Algebra 1 EOC: Number and Algebraic Methods
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Questions and Answers

What is absolute value?

The distance a number is from zero (y=|x|)

What is an algebraic expression?

Contains numbers, variables, and operations (no equal sign)

What is area?

The amount of space within a 2-dimensional figure

What is a binomial?

<p>An expression that contains two terms</p> Signup and view all the answers

What is a coefficient?

<p>The 'big' number in front of the variable</p> Signup and view all the answers

What is common difference?

<p>The constant difference between consecutive terms in a sequence</p> Signup and view all the answers

What is common ratio?

<p>The ratio of a term in a geometric sequence with the previous term (1:2 = 1/2)</p> Signup and view all the answers

What is a constant of variation?

<p>The 'k' value that remains the same in direct (y = kx) or inverse variation (xy = k)</p> Signup and view all the answers

What is a constant term?

<p>A term with no variable part; a value that stays the same (2x + 3 where 3 is the constant term)</p> Signup and view all the answers

What are coordinates?

<p>The ordered pair that represents a point (x, y)</p> Signup and view all the answers

What is the degree of a monomial?

<p>The sum of the exponents of the variables (degree = 5)</p> Signup and view all the answers

What is the degree of a polynomial?

<p>The greatest degree of the terms of a polynomial (degree = 5)</p> Signup and view all the answers

What is difference?

<p>The answer to subtraction</p> Signup and view all the answers

What is the distributive property?

<p>a(b + c) = ab + ac</p> Signup and view all the answers

What is an equation?

<p>Has an equal sign</p> Signup and view all the answers

What are equivalent expressions?

<p>Two expressions that are equal (3x + 5 = 2x - 6)</p> Signup and view all the answers

What does evaluate mean?

<p>To find the value of an expression by substituting a numbers in for the variables</p> Signup and view all the answers

What is an exponent?

<p>The 'little' number in a power (x)</p> Signup and view all the answers

What is a factor?

<p>An expression that is part of a product; (2x - 1) and (x - 1) are factors</p> Signup and view all the answers

What does it mean to factor completely?

<p>To factor a polynomial until all factors are prime</p> Signup and view all the answers

What is factoring?

<p>To find the factors of a polynomial; (2x-1)(x-1) is the factored form</p> Signup and view all the answers

What is a formula?

<p>An equation that can be used to find a specified value</p> Signup and view all the answers

What is a function?

<p>For every input (x) there is only one output (y); All the x-values have to be different.</p> Signup and view all the answers

What is function notation?

<p>Uses f(x) instead of y; f(x) = 3x + 5</p> Signup and view all the answers

What is a function rule?

<p>An expression that can be used to represent a functional set of data</p> Signup and view all the answers

What is the greatest common factor?

<p>The biggest term that can be divided into all terms</p> Signup and view all the answers

What is an inequality?

<p>Contains an inequality symbol</p> Signup and view all the answers

What are integers?

<p>Numbers that belong to the set... -3, -2, -1, 0, 1, 2, 3...</p> Signup and view all the answers

What are inverse operations?

<p>Opposite operations (+ and - or * and /)</p> Signup and view all the answers

What are irrational numbers?

<p>Numbers that cannot be written as a fraction</p> Signup and view all the answers

What is a leading coefficient?

<p>The coefficient of the first term when a polynomial is written so that the exponents decrease from left to right; 2 is the leading coefficient</p> Signup and view all the answers

What are like terms?

<p>Terms that have the same variable parts</p> Signup and view all the answers

What is a literal equation?

<p>An equation where letters are used to represent numbers (A=lw)</p> Signup and view all the answers

What is a monomial?

<p>A polynomial with only one term</p> Signup and view all the answers

What is a negative exponent?

Signup and view all the answers

What are opposites?

<p>Positive/negative; multiplication/division; addition/subtraction</p> Signup and view all the answers

What is the order of operations?

<p>Rules for evaluating an expression (PEMDAS)</p> Signup and view all the answers

What is a perfect square?

<p>A number that has a whole number square root; 1=1(1); 4=2(2); 9=3(3); 16=4(4)</p> Signup and view all the answers

What are perpendicular lines?

<p>Two lines that intersect at a 90 degree angle</p> Signup and view all the answers

What is a quotient?

<p>The answer to division</p> Signup and view all the answers

What is a ratio?

<p>The comparison of two numbers using division (6:4 or 6/4)</p> Signup and view all the answers

What are rational numbers?

<p>Numbers that can be expressed as a fraction (i.e: 1/3)</p> Signup and view all the answers

What are real numbers?

<p>The set of all rational and irrational numbers</p> Signup and view all the answers

What does simplify mean?

<p>To perform all indicated operations</p> Signup and view all the answers

What is a square root?

<p>b is the square root of b(b)</p> Signup and view all the answers

What is substitution?

<p>Used to solve a system of equations by substituting the expression for one variable in for that variable for the other equation</p> Signup and view all the answers

What is sum?

<p>The answer to addition</p> Signup and view all the answers

What are the terms of an expression?

<p>Parts of an expression separated by a + or - sign</p> Signup and view all the answers

What is a trinomial?

<p>A polynomial with three terms</p> Signup and view all the answers

What is a variable?

<p>A letter used to represent a number</p> Signup and view all the answers

What are whole numbers?

<p>The numbers 0, 1, 2,...</p> Signup and view all the answers

What is a zero exponent?

Signup and view all the answers

What is a zero term?

<p>The value before a function rule has been applied to the situation</p> Signup and view all the answers

What does prime mean?

