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Questions and Answers
What is the definition of a term in algebra?
What is the definition of a term in algebra?
What is the distributive property of algebra?
What is the distributive property of algebra?
What is the definition of a linear equation in algebra?
What is the definition of a linear equation in algebra?
What is the definition of a point in geometry?
What is the definition of a point in geometry?
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What is the definition of a congruent shape in geometry?
What is the definition of a congruent shape in geometry?
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What is the Pythagorean theorem in geometry?
What is the Pythagorean theorem in geometry?
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What is the definition of an angle in geometry?
What is the definition of an angle in geometry?
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What is the Ruler Postulate in geometry?
What is the Ruler Postulate in geometry?
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Study Notes
Algebra
Definitions
- Variable: a symbol that represents a value that can change
- Constant: a value that does not change
- Term: a constant or variable multiplied by a coefficient
- Expression: a group of terms combined using addition, subtraction, multiplication, and division
Operations
- Simplification: combining like terms to simplify an expression
- Distributive Property: a(b + c) = ab + ac
- FOIL Method: a method for multiplying two binomials
Equations and Inequalities
- Linear Equation: an equation in which the highest power of the variable is 1
- Quadratic Equation: an equation in which the highest power of the variable is 2
- Inequality: a statement that compares two expressions using <, >, ≤, or ≥
Functions
- Domain: the set of input values for a function
- Range: the set of output values for a function
- Function Notation: f(x) = output value
Geometry
Points, Lines, and Planes
- Point: a location in space, represented by a set of coordinates
- Line: a set of points extending infinitely in two directions
- Plane: a flat surface that extends infinitely in all directions
- Collinear: points that lie on the same line
- Coplanar: points that lie on the same plane
Angles and Measurements
- Angle: the measure of the amount of rotation between two lines or planes
- Degree: a unit of measurement for angles
- Right Angle: an angle of 90 degrees
- Straight Angle: an angle of 180 degrees
Properties of Shapes
- Perimeter: the distance around a shape
- Area: the amount of space inside a shape
- Congruent: shapes that have the same size and shape
- Similar: shapes that have the same shape but not necessarily the same size
Theorems and Postulates
- Pythagorean Theorem: a^2 + b^2 = c^2 for right triangles
- Ruler Postulate: the points on a line can be paired with real numbers
- Angle Addition Postulate: the sum of the measures of two adjacent angles is equal to the measure of their sum
Algebra
- Variables and Constants: Variables are symbols representing changing values, while constants are values that do not change.
- Terms and Expressions: Terms are constants or variables multiplied by coefficients, and expressions are groups of terms combined using addition, subtraction, multiplication, and division.
Operations
- Simplifying Expressions: Combining like terms to simplify an expression.
- Distributive Property: The rule a(b + c) = ab + ac applies when multiplying an expression by a single value.
- FOIL Method: A method for multiplying two binomials.
Equations and Inequalities
- Linear Equations: Equations with the highest power of the variable being 1.
- Quadratic Equations: Equations with the highest power of the variable being 2.
- Inequality Statements: Statements comparing two expressions using <, ≤, >, or ≥.
Functions
- Domain and Range: The domain is the set of input values, while the range is the set of output values.
- Function Notation: Representing a function as f(x) = output value.
Geometry
Points, Lines, and Planes
- Defining Points: Locations in space represented by a set of coordinates.
- Lines and Planes: A line is a set of points extending infinitely in two directions, while a plane is a flat surface extending infinitely in all directions.
- Collinear and Coplanar Points: Points that lie on the same line or plane.
Angles and Measurements
- Angles and Degrees: Angles measure the amount of rotation between two lines or planes, with degrees as the unit of measurement.
- Right and Straight Angles: Right angles measure 90 degrees, while straight angles measure 180 degrees.
Properties of Shapes
- Perimeter and Area: Perimeter is the distance around a shape, while area is the amount of space inside a shape.
- Congruent and Similar Shapes: Congruent shapes have the same size and shape, while similar shapes have the same shape but not necessarily the same size.
Theorems and Postulates
- Pythagorean Theorem: The rule a^2 + b^2 = c^2 applies to right triangles.
- Ruler Postulate: Points on a line can be paired with real numbers.
- Angle Addition Postulate: The sum of the measures of two adjacent angles equals the measure of their sum.
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Description
Get familiar with fundamental algebra concepts, including variables, constants, terms, and expressions. Learn about operations like simplification, distributive property, and the FOIL method.
