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Unit 4 Honors Study Guide Cumulative Exam 100 points – Thursday, October 29, 2015 Unit 1 Tools of Algebra 1.1 Variables and Expressions o o Translate from words to algebra Translate from algebra to words 1.2 Exponents and Order of Operations o o PEMDAS Evaluating Expressions 1.3 Exploring Real Numbers System o Rational/Irrational, Integer, Whole, Natural, 1.4 Adding Real Numbers 1.5 Subtracting Real Numbers 1.6 Multiplying and Dividing Real Numbers o Matrix operations 1.7 The Distributive Property o Simplifying expressions using the distributive property. 1.8 Properties of Real Number o Identify the Algebraic Properties including; Commutative Property of Addition/Commutative Property of Multiplication Associative Property of Addition/Associative Property of Multiplication Identity Property of Addition/Identity Property of Multiplication Inverse Property of Addition/ Inverse Property of Multiplication Distributive Property Zero Property 2.1 Solving One Step Equations 2.2 Solving Two-Step Equations 2.3 Solving Multi-Step Equations **Make sure you can combine like terms** **Always Express your answers in standard form (LEFT to RIGHT: highest exponent first, alphabetical order, constants always last) Unit 2 Equations and Inequalities EQUATIONS 2.3 Solving Two Step and Multi-Step Equations Clearing fractions and decimals. Translate word problems and verbal expressions into an equation. 2.4 Solving Equations with Variables on Both Sides REMEMBER: Simplify each side first, then collect all the variables on one side to solve! Special Cases: (All Real Solutions/ No Solution/ One Solution) 2.6 Solving Absolute Value Equations YOU SHOULD HAVE 2 SOLUTIONS UNLESS IT’S A SPECIAL CASE Remember: Isolate your absolute value, check for special cases, if it’s not a special case, split into two equation and remove your absolute value signs and solve separately, Don’t forget to check your answers. INEQUALITIES – Remember to ALWAYS reverse the inequality symbol when multiplying or dividing through by a negative!!! 3-4 Multi-Step Inequalities Clearing fractions and decimals. Translate word problems and verbal expressions into an inequality Special Cases: o all real numbers – yields a true statement ex: 2𝑥 + 2 > 2𝑥 + 1 o no solution - yields a false statement ex: 2𝑥 + 2 > 2𝑥 + 2 3-5 Inequalities with Variables on Both Sides Be aware of special cases (All Real Solutions/No Solutions) 3-6 Compound Inequalities Model real world situations using compound inequalities. Solve and graph simple compound inequalities using “and” and “or”. Translate between an in between statement and an “and” inequality. o ex: 𝑥 > −2 𝑎𝑛𝑑 𝑥 < 5 is the same as … −2 < 𝑥 < 5 Special Cases: (All real solutions, no solution, infinite solutions) 3.7 Solving Absolute Value Inequalities: Isolate absolute value, then break into two cases, solve both inequalities, graph Final answer should be written as an “AND” or “OR” Recall: GreatOR and LessthAND Unit 3 Applications of Equations and Inequalities 2-5 Equations and Problem Solving (Number; Age; Geometry; Break-even; Consecutive) 2-6 Formulas/ Literal Equations Unit 4 Functions 5-1 Relating Graphs to Events 5-2 Relations and Functions 5-3 Graphing Functions 5- 4 Function Rules, Tables, and Graphs TIPS FOR SUCCESS Study vocabulary words, quizzes, tests and previous study guides. Check out my website for supplemental material On the day of the test come prepared with a pencil and calculator!! I will provide scrap paper. The test will take the FULL class period, so be punctual!