P.1 Prerequisite skills Basic Algebra Skills Topics: Evaluate an algebraic expression for given values of variables Combine like terms/simplify algebraic expressions Solve equations for a specified variable A: Evaluate Expressions for Given Values (Lesson 1.3) Example: What is the value of the expression for the given values of the variables? A1. 3x(x + 2) 3x 2 for x = 19 A2. 4(y 2 3) + 7(y 2) for y = 5 A3. x 2 5(3x 12) for x = 10 A4. What is the value of y for each of the given values of x. y = 2x + 7 x 3 y 0-8 B: Simplify Expressions using Order of Operations (Lesson 1.3) Recall: Example: Rewrite the expression in its simplest form. B1. a 2 + a + a 2 B2. 5(x 2y) 3(x 2y) B3. 7xy (10xy 3x 2 )
C: Solving One-Variable Equations (Lesson 1.4) Example: Solve for the given variable C1. x + 5 = 9 C2. -3y = 15 C3. 2a 3 6 C4. 7 x = 10 Expectations: I want to see for any problem: The original problem Any key steps in getting to your solution- the work Clearly stated solution Answers: Should use original variable if applicable x = 2 or y = 5, etc. FRACTIONS should always be reduced to lowest terms. DECIMALS only if they are terminating and you write the entire thing never round unless the directions say so. 24 56 = 3 7.4285714 C5. 6x 5 7 9x C6. 5(6 4 y) y 21 You should answer 3 7 14 56 = 1 4 = 0.25 You should answer 1 or 0.25 4 C7. 53 = 3(y 2) (3y 1) C8. 2( x + 5) + 2 = 5 (2x 7)
P.2 Prerequisite skills Special Equations and Inequalities Topics: Solving Formulas for a specified variable (Literal Equations Solve absolute value equations and inequalities A: Solving Literal Equations (Lesson 1.4) Solve for A in terms of B Goal: Use algebra to get A = on one side of the equation and a simplified expression that contains B on the other side of the equation. Example: A1. S = 2πrh solve for r A2. 3x 5y = 15 solve for y A3. ax + bx = c solve for x A4. A = 1 2 (b 1 + b 2 )h solve for b 1 B: Solving Absolute Value Equations (Lesson 1.6) Perhaps you remember from a previous math class the concept of absolute value. Solve this equation: x 5
Strategy: 1. Isolate the absolute value stuff = value 2. Set up 2 equations: stuff = value OR stuff = value 3. Solve each new equation and check your solution. Example: Solve the following absolute value equation. Be sure to check your answers. B1. x 18 5 B2. 3 a 9 30 B3. 5 2x 4 7 17 B4. 5x 6 9 0 B5. 5 3 2 2w 7 B6. x 6 3x 2
C: Inequalities (Lesson 1.5) RECALL: Inequalities represent values that may not necessarily be equal. Inequality Summary greater than less than greater than or equal less than or equal Graphing Inequalities: Solving inequalities is the same as solving equations EXCEPT if you multiply or divide by a negative number, you have to FLIP the inequality symbol. Example: Solve each compound inequality. Graph the solution. C1. 3x 12 and 8x 16 C2. 3x + 4 > 16 or 2x > 14
D: Solving Absolute Value Inequalities (Lesson 1.6) There are two types of absolute value inequalities: Less than and Greater than GO L.A.! can help you remember the difference Greater than = Rewrite and solve like an Or inequality. Less than = Rewrite and solve like an And inequality. Example: Solve each inequality. Graph the solution. D1. 4x 8 20 D2. 3x 12 + 8 14 D3. 4s 1 27 D4. 2 10 2k 2
P.3 Prerequisite skills Binomials and Radicals Topics: Multiplying Binomial Algebraic Expressions Rewrite Square roots in simplest radical form A: Multiplying Binomials The FOIL Method Example: Multiply and simplify the following expressions. A1. (x + 3)(x + 5) A2. (x 6) 2 A3. (2x 5)(3x + 9) A4. (x 2 + 5)(x + 2) A5. (x + 3)(x 2 + 4x 7) A6. (2x 3)(3x 2 x + 4)
B: Simplest Radical Form Recall: A perfect square is a number that has an integer square root Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144,... Using the Multiplication Property to simplify square roots: Strategy: 1. Break the square root into two factors, one of which is a perfect square. 2. Simplify the perfect square. 3. Continue until the radicand (number under the radical) has no more perfect square factors. Example. B1. 50 B2. 160 B3. 27 B4. 3 12 B5. 5 162 Using the Division Property to simplify square roots: Strategy: It s not simplified until there are no radicals left in the denominator 1. Break the square root into a quotient of two radicals, top & bottom 2. Multiply the numerator and denominator by the denominator of the fraction 3. Simplify B6. 2 5 B7. 7 10
P.4 Prerequisite skills Using a scientific calculator Topics: Use a scientific calculator properly and efficiently A: Fraction Key Examples: A1. Reduce 14 240 A2. Reduce 15 25 A3. 2 3 + 3 7 A4. 4 5 6 1 10 A5. 5 8 2 1 2 A6. Solve 2 5 x 3 8 = 4 5 A7. Solve 1 3 x 10 = 2 5 x + 4 B: F D (Fraction to Decimal Shift) Convert Decimals to fractions and fractions to decimals. Example: B1. Solve: 14x = 10 B2. Solve: 90x = 80 B3. Convert to a fraction in lowest terms: 0.372.45 0. 3
C: Exponents Example: Simplify the following expressions C1. 4 2 C2. ( 8) 2 C3. 5 3 C4. ( 5) 3 C5. 7 2 Example: Evaluate the following expressions when x = 6 and y = 2. C6. xy 3 C7. 5y 4 C8. 10 x 2 D: General Calculations Simplify the following expressions D1. 5 2 4(1)(3) D2. ( 3) 2 4(2)( 5) D3. 2 10 12+14 D4. 2( 1) 2 + 3( 1) + 6 D5. 2(5) 2 7(5) 1 D6. 2 3 (24x + 4 5 ) D7. 1 4 x+10 2