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Algebra 2H Ch 1.
Formulas and Vocabulary
| Term | Definition or Example or Formu | |
|---|---|---|
| Recipriocal | Multiplicative Inverse; if b then 1/b (Definition of Division) | |
| Numerical Expression | Consists of numbers, operations, and grouping symbols. | |
| Power | An expression formed by repeated multiplication of the same factor. Consists of an exponent and a base. | |
| Exponent | Represents the number of times the base is used as a factor. | |
| Base | The number in a power. | |
| Variable | A letter that is used to represent one or more numbers. | |
| Algebraic Expression | An expression involving variables is called an algebraic expression. You evaluate the algebraic expression when you simplify. | |
| Term | The parts of an expression that can be written as a sum added together is called a term. | |
| Variable Term | A term that has a variable term is called a variable term. | |
| Constant Term | A term that has no variable part is called a constant term. | |
| Coefficient | When a term is a product of a number and a power of a variable, the number is called the coefficient of a power; the number in front of the variable. | |
| Like Terms | Terms that have the same variable parts. (Including the variable and the exponent, but not the coefficient) | |
| Equivalent Expressions | Two algebraic expressions if they have the same value for all values of their variables. | |
| Identity | A statement that equates equates two equivalent expressions. | |
| Equation | A statement that two expressions are equal. | |
| Linear Equation | An equation that has one variable and can be written in the form ax+b=0 where a and b are constants and a cannot equal zero. | |
| Solution of an Equation | A number that if substituted for the variable results in a true statement. | |
| Equivalent Equation | Two equations if they have the same solutions. | |
| Additive 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 and c is not 0, then a*c=b*c | |
| Division Property of Equality | If a=b and c is not 0, then a/c=b/c | |
| Real Numbers | (R)Any number that is R | |
| Rational Numbers | (Q) Any number that is terminating or repeating decimal | .5(Terminating), -3/4, .1212(Repeating) 9 |
| Irrational Numbers | (I) Any number that is a non-terminating and non repeating decimal | Root 2, Root 3, Root 5, Pie, -3.164916495164958(Pattern Decimal) |
| Integers | (Z)Whole numbers both negative and positive | (Infinite Set) -2,0,1 |
| Whole Numbers | (W) Any whole number that is positive | 0, 1, 2, 3, |
| Quadratic Term | Power with the variable and exponent of 2 | |
| Linear Term | Variable and constant term with exponent of 1 | |
| Natural/Counting Numbers | (N) Any whole numbers excluding 0 | (Infinite Sets)1,2,3 |
| Relations of Types of Numbers | R consists of Q and I. Q consists of Z consists of W consists of N consists of 0. | |
| Closure Property of Addition | a+b is a R Number. | |
| Closure Property of Multiplication | ab is a R Number. | |
| Commutative Property of Addition | a+b=b+a | |
| Commutative Property of Mulitiplication | ab=ba | |
| Associative Property of Addition | (a+b)+c=a+(b+c) | |
| Associative Property of Multiplication | (ab)c=a(bc) | |
| Identity Property of Addition | a+0=a, 0+a=a | |
| Identity Property of Multiplication | a*1=a, 1*a=a | |
| Inverse Property of Addition | a+(-a)=0 | |
| Inverse Property of Multiplication | a*1/a=1, where a cannot be 0 | |
| Distributive | a(b+c)=ab+ac | |
| Formula | An equation that relates two or more quantities, usually represented by variables. | |
| Formula of distance | d=rt | D is distance, r is rate, t is time |
| Formula of temperature | F=(9/5)C+32 | F is degrees Farenheit, C is degrees Celsius |
| Formula of the Area of a triangle | A=1/2bh | A is Area, b is base, h is height |
| Formula of the Area of a rectangle | A=lw | A is area, l is length, w is width |
| Formula of the Area of a Trapezoid | A=(1/2)(Bone+Btwo)h | A is area, bone is one base, btwo is the other base, h is height |
| Area of a circle | A=Pier^2 | A is area, r is radius |
| Circumference of a circle | 2Pier | C is circumference, r is radius |
| Perimeter of a Rectangle | P=2l+2w | P is perimeter, l is length, w is width |
| Solve for a variable | To rewrite an equation as an equivalent equation in which the variable is on one side and does not appear on the other side | |
| Verbal Model | An equation written in words | |
| Linear Inequality | A linear inequality in one variable can be written in one of the following forms where a and b are real numbers and a cannot be 0 | |
| Solution of an Inequality | An inequality in one variable is a value that, when substituted for the variable, results in a true statement | |
| Graph of an Inequality | Consists of all points on a number line that represent solutions. | |
| Compound Inequality | An inequality with two solutions joined by and or or. | |
| Equivalent Inequalities | Inequalities that have the same solution as the original inequality. | |
| Absolute Value | |x| the distance the number is from 0 on a number line. | |
| Extraneous Solution | An apparent solution that must be rejected because it does not satisfy the original equation. | |
| Opposite | Additive Inverse; if b then -b (Definition of Subtraction) |
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