Algebra II Midterm Exam Review Packet

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Algebra IIMidterm Exam Review PacketName:Hour:

CHAPTER 1 Midterm ReviewEvaluate the power.1. 3 42. 5 53. 6 4. 7 43Find the value of each expression given the value of each variable.25. 10 2 x when x 56. 10 x x 2 when x 67. x 2 5x 4 when x 28. x 4 y when x 4 and y 7Simplify the expression.9. 7 x 5 y 3x 2 y10. 8 3 2 x 11. 3 x 3 5 x 10 12. 3 2 x 4 x 5 2

Solve the equation. Check your solution.13. 7s 3 2414. 5c 6 3616. 6 x 3 2 x 5 Solve each equation for y.19. 2 x 5 y 1515.17. 3 2 x 1 4 x 720. 6 x 3 y 241(6w 2) 19218. 5 y 3 2 y 9

CHAPTER 2 Midterm ReviewIdentify the domain and range. Then tell whether the relation is a function.1.2.3. {(–4, 2), (–2, 0), (0, –2), (2, 0), (4, 2)}Domain:Range:Domain:Function: YESRange:NOFunction: YESDomain:NORange:Function: YESEvaluate the function when x 4 .4. h x 6 xNO5. f x 3x 2 56. v x 3x 2 4 x 1Find the slope of the line passing through the given points.7. 3, 8 1, 7 8. 5, 1 5, 0 9. 0, 4 m m m Find the slope and y-intercept of the line. Then graph the equation.10. y 2 x 1211. y x 53m b (,)m b (, 8, 4 412. y x 43)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.13. slope 3 and goes through the point (1, 4)14. slope ½ and goes through the point (4, 2)EquationEquationPARALLEL LINES HAVE THESLