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Algebra I Definition
Algebra I Definitions and formulas
| Question | Answer |
|---|---|
| Variable | A letter or symbol used to represent a number |
| Expression | A combination of variables, numbers, grouping symbols, and operational signs. |
| Whole numbers | Counting numbers plus zero. {0,1,2,3...} |
| What is another name for the counting numbers? | Natural numbers |
| List the set of counting numbers. | {1,2,3...} |
| What are integers? | Whole numbers and their opposites |
| List the set of integers | {...-3,-2,-1,0,1,2,3,...} |
| What are rational numbers? | Numbers that can be expressed as a/b where a and b are integers. |
| What is the value of a variable? | It is the number which replaces the variable. |
| 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 |
| What is a variable expression? | An expression that contains a variable. |
| what is a numerical expression? | An expression that names a particular number. 4 + 5 is a numerical expression. |
| What does "simplifying the expression" mean? | Replacing an expression by the simplest name for its value. 4 + 5 can be simplified to 9. |
| What does "evaluate mean"? | To substitute and then simplify |
| What is the substitution principal? | An expression maybe replaced by another expression that has the same value. |
| What is the formula for the perimeter of a rectangle? | P = 2L + 2W |
| What is the formula for the perimeter of a parallelogram? | P = 2a + 2b |
| What is the formula for the area of a circle? | A=πr^2 )(^ means "to the power") |
| What is the formula for the area of a trapezoid? | A = 1/2 h(a + b) |
| What is the formula for the area of a triangle? | A = 1/2 bh |
| What is the formula for the area of a rectangle? | A = lw |
| What is the formula for the perimeter of a triangle? | P = a + b + c |
| What is the formula for the surface area of a rectangular prism? | SA = 2(lw + wh + lh) |
| Open Sentence | Sentences that contain variables |
| Equation | Two expressions set equal to each other. |
| Domain | The set of numbers that a variable may represent |
| Solution | The value(s) of the variable that makes the equation a true statement |
| Solving | Finding the solution of an equation |
| Grouping symbol | A device used to enclose an expression that should be simplified first |
| How many solutions can an equation have? | None,one,or many |
| Solve | The process of finding the value of the variable that will make the open sentence true. |
| What is the distance formula? | d = rt where d = distance; r = rate; and t = time |
| What is the cost formula? | C = np where C = cost; n = number; and p = price |
| What is a formula? | An equation that states a rule about a relationship. |
| 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 |
| 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 |
| What is the formula for the surface area of a cylinder? | SA = 2πr^2 + 2πrh or SA = 2πr^2 + πdh where d = diameter. |
| What is the formula for the volume of a rectangular prism? | V = lwh |
| How do you find the diameter of a circle if you know the radius? | d = 2r |
| What is the formula for the area of a square? | A = s^2 |
| What is the formula for the perimeter of a square? | P = 4s |
| 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) |
| 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. |
| Origin | The zero point on a number line |
| Negative side | Points to the left of the origin |
| Positive side | Points to the right of the origin |
| Is zero positive or negative? | It is neither positive nor negative |
| Graph | A POINT paired with a number |
| Coordinate | A NUMBER that is paired with a point |
| To Graph is to _____________. | place a point on the number line |
| Inequality symbols | > Greater than < Less than |
| Opposites | Numbers that are the same distance from zero but on opposing sides of the origin |
| What is the opposite of 3? | -3 |
| What is the opposite of -5? | 5 |
| What is the opposite of zero? | Zero |
| Absolute Value | The distance a number is from the origin. |
| How do you read -X? | "The opposite of X" |
| What is the absolute value of -7? | 7 |
| What is the absolute value of 8? | 8 |
| What is the symbol for absolute value? | || |
| closure property | For all Real numbers a and b, a + b is a unique number and ab is a unique number |
| Commutative property of addition | For all real numbers a and b, a + b = b + a |
| Commutative property of multiplication | For all real numbers a and b, ab=ba |
| Associative property of addition | For all real numbers a, b, and c, (a + b) + c = a + (b + c) |
| Associative property of multiplication | For all real numbers a, b, and c, (ab)c - a(bc) |
| Terms | Expressions that are added together. 4 + 5 are terms. 3X + 5X are terms. |
| Factors | Expressions that are multiplied together. 4•3 are factors. 2X has two factors: 2 and X |
| Reflexive property of equality | For all real numbers a, a = a |
| Addition property of equality | if a = b, then a + c = b + c |
| Subtraction property of equality | if a = b, then a - c = b - c |
| Multiplication property of equality | if a = b, the ac = bc |
| Division property of equality | if a = b the a/c = b/c |
| Transform means to ______. | change |
| Equivalent equations | equations that have the same solution set |
| List 5 ways to transform an equation | Substitution, subtraction, addition, multiplication, and division |
| Inverse Operations | Operations that UNDO each other |
| What is the inverse operation of addition? | Subtraction |
| what is the inverse operation of division? | Multiplication |
| What is the cost formula? | Cost = number of items x price per item |
| What is the profit formula? | Profit = selling price - buying price |
| What is the income formula? | Income = wage per hour X number of hours worked |
| What is the total value formula? | Total value = value per item X number of items. |
| Property of opposite of a sum? | -(a + b) = -a + (-a) or -a - b |
| Property of opposite of a difference? | -(a - b)= -a + b |
| What is the definition of subtraction? | a - b = a + (-b) (To subtract you add the opposite) |
| Id property of addition | There is a unique number 0 such that for all a, a + 0 = a and 0 + a = a |
| Property of opposites | For every real number a, there is a unique number -a, such that a + (-a) = 0 and (-a) + a = 0 |
| Distributive property with respect to addition | a(b + b) = ab + ac |
| Distributive property with respect to subtraction | a(b - c) = ab - ac |
| Identity property of multiplication | There is a unique number 1, such that for every a 1 • a = a and a • 1 = a |
| Multiplicative property of zero | For every real number a, a • 0 = 0 and 0 • a = 0 |
| Multiplicative property of -1 | for every real number a, a(-1) = -a and (-1)a = -a |
| Property of opposites of products | (-a)(b) = -ab a(-b) = -ab (-a)(-b) = ab |
| Property of reciprocals | for every nonzero number a, there is a unique number 1/a such that a • 1/a = 1 |
| Property of the reciprocal of the Opposite of a number | for every nonzero a, 1/-a = -1/a |
| Property of the reciprocal of a product | 1/ab = 1/a • 1/b |
| Definition of division | a ÷ b = a • 1/b (To divide you multiply by the reciprocal.) |
| (a + b)/c = ? | a/c + b/c |
Created by:
barr04
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