Foundations of Algebra. Learning Goal 3.1 Algebraic Expressions. a. Identify the: Variables: Coefficients:
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1 Learning Goal 3.1 Algebraic Expressions What you need to know & be able to do 1. Identifying Parts of Algebraic Expressions 3.1 Test Things to remember Identify Parts of an expression Variable Constant Term Coefficient Factors a. Identify the: 3x x y 9 Variables: Coefficients: Examples b. Identify the: x x 7 Terms: Coefficients:. Creating Algebraic Expressions Remember to look for key words a. Create an expression for four less than three times a number b. Write verbal descriptions of x Test 3. Simplify algebraic expressions Distribute first, if possible Then combine like terms a. Simplify: 15x 5(x ) 11 b. Simplify: -x + (7x + ) 3(5x ) 3.1 Test. Dimensional Analysis Conversion Factor: a. Convert years into days. (35 days = 1 year) b. Convert 1 pints to gallons. (1 gallon = quarts, pints = 1 quart) 3.1 Test
2 Learning Goal 3. Radical Expressions 1. Simplify radicals 3. Test -Break each number down into its prime factors and circle pairs of the same number (perfect squares) a x y b. x 10x y 5 -Keep each factor without a buddy underneath the square root.. Multiply radicals -Multiply the outside numbers and variables a. y y b a 3a 3 3. Test -Multiply the inside numbers and variables -Simplify radical 3. Add and Subtract Radicals -Distribute if necessary -Simplify each radical a. 5 b Test -Add or subtract like terms. Irrational vs Rational Numbers 3. Test a. Explain the outcome of 1. b. Explain the outcome of 3 9
3 Learning Goal.1 Solving Equations What you need to know & be able to do 1. Solving Two Step Equations Things to remember Use Inverse operations a. Solve x 15 Examples b. Solve x 3.1 Test. Solving Multi-Step Equations Use Inverse operations a. Solve -5(3 + x) + 5 = 15 b. Solve 3x = 1 3x.1 Test 3. Isolating a Variable (Literal Equations).1 Test Using the properties of equalities solve an equation with more than one variable for a chosen variable. a. Solve the equation for b: a bh b. Solve for l: P = l + w. Creating Equations from a Context.1 Test Define a variable for what you are solving for Look for key words a. Alex belongs to a music club. In this club, students can buy a student discount card for $ This card allows them to buy CDs for $3.95 each. After one year, Alex has spent $3.0. How many CDs did Alex buy? b. Jacqueline had $0 to spend on 7 raffle tickets. After purchasing them she had $ left. How much did each raffle ticket cost?
4 Learning Goal. Solving Inequalities 1. Graphing Inequalities Remember to rewrite so the variable is on the left ALWAYS! a. Graph the inequality: m -3 b. Graph the inequality: > y. Solving and Graphing Linear Inequalities. Solve an inequality by isolating the variable. a. Solve and graph 3( x ) b. Solve: 7 t 1. Test Golden Rule: Dividing by a negative number flips the inequality. Is t = -5 a solution? Is t = -9 a solution? 3. Creating Inequalities from a Context. Test Define a variable for what you are solving for Look for key words Think about your answer in relation to your inequality sign You do not always round up!!! Your solution must work with your inequality sign! a. Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $ per hour to babysit and her Father gave her $10 for mowing the lawn. What is the minimum amount of hours she will need to babysit in order for her to buy her calculator? b. Cecilia has $30 dollars to spend at a carnival. Admission costs $5 and each ride ticket costs $1.50. What is the maximum amount of tickets she can purchase?
5 Learning Goal 5.1 Linear Functions & Graphs What you need to know & be able to do 1. Determine if a relation is a function. 5.1 Test Things to remember Every input only has one output (each x only has one y ) Use the vertical line test on graphs. a. Determine if the graph is a function. Examples b. Determine if the table represents a function. x y Evaluate functions. 5.1 Test f(x) function notation f() means you must substitue a for every x in the function! a. Evaluate f(). f(x) = x + 3x 1 b. Find the value of f(x) = x when x = Graph a linear function 5. Test y = mx + b *Always graph the y- intercept first and then use slope to determine next point. a. Graph: f(x) = x + b. Graph: x + y =
6 . Graph Special Lines HOY VUX a. Graph x = -3. Name slope & y- intercept b. Graph y =. Name slope & y- intercept Convert from standard to slope intercept form 5. Test Slope Intercept: y =mx + b Standard: Ax + By = C a. Solve for y: x + y = b. Determine the slope and y- intercept: 3x y = -1.. Write the equation of a line. y = mx + b a. Write the equation of the line. b. Write the equation of the line. 5. Test
7 Learning Goal.1 Systems of Equations What you need to know & be able to do 1. Solve a system of linear equations by graphing. Things to remember Make sure each equation is solved for y. a. Solve the system. y = x + 3 y = x 5 Examples b. Solve the system..1 Test Graph both equations and find where they intersect Solve a system of equations Substitution Elimination a. Solve the system: y = 5x x 7y = 1 b. Solve the system: y = x 1 y = 3x 5.1 Test Refer to Green Graphic Organizer for help c. Solve the system: x y = 11 x + y = 19 d. Solve the system: x + 3y = 1 5x y = 13
8 3. Systems with Real World Scenarios.1 Test Define your variables Determine if slope intercept or standard form is best Set up your equations and solve using elimination or substitution. a. When is it cheaper for Beck to make copies? Break Even Point: where the cost equal the income b. When is Ace Car Rental the better deal?
9 Learning Goal. Systems of Inequalities 1. Solve a system of linear inequalities by graphing.. Test Determine if you have a solid or dashed line Then determine whether to shade above or below. Find the region where the shading overlapped. a. Solve the system. Label the different regions as solution or not a solution. y < 3x + y x 1 b. Are the following points solutions to the system of inequalities? a. (-, 5) x + y > y > x b. (3, ) Naming Linear Inequalities. Test Identify: *Slope *Y-intercept *Type of Line *Shading a. Name the inequality. b. Name the inequality.
10 3. Naming Linear Inequalities and Systems. Test Identify: *Slope *Y-intercept *Type of Line *Shading a. Name the system of ineqalities. b. Name the system of ineqalities.. Real World with Systems of Inequalities. Test a. Write a system to describe: The maximum capacity for an elevator is 15 people and 3000 pounds. It is estimated that adults weight 00 pounds and children under 1 weight 100 pounds. b. Write a system to describe: Megan is selling tickets to Allatoona s production of Footloose. Allatoona s theater holds at most 700 people. Children s tickets are $.00 and adult tickets are $ She hopes to sell at least $500 worth of tickets.
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