Shormann Prealgebra Exam 2 Definitions

Questions and Answers

What are comparison symbols?

Symbols used to compare values

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?

Don't include this value.

What does a closed circle (●) on a graph mean?

Include this value. Signup and view all the answers

What does it mean to find the absolute value of a number?

Remove the sign if negative; |a| = |-a| = a. Signup and view all the answers

What is the notation used for absolute value?

Two vertical bars enclosing a number, like this: |a|. Signup and view all the answers

What is a descriptive variable?

A letter or letter and subscript that also means something. Signup and view all the answers

What are real numbers divided into?

Rational and irrational numbers. Signup and view all the answers

What is a rational number?

A number that can be written as a ratio of integers. Signup and view all the answers

What is an irrational number?

A number that cannot be written as a ratio of integers. Signup and view all the answers

In algebra, what does 'of' mean?

Multiply. Signup and view all the answers

What does 'is' mean in story problems?

Equal to. Signup and view all the answers

What is the average?

The sum of all values divided by the number of values. Signup and view all the answers

What is a rate?

A ratio of two measurements. Signup and view all the answers

Define algebra.

A generalization of arithmetic using letters to represent numbers. Signup and view all the answers

In algebra, you have to write the 1.

False Signup and view all the answers

Anything raised to the power of 0 equals 1.

True Signup and view all the answers

What does x⁻ⁿ equal?

1/xⁿ. Signup and view all the answers

Define a formula in mathematics.

An equation that uses symbols. Signup and view all the answers

How many kilometers are in a mile?

1 mile = 1.61 kilometers. Signup and view all the answers

What does it mean for a quantity to be proportional?

Having a constant ratio. Signup and view all the answers

What is an analogy?

Resemblance in some particulars between things otherwise unlike. Signup and view all the answers

What is rhetoric?

The art of speaking or writing effectively. Signup and view all the answers

What is a scale factor?

A number that scales or multiplies another number. Signup and view all the answers

What are the equivalent measures for 1 cm³?

1 cm³ = 1 mL. Signup and view all the answers

What is the product rule for exponents?

xⁿ · xᵐ = xⁿ⁺ᵐ. Signup and view all the answers

What is the rule for the sum of complementary angles?

The sum equals 90°. Signup and view all the answers

What is the sum of supplementary angles?

The sum equals 180°. Signup and view all the answers

What is the formula for converting Celsius to Fahrenheit?

F = 1.8C + 32. Signup and view all the answers

What do you call two line segments that intersect?

Vertical angles are equal. Signup and view all the answers

What does bisect mean?

To split something into two equal parts. Signup and view all the answers

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

Perimeter: The total distance around a shape. Formulas include:
- Rectangle: 2(l + w)
- Square: 4s
- Circle: 2πr or πD
Circumference: Distance around a circle.
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.