Algebra I Definitions and formulas
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| Variable | A letter or symbol used to represent a number
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| Expression | A combination of variables, numbers, grouping symbols, and operational signs.
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| Whole numbers | Counting numbers plus zero. {0,1,2,3...}
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| What is another name for the counting numbers? | Natural numbers
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| List the set of counting numbers. | {1,2,3...}
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| What are integers? | Whole numbers and their opposites
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| List the set of integers | {...-3,-2,-1,0,1,2,3,...}
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| What are rational numbers? | Numbers that can be expressed as a/b where a and b are integers.
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| What is the value of a variable? | It is the number which replaces the variable.
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| What is the value of an numerical expression? | The number named by the numerical expression. 4 + 6 = 10. 10 is the value of the expression 4 + 6
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| What is a variable expression? | An expression that contains a variable.
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| what is a numerical expression? | An expression that names a particular number. 4 + 5 is a numerical expression.
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| What does "simplifying the expression" mean? | Replacing an expression by the simplest name for its value. 4 + 5 can be simplified to 9.
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| What does "evaluate mean"? | To substitute and then simplify
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| What is the substitution principal? | An expression maybe replaced by another expression that has the same value.
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| What is the formula for the perimeter of a rectangle? | P = 2L + 2W
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| What is the formula for the perimeter of a parallelogram? | P = 2a + 2b
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| What is the formula for the area of a circle? | A=πr^2 )(^ means "to the power")
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| What is the formula for the area of a trapezoid? | A = 1/2 h(a + b)
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| What is the formula for the area of a triangle? | A = 1/2 bh
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| What is the formula for the area of a rectangle? | A = lw
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| What is the formula for the perimeter of a triangle? | P = a + b + c
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| What is the formula for the surface area of a rectangular prism? | SA = 2(lw + wh + lh)
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| Open Sentence | Sentences that contain variables
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| Equation | Two expressions set equal to each other.
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| Domain | The set of numbers that a variable may represent
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| Solution | The value(s) of the variable that makes the equation a true statement
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| Solving | Finding the solution of an equation
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| Grouping symbol | A device used to enclose an expression that should be simplified first
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| How many solutions can an equation have? | None,one,or many
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| Solve | The process of finding the value of the variable that will make the open sentence true.
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| What is the distance formula? | d = rt where d = distance; r = rate; and t = time
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| What is the cost formula? | C = np where C = cost; n = number; and p = price
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| What is a formula? | An equation that states a rule about a relationship.
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| What is the formula for the circumference of a circle? | c = π d where d is the diameter
c = 2πr where r is the radius
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| What is the formula for the volume of a cylinder? | V = πr^2h where h is the height of the cylinder and r is the radius
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| What is the formula for the surface area of a cylinder? | SA = 2πr^2 + 2πrh or SA = 2πr^2 + πdh where d = diameter.
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| What is the formula for the volume of a rectangular prism? | V = lwh
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| How do you find the diameter of a circle if you know the radius? | d = 2r
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| What is the formula for the area of a square? | A = s^2
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| What is the formula for the perimeter of a square? | P = 4s
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| What is the formula for the volume of a cone? | V = 1/3 π r^2 h ( A cone's volume is 1/3 that of a cylinder)
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| What is the volume of a pyramid? | V = 1/3 Bh where B is the area of the base of the pyramid. h is height of the pyramid.
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| Origin | The zero point on a number line
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| Negative side | Points to the left of the origin
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| Positive side | Points to the right of the origin
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| Is zero positive or negative? | It is neither positive nor negative
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| Graph | A POINT paired with a number
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| Coordinate | A NUMBER that is paired with a point
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| To Graph is to _____________. | place a point on the number line
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| Inequality symbols | > Greater than
< Less than
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| Opposites | Numbers that are the same distance from zero but on opposing sides of the origin
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| What is the opposite of 3? | -3
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| What is the opposite of -5? | 5
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| What is the opposite of zero? | Zero
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| Absolute Value | The distance a number is from the origin.
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| How do you read -X? | "The opposite of X"
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| What is the absolute value of -7? | 7
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| What is the absolute value of 8? | 8
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| What is the symbol for absolute value? | ||
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| closure property | For all Real numbers a and b, a + b is a unique number and ab is a unique number
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| Commutative property of addition | For all real numbers a and b, a + b = b + a
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| Commutative property of multiplication | For all real numbers a and b, ab=ba
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| Associative property of addition | For all real numbers a, b, and c, (a + b) + c = a + (b + c)
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| Associative property of multiplication | For all real numbers a, b, and c, (ab)c - a(bc)
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| Terms | Expressions that are added together. 4 + 5 are terms. 3X + 5X are terms.
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| Factors | Expressions that are multiplied together. 4•3 are factors. 2X has two factors: 2 and X
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| Reflexive property of equality | For all real numbers a,
a = a
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| Addition property of equality | if a = b, then a + c = b + c
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| Subtraction property of equality | if a = b, then a - c = b - c
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| Multiplication property of equality | if a = b, the ac = bc
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| Division property of equality | if a = b the a/c = b/c
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| Transform means to ______. | change
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| Equivalent equations | equations that have the same solution set
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| List 5 ways to transform an equation | Substitution, subtraction, addition, multiplication, and division
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| Inverse Operations | Operations that UNDO each other
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| What is the inverse operation of addition? | Subtraction
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| what is the inverse operation of division? | Multiplication
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| What is the cost formula? | Cost = number of items x price per item
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| What is the profit formula? | Profit = selling price - buying price
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| What is the income formula? | Income = wage per hour X number of hours worked
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| What is the total value formula? | Total value = value per item X number of items.
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| Property of opposite of a sum? | -(a + b) = -a + (-a) or -a - b
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| Property of opposite of a difference? | -(a - b)= -a + b
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| What is the definition of subtraction? | a - b = a + (-b)
(To subtract you add the opposite)
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| Id property of addition | There is a unique number 0 such that for all a, a + 0 = a and 0 + a = a
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| Property of opposites | For every real number a, there is a unique number -a, such that a + (-a) = 0 and (-a) + a = 0
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| Distributive property with respect to addition | a(b + b) = ab + ac
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| Distributive property with respect to subtraction | a(b - c) = ab - ac
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| Identity property of multiplication | There is a unique number 1, such that for every a 1 • a = a and a • 1 = a
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| Multiplicative property of zero | For every real number a, a • 0 = 0 and 0 • a = 0
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| Multiplicative property of -1 | for every real number a, a(-1) = -a and (-1)a = -a
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| Property of opposites of products | (-a)(b) = -ab
a(-b) = -ab
(-a)(-b) = ab
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| Property of reciprocals | for every nonzero number a, there is a unique number 1/a such that a • 1/a = 1
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| Property of the reciprocal of the Opposite of a number | for every nonzero a, 1/-a = -1/a
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| Property of the reciprocal of a product | 1/ab = 1/a • 1/b
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| Definition of division | a ÷ b = a • 1/b
(To divide you multiply by the reciprocal.)
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| (a + b)/c = ? | a/c + b/c
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