Algebra II Midterm Eam Review Packet Name: Hour:
CHAPTER 1 Midterm Review Evaluate the power. 1.. 5 5. 6. 7 Find the value of each epression given the value of each variable. 5. 10 when 5 10 6. when 6 7. 5 when 8. y when and y 7 Simplify the epression. 9. 7 5y y 10. 8 11. 5 10 1. 5
Solve the equation. Check your solution. 1. 7s 1. 5c 6 6 1 15. (6w ) 19 16. 6 5 17. 1 7 18. 5y y 9 Solve each equation for y. 19. 5y 15 0. 6 y
CHAPTER Midterm Review Identify the domain and range. Then tell whether the relation is a function. 1... {(, ), (, 0), (0, ), (, 0), (, )} Domain: Range: Domain: Function: YES NO Range: Domain: Range: Function: YES NO Evaluate the function when.. h 6 Function: YES NO 5. f 5 6. v 1 Find the slope of the line passing through the given points.,8 1,7 5, 1 5,0 7. 8. 9. 0, 8, m = m = m = Find the slope and y-intercept of the line. Then graph the equation. 10. y 1 11. y 5 m = b = (, ) m = b = (, ) 1. y m = b = (, )
Write each form of a line. SLOPE INTERCEPT FORM: POINT SLOPE FORM: Write an equation of the line in slope intercept form given the slope and a point. 1. slope = and goes through the point (1, ) 1. slope = ½ and goes through the point (, ) Equation Equation PARALLEL LINES HAVE THE SLOPE. PERPENDICULAR LINES HAVE SLOPES. Given the equation of a line, write the slope of a parallel line and the slope of a perpendicular line. 16. y m = 15. y 1 m = Slope of a parallel line: Slope of a parallel line: Slope of a perpendicular line: Write an equation of a parallel line. 17. passes through (7, ), parallel to the line y 1 Slope of a perpendicular line: 18. passes through (, 5), parallel to the line y 1 Equation Equation
Write an equation of a perpendicular line. 19.passes through (, 16), perpendicular to the line y 8 0. passes through (1, 1), perpendicular to the line y 5 Equation Equation Draw a scatter plot of the data. Determine whether the data has positive, negative, or no correlation. 1. Match each inequality on the left with its graph on the right.. y A.. y B. C.. y
Graph the inequality in a coordinate plane. 5. y 6. y 5 1 7. y 7 CHAPTER 5 Midterm Review STANDARD FORM: VERTEX FORM: Write each quadratic equation in standard form. 1. 5 7 y. y. y 6
For #-5, Given the quadratic in STANDARD FORM, y a b c : find all the information and then graph it. b Use the formula to help. a. y 6 5 5. y 6 8 a = b = c = a = b = c = Y-intercept Verte (, ) Ais of Symmetry = Y-intercept Verte (, ) Ais of Symmetry = Opens Up or Opens Down Opens Up or Opens Down Maimum or Minimum Ma/Min Value Maimum or Minimum Ma/Min Value For #6-7, Given the quadratic equation in VERTEX FORM, 6. y a = h = k = y a( h) k, find all the information and then graph. Verte (, ) Ais of Symmetry = Opens Up or Opens Down Maimum or Minimum Ma/Min Value Y-intercept:
7. y a = h = k = Verte (, ) Ais of Symmetry = Opens Up or Opens Down Maimum or Minimum Ma/Min Value Y-intercept: (a little big sorry!) Identify which graph matches each equation. Use what you know about a, h, and k to help you match the graphs! A. B. C. 8. y 1 9. y 1 9 10. y 1 Factor the following epressions completely. 11. 1 1. 9 1. 8 1. 9 5
15. 9 9 16. 8 10 17. 1 9 18. 1 9 19. 5 0. 9 1 Solve the quadratic equation by factoring. Don t forget to set the equation equal to 0 first! 1. 5 1 0. 56 15
. 11 0. 16 5 0 5. 6 11 0 6. 10 Simplify the following radical epressions. 7. 8. 75 9. 6 0. 99 1. 1 50. 5 10 0
Rationalize the denominators... 7 5 5. i 6. 5 i 7. i i 8. 6i i 9. i 5i 0. 6i1 i
Find the solutions of each equation using square roots. 1. 9. 81. 5 0. 18 ( b) Solve the quadratic equations using the Quadratic Formula. 5. 8 10 0 6. 9 0 ( b) ( a) ( )( a)( c)
Find the discriminant and describe the nature of the roots for each quadratic equation. 7. 1 6 0 8. 17 0 Discriminant: Discriminant: Nature of the roots: Nature of the roots: CHAPTER 6 Midterm Review EXPONENT PROPERTIES Simplify the epressions. 1.... 0 7 5. 6. 5 7. y 7 8. 5 y y
5 9. y y 8 y 10. 1 5 y 11. 5 y z 1. 6 y z 10ab 1. 6 15a b 5y y 15. 1. 16. y 0 17. 8 18. 19. 5 6 6a b c 0. 1 18a b c Tell whether the function is a polynomial function, if it is write it in standard form, find the degree, determine the leading coefficient, determine the constant and determine the type. 1. ( ) 5 5 f 7. f ( ) 7 1. f ( ) 7 Polynomial? Yes or No Polynomial? Yes or No Polynomial? Yes or No Standard form: Degree= Leading coefficient= Constant= Type of function: Standard form: Degree= Leading coefficient= Constant= Type of function: Standard form: Degree= Leading coefficient= Constant= Type of function:
. 5. 5 1 6. 9 5 5 7. 7 5 Multiply. 8. 11 7 9. 1 8 1 0. 1. 1 7
Divide using synthetic division. 8 6.. 9. 5 5 5. 8 8 15 Factor the polynomial in quadratic form. 6. 11 7. 5 8. 11 18 9. 5 1
Find ALL of the solutions for each polynomial. Don t forget to use the degree to help determine how many TOTAL solutions/roots there should be! 0. 1 10 0 **This is factored already! 1. 9 0. 8. 81 0 Match the following equation with its graph. Use the solutions/roots to help match! Think about where the solutions/roots are on the graph. y. 5. y 1 6. y 1
Use the following graph to answer each question. 7. How many turning points does the polynomial graphed have? How many real zeros does the polynomial have? Describe the end behavior of the graph: y y 8. How many turning points does the polynomial graphed have? How many real zeros does the polynomial have? Describe the end behavior of the graph: y y 9. How many turning points does the polynomial graphed have? How many real zeros does the polynomial have? Describe the end behavior of the graph: y y
CHAPTER 9 Midterm Review Determine the asymptotes of each function. 1 1 1. y. y 5. y 6 = y = = y = = y = Determine the domain and the range of each function. 1 9. y 5. y 6 8 6. y 5 Domain: Range: Domain: Range: Domain: Range: Match each graph to its equation. Use the asymptotes to help! A. B. C. 7. y 8. y 1 9. y Simplify. 1 10. 50 11. a a 5a 6 1. 7 7 Find the product. 9 1 1. 1 1. 1 6 8 15. 11 8 1 9 18 6 7
Find the quotient. 16. 1 7 1 5 10 17. 5 18. 5 5 1 Simplify each epression. 19. 6 1 0. 6 6 Simplify the following epressions. 1 1. 5.. 7. 5 5
Solve the equations. 8 5. 6. 7. 1 1 8 1 8. 5 Make sure everything is on your note card for the eam! Just a little more studying and you are going to ROCK this eam.