Foundations of Algebra Name: Date: Block: Cumulative Eam # Review Guide What you need to know & be able to do 1. Adding and Subtracting Radicals Things to remember Adding & Subtracting: Simplify radicals Add/subtract like radicals Eamples 5 b. 3 1 7. Determine if a Sum or Product is Rational or Irrational Multiplying Radicals: -Multiply coefficients -Multiply numbers underneath radical -Simplify the ONE radical 1 b. 5 0 3. Simplifying Epressions Distribute first, if possible Then combine like terms Simplify: 5 3 3 8 b. Simplify: 15 5( ) 11. Solving Equations Use Inverse operations Solve -5(3 + ) + 5 = 15 b. Solve 3 = 1 3 c. Solve 15 d. Solve 3
5. Evaluating Functions Replace the variable with the value stated. Use parenthesis each time you substitute a value in for the variable! Evaluate + 7 when = -3 b. Evaluate f() if f() = + 3 1. Determine if a relation is a function. Every input only has one output (each only has one y ) Use the vertical line test on graphs. Determine if the graph is a function. b. Determine if the table represents a function. y -1 0 5-1 7 7. Writing Equations of Lines from a Graph Determine Slope Determine y- intercept y=m + b Write the equation of the line. b. Write the equation of the line. y 5 3 1 - -3 - -1 1 3 8. Writing Equations of Lines from a Table Determine Slope Determine y- intercept y=m + b b. 8 y - - - 0
9. Comparing Linear Functions Typically you are comparing SLOPE or Y-INTERCEPTS. 15. Which function has the greatest y-intercept? Function A: f() = 3 Function B: + 3y = 1 Function C: a line that has a slope of Function D: and passes through (1, -). (Hint: 5.1 Day 10) 10. Dimensional Analysis All units must be the same units of measure before calculating. A = l w P = l + w The length of a rectangle is 3 cm and the width is 170 mm. What is the area and perimeter of the rectangle in centimeters? (10 millimeters = 1 centimeter) 11. Identifying Parts of Algebraic Epressions Identify Parts of an epression Variable Constant Term Coefficient Identify the: 3 8 y 9 Variables: Constants: Coefficients: b. Identify the: 7 Terms: Coefficients: Constants: 1. Simplifying Radicals with Variables -Multiply the outside numbers and variables 8 y b. y 10y 3 3 -Multiply the inside numbers and variables -Simplify radical
13. Equations with Special Solutions False Equation, variables drop out No Solution True Equation, variables drop out Infinite Solutions Variable = # - One Solution Solve ( + 1) = 5 + 3 + 9 b. Solve 5( + ) 3 = ( + 5) 1. Solving Literal Equations Using the properties of equalities solve an equation with more than one variable for a chosen variable. You cannot move the variable you are solving for. Solve the equation for h: S rh b. Solve for y: 8 y = 1 15. Solving Inequalities Solve an inequality by isolating the variable. Golden Rule: Dividing by a negative number flips the inequality. Rewrite if variable is on right side. Solve and graph: 9 < 3 b. Solve and name 3 solutions 7 t 1 1. Writing and Solving Inequalities Think about the sign and keywords! Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 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 maimum amount of tickets she can purchase?
17. Evaluating Functions from a Graph 18. Calculate slope slope m = y y 1 1-7 - -5 - -3 - -1-1 1 3 5 - -3 - -5 - -7 Calculate the slope. Give a labeled answer. 7 5 3 1 y Use the graph to the left to answer the following: f(1) = b. f(-7) = c. f( ) = 3 d. f( ) = -5 b. Calculate the slope. Give a labeled answer. Change in y Change in 19. Graphing Special Lines HOY VUX Graph = -3. Name slope & y- intercept b. Graph y =. Name slope & y- intercept. 8 8-8 - - - 8 - - - -8-8 - - - 8 - - - -8 0. Convert from standard to slope intercept form Slope Intercept: y =m + b Standard: A + By = C Determine the slope and y- intercept: + y = 8 b. Determine the slope and y-intercept: 3 y = -1.
1. Writing Equations of Lines Given Slope and Point Y = m + b m: slope b: y-intercept (, y): point Write the equation of the line that has a slope of 1 and contains the point (, ).. Characteristics of Linear Functions 3. Interpreting and y intercepts -intercept: (, 0) y-intercept: (0, y) Ed has $3 to buy paints and brushes for a school project. Jars of paint cost $ each. The brushes are $ each. Write an equation to determine the combination of brushes and paint he can buy. Calculate the and y-intercepts and eplain what they mean in terms of the problem scenario. Things I may want to brain dump: