what does 'of' mean?
In algebra, what does 'of' mean?
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What does 'is' mean in story problems?
What does 'is' mean in story problems?
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What is the average?
What is the average?
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What is a rate?
What is a rate?
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Define algebra.
Define algebra.
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In algebra, you have to write the 1.
In algebra, you have to write the 1.
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Anything raised to the power of 0 equals 1.
Anything raised to the power of 0 equals 1.
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What does x⁻ⁿ equal?
What does x⁻ⁿ equal?
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Define a formula in mathematics.
Define a formula in mathematics.
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How many kilometers are in a mile?
How many kilometers are in a mile?
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What does it mean for a quantity to be proportional?
What does it mean for a quantity to be proportional?
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What is an analogy?
What is an analogy?
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What is rhetoric?
What is rhetoric?
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What is a scale factor?
What is a scale factor?
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What are the equivalent measures for 1 cm³?
What are the equivalent measures for 1 cm³?
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What is the product rule for exponents?
What is the product rule for exponents?
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What is the rule for the sum of complementary angles?
What is the rule for the sum of complementary angles?
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What is the sum of supplementary angles?
What is the sum of supplementary angles?
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What is the formula for converting Celsius to Fahrenheit?
What is the formula for converting Celsius to Fahrenheit?
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What do you call two line segments that intersect?
What do you call two line segments that intersect?
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What does bisect mean?
What does bisect mean?
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Study Notes
Mathematical Concepts
- Comparison Symbols: Used to compare values and establish inequalities.
- Set: A collection of distinct objects or numbers used mathematically.
- Open Circle (○): Indicates exclusion of a value on a graph or number line.
- Closed Circle (): Indicates inclusion of a value on a graph or number line.
Absolute Value
- Finding the Absolute Value: Absolute value is represented as |a|, meaning the distance from zero on a number line, regardless of sign.
- Absolute Value Definition: Enclosed by vertical bars, |a| signifies the non-negative value of a number.
Variables and Numbers
- Descriptive Variable: A letter or letters used in equations to represent specific quantities, making expressions more relatable.
- Real Number Chart: Real numbers can be split into rational (can be expressed as a ratio) and irrational (cannot be expressed as a ratio).
Rational and Irrational Numbers
- Rational Number: Can be expressed as a fraction; decimal form displays a repeating pattern.
- Irrational Number: Cannot be expressed as a fraction; decimal form is non-repeating and non-terminating.
Algebra Basics
- Algebra Definition: A method of solving equations using symbols and letters representing quantities.
- Coefficient: The numerical factor in a term, e.g., in 3x², the coefficient is 3.
- Like Terms: Terms that have the same variable factors and powers can be combined in algebraic expressions.
Algebraic Properties
- Additive Property of Equality: If a = b, then a + c = b + c holds true for any real numbers a, b, and c.
- Multiplicative Property of Equality: If a = b, then ac = bc for any real number c.
- Algebraic Subtraction: Can be expressed as a + (-b).
Geometry
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Perimeter: The total distance around a shape. Formulas include:
- Rectangle: 2(l + w)
- Square: 4s
- Circle: 2πr or πD
- Circumference: Distance around a circle.
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Triangle Properties:
- The sum of interior angles equals 180°.
- Opposite angles of equal sides are also equal.
Euclidean Geometry
- Axioms and Postulates: Basic assumptions in geometry, such as a unique line through two points and the equality of right angles.
Angles
-
Angle Relationships:
- Vertical angles formed by intersecting lines are equal.
- Complementary angles sum to 90°.
- Supplementary angles sum to 180°.
Temperature Conversion
- Temperature Formula: F = 1.8C + 32 establishes the relationship between Fahrenheit (F) and Celsius (C).
Probability
- Probability (P): Represents the likelihood of an event occurring, quantified as a fraction or decimal between 0 and 1.
Exchange Rates (2020)
- Values of the US dollar against several currencies include:
- 0.92 Euros (EU)
- 75.9 Rupees (India)
- 1.41 Dollars (Canada)
- 73.6 Rubles (Russia)
Additional Mathematical Concepts
- Scale Factor: A ratio that describes how a figure is enlarged or reduced proportionally.
- Polynomial Definition: An expression consisting of variables and coefficients combined using addition, subtraction, and multiplication.
Creativity and Discovery
- Inductive Reasoning: The process of recognizing patterns to formulate rules.
- Deductive Reasoning: Applying known rules to explore new situations.
- Creativity: The ability to generate original ideas and solutions.
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Description
This quiz focuses on key rules and definitions for the Shormann Prealgebra course. It includes terms like comparison symbols, sets, and the meanings of open and closed circles on graphs. Test your understanding and retention of these important concepts.