<p>Is only divisible by 1 and itself</p> Signup and view all the answers

Study Notes

Key Concepts in Algebra

  • Absolute Value: Represents the distance of a number from zero on a number line, denoted mathematically as ( y = |x| ).

  • Algebraic Expression: Composed of numbers, variables, and operations, but does not hold an equal sign.

  • Area: Measures the amount of space enclosed within a two-dimensional shape.

  • Binomial: An algebraic expression containing exactly two distinct terms.

  • Coefficient: A numerical factor that multiplies a variable in an expression, often referred to as the "big" number.

  • Common Difference: The fixed amount added to each term in an arithmetic sequence, establishing a uniform gap between consecutive terms.

  • Common Ratio: The constant factor between consecutive terms in a geometric sequence, expressed as a ratio.

  • Constant of Variation: The constant value (denoted as ( k )) that remains unchanged in direct (e.g., ( y = kx )) or inverse variation (e.g., ( xy = k )) relationships.

  • Constant Term: A term in an expression that has no variable part, maintaining a specific value (e.g., in ( 2x + 3 ), the constant term is 3).

  • Coordinates: An ordered pair of numbers, usually represented as ( (x, y) ), defining a specific point on a coordinate plane.

  • Degree of a Monomial: Sum of the exponents in a term containing variables, indicating its overall degree.

  • Degree of a Polynomial: Determined by the highest degree among its constituent terms.

  • Difference: The result derived from performing subtraction between two quantities.

  • Distributive Property: A fundamental property of multiplication over addition, expressed as ( a(b + c) = ab + ac ).

  • Equation: A mathematical statement containing an equal sign, asserting the equality of two expressions.

  • Equivalent Expressions: Two expressions that yield the same value under all substitutions, demonstrated by an equality (e.g., ( 3x + 5 = 2x - 6 )).

  • Evaluate: The process of determining the value of an expression by substituting specific numbers for the variables.

  • Exponent: The small number in a power that indicates how many times the base is multiplied by itself.

  • Factor: An expression that, when multiplied together with others, forms a product (e.g., ( (2x - 1) ) and ( (x - 1) ) are factors).

  • Factor Completely: The act of breaking down a polynomial into its prime factors.

  • Factoring: The method of determining the factors of a polynomial, often rewriting it in its factored form.

  • Formula: A mathematical equation that provides a method to calculate a specific value.

  • Function: A relationship where each input has a single output, ensuring that no x-values repeat, although y-values can vary.

  • Function Notation: A method of representing functions using symbols, commonly denoted as ( f(x) ).

  • Function Rule: An expression that defines how output values are derived from input values in a function.

  • Greatest Common Factor (GCF): The largest term that can evenly divide all terms in a polynomial.

  • Inequality: A mathematical expression that features an inequality sign instead of an equal sign, representing non-equal relationships.

  • Integers: The set of whole numbers including negative numbers, zero, and positive numbers.

  • Inverse Operations: Pairs of operations that reverse each other's effects, such as addition and subtraction or multiplication and division.

  • Irrational Numbers: Numbers that cannot be expressed as a simple fraction, including many roots and specific decimal forms.

  • Leading Coefficient: The coefficient associated with the term of the highest degree in a polynomial, influencing its end behavior.

  • Like Terms: Terms that share the same variable parts, allowing for simplification through addition or subtraction.

  • Literal Equation: An equation in which letters symbolize numbers, commonly used to express mathematical relationships (e.g., ( A = lw )).

  • Monomial: A polynomial that consists of only one single term.

  • Negative Exponent: An exponent that indicates the reciprocal of the base raised to the opposite positive exponent.

  • Opposites: Refers to the reciprocal nature of mathematical operations, including positive/negative and addition/subtraction.

  • Order of Operations: A set of rules for simplifying mathematical expressions in a specific sequence, often remembered by the acronym PEMDAS.

  • Perfect Square: A number whose square root is an integer, such as ( 1, 4, 9, 16 ).

  • Perpendicular Lines: Lines that intersect at right angles, creating a 90-degree angle.

  • Quotient: The result obtained from dividing one number by another.

  • Ratio: A mathematical comparison between two quantities expressed through division, such as ( 6:4 ) or ( 6/4 ).

  • Rational Numbers: Numbers that can be expressed as a fraction of two integers, including terminating and repeating decimals.

  • Real Numbers: The complete set of all rational and irrational numbers, encompassing all number types.

  • Simplify: The process of executing all operations in an expression to reduce it to its simplest form.

  • Square Root: A number that produces a specified value when multiplied by itself.

  • Substitution: A method for solving equations by replacing a variable with an expression representing its value in other equations.

  • Sum: The final result obtained after performing addition on two or more numbers.

  • Terms of an Expression: Individual components of an expression that are separated by either addition or subtraction.

  • Trinomial: A polynomial consisting of three distinct terms.

  • Variable: A symbol, often a letter, utilized to stand in for an unknown value in mathematical expressions.

  • Whole Numbers: Non-negative integers that start from zero and increment upward (0, 1, 2, ...).

  • Zero Exponent: A mathematical principle where any non-zero base raised to the zero power equals one.

  • Zero Term: The output of a function rule when no operational adjustments have been applied.

  • Prime: A natural number greater than one that has no divisors other than one and itself.

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Test your knowledge with these flashcards covering key concepts in Algebra 1, specifically focusing on number and algebraic methods. Each card presents a term with its definition to help reinforce your understanding. Perfect for EOC exam preparation!

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