Unit 3 Vocabulary. An algebraic expression that can contains. variables, numbers and operators (like +, An equation is a math sentence stating

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1 Hart Interactive Math Algebra 1 MODULE 2 An algebraic expression that can contains 1 Algebraic Expression variables, numbers and operators (like +,, x and ). 1 Equation An equation is a math sentence stating that two expressions are equal. A term is either a single variable or 2 Term numbers or numbers and variables multiplied together. 2 Like Terms Terms whose variable and their exponents are the same. 2 Combine Like Terms To combine like terms in an expression means using the rules of arithmetic and algebra to rewrite an expression as simply as possible. In general, there will be the same or fewer terms in the simplified expression. Rating: Unit 3: Solving Equations and Inequalities 9

2 3 Solutions Solutions of an equation are all values that make the equation true. 3 Algebraic Equation A statement with two equal expressions. Algebraic equations can be number sentences (when both expressions are numerical), but often they contain symbols (variables) whose values have not been determined. 3 Solving Equations Solving equations is the process of finding the values of the variables that makes the equation true. 4 Commutative Property a + b = b + a a b = b a 4 Associative Property a (b c) = (a b) c a + (b + c) = (a + b) + c Rating: Unit 3: Solving Equations and Inequalities 10

3 ab ( + c) = ab + ac 4 Distributive Property ab ( c) = ab - ac 4 Properties of Equality Addition: If a = b, then a + c = b + c Subtraction: If a = b, then a c = b c Multiplication: If a = b, then a c = b c Division: If a = b & c 0, then a c = b c 5 Monomial A monomial is a polynomial with one term. 5 Binomial A binomial is a polynomial with two terms. 5 Trinomial A trinomial is a polynomial with three terms. A polynomial is an expression that has variables and numbers with the operations 5 Polynomial addition, subtraction and multiplication. Any exponent must be an integer and greater than or equal to 0. Rating: Unit 3: Solving Equations and Inequalities 11

4 5 Degree of Term The degree of a term is the sum of the degrees in each of its variables. 5 Degree of Polynomial The degree of a polynomial is the highest degree of its terms Standard Form of a Polynomial Excluded Values Absolute Value The standard form of a polynomial has the terms rewritten so that the terms are in order from greatest degree to least degree. Excluded values make the denominator equal to 0. For a number, the absolute value of a number is the distance the number is from zero. 8 Absolute Value Equation An absolute value equation contains an algebraic expression within absolute value symbols. An inequality is a mathematical sentence 9 using one or more of the symbols <, >, <, or >. Rating: Unit 3: Solving Equations and Inequalities 12

5 10 10 Solving Inequalities Addition Solving inequalities is the process of finding the values of the variables that makes the inequality true. If a > b, then a + c > b + c. If a < b, then a + c 0 and a > b, then a c > b c 10 Multiplication and a < b, then a c b, then a c b c. 11 Open Interval An open interval is one that does include the end points. not 11 Closed interval A closed interval is one that does include the end points. 11 AND When and is used both parts of the statement must be true. Rating: Unit 3: Solving Equations and Inequalities 13

6 When or is used either part of the 11 OR statement may be true or they can both be true. A conjunction is a compound statement 11 Conjunction formed by joining two statements with and. A disjunction is a compound statement 11 Disjunction formed by joining two statements with or. 11 Interval Notation Interval notation is a way to describe a set of values. 12 Absolute Value An absolute value inequality contains an algebraic expression within absolute value symbols. Rating: Unit 3: Solving Equations and Inequalities 14

7 Bingo On the blank Bingo sheet below, write the numbers from 1 to 24 in any order in the 24 empty boxes. These numbers correspond to the vocabulary words in this unit, but you do NOT need to write the complete word in the box. Your teacher will call out a definition or give an example of the word. If you know the word it is referring to, cross off that number on your Bingo board. When you have five crossed off boxes in a row (horizontally, vertically or diagonally), shout out Bingo! 1. Absolute Value Equation 2. Addition 13. Binomial 14. Interval Notation BINGO SHEET 3. Equation 15. Multiplication Absolute Value 5. Conjunction 17. AND 6. Excluded Values 18. Closed Interval 7. Disjunction 19. Monomial 8. OR 20. Solutions FREE SPACE 9. Open Interval 21. Solving Equations 10. Absolute Value 11. Addition Equality 12. Degree of Polynomial 22. Solving Inequalities 23. Multiplication Equality 24. Commutative Property Unit 3: Solving Equations and Inequalities 15

8 1. Absolute Value Equation contains an algebraic expression within absolute value symbols 2. Addition If a > b, then a + c > b + c. If a < b, then a + c , <, or > 5. Conjunction a compound statement formed by joining two statements with and 6. Excluded Values values that make the denominator equal to 0 7. Disjunction a compound statement formed by joining two statements with or 8. OR either part of the statement may be true or they can both be true 9. Open Interval does not include the end points Unit 3: Solving Equations and Inequalities 16

9 10. Absolute Value contains an algebraic expression within absolute value symbols 11. Addition Equality If a = b, then a + c = b + c 12. Degree of Polynomial highest degree of its terms 13. Binomial a polynomial with two terms 14. Interval Notation a way to describe a set of values. If c > 0 and a > b, then a c > b c 15. Multiplication and a < b, then a c b, then a c b c. 16. Absolute Value the distance the number is from zero 17. AND both parts of the statement must be true Unit 3: Solving Equations and Inequalities 17

10 18. Closed Interval does include the end points 19. Monomial a polynomial with one term 20. Solutions all values that make the equation true 21. Solving Equations the process of finding the values of the variables that makes the equation true 22. Solving Inequalities the process of finding the values of the variables that makes the inequality true 23. Multiplication Equality If a = b, then a c = b c 24. Commutative Property a + b = b + a a b = b a Unit 3: Solving Equations and Inequalities 18

Algebra I. Course Outline

Algebra I. Course Outline Algebra I Course Outline I. The Language of Algebra A. Variables and Expressions B. Order of Operations C. Open Sentences D. Identity and Equality Properties E. The Distributive Property F. Commutative