Questions and Answers
What are real numbers?
The set consisting of all rational and irrational numbers.
What are opposites in terms of numbers?
Numbers that are the same distance away from zero but on opposite sides of it.
What is the absolute value of a number?
The distance between the graph of a number and zero.
What is an algebraic expression?
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What does the commutative property state?
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What does the associative property state?
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What is the distributive property?
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What is a conjunction?
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What is a disjunction?
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What is a coordinate?
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What is the origin in a coordinate plane?
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What is a quadrant in a coordinate system?
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What is the slope of a line?
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What is standard form?
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What is point-slope form?
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What is a coefficient?
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What is slope-intercept form?
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What is a monomial?
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What is the degree of a polynomial?
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What is a function?
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What is a relation?
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What is a prime number?
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What is prime factorization?
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What is a rational expression?
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What is an extraneous root?
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What are like radicals?
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What is a rational number?
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What is an irrational number?
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What is a pure imaginary number?
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What is a complex number?
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What is the quadratic formula?
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What is the discriminant?
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What is a parabola?
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What is a vertex?
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What is a dividend?
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What is a divisor?
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What is the division algorithm?
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Study Notes
Real Numbers
- Include both rational (fractions, integers) and irrational numbers (non-repeating decimals).
Opposites
- Defined as numbers equidistant from zero but located on opposite sides of the number line.
Absolute Value
- Represents the distance from zero on the number line, always positive.
Algebraic Expression
- Combinations of numbers, variables, and operational symbols (sum, difference, product, quotient).
Commutative Property
- In both addition and multiplication, order of operations does not affect the result.
Associative Property
- For addition and multiplication, how numbers are grouped does not change the outcome.
Distributive Property
- Multiplication can be distributed across addition, facilitating simplification of expressions.
Conjunction
- A logical statement formed by combining two statements with "and".
Disjunction
- A logical statement formed by combining two statements with "or".
Coordinate
- An ordered pair (x, y) representing a specific point in the xy-coordinate plane.
Origin
- The point of intersection for the x and y axes, denoted as (0,0).
Quadrant
- The coordinate plane is divided into four regions by the intersecting axes.
Slope of a Line
- Measures how steep a line is, calculated as the ratio of vertical change to horizontal change.
Standard Form
- Represents a linear equation in the form Ax + By = C.
Point-Slope Form
- Format for linear equations expressed as y - Y = M(x - X), capturing slope and a point on the line.
Coefficient
- The numerical factor that multiplies a variable in an algebraic term.
Slope-Intercept Form
- Linear equations expressed as y = mx + b, where m is the slope and b is the y-intercept.
Monomial
- A single term that can be a constant, variable, or a product of constants and variables.
Degree of a Polynomial
- Identifies the highest degree among the terms in a polynomial after simplification.
Function
- A relation where each input has a unique output, ensuring no repeated first coordinates.
Relation
- A set of ordered pairs that can represent various mathematical relationships.
Prime Number
- An integer greater than one with no divisors other than one and itself.
Prime Factorization
- The process of breaking down a positive integer into a product of prime numbers.
Rational Expression
- An algebraic expression that can be simplified into a quotient of two polynomials.
Extraneous Root
- A solution to a modified equation that does not satisfy the original equation.
Like Radicals
- Radicals that share the same index and radicand, permitting direct addition or subtraction.
Rational Number
- Any number that can be expressed as a fraction or ratio of two integers.
Irrational Number
- A number that cannot be expressed as a simple fraction, characterized by infinitely non-repeating decimals.
Pure Imaginary Number
- A complex number exclusively of the form bi, where b is a real number.
Complex Number
- A number expressed in the form a + bi, combining a real part (a) and an imaginary part (bi).
Quadratic Formula
- The solution for quadratic equations in the standard form ax² + bx + c = 0.
Discriminant
- Calculated as b² - 4ac, helps determine the nature and number of roots of a quadratic equation.
Parabola
- The graph representation of a quadratic equation characterized by the form y - k = a(x - h)².
Vertex
- The highest or lowest point of a parabola, identified as the point (h, k).
Dividend
- The quantity that is being divided in a division operation.
Divisor
- The quantity by which another quantity is divided during the division process.
Division Algorithm
- Describes the relationship: Dividend = Quotient × Divisor + Remainder.
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Test your understanding of key vocabulary in Algebra 2 Honors. This quiz includes definitions of important terms such as real numbers, opposites, absolute value, and algebraic expressions. Perfect for students looking to reinforce their algebra vocabulary skills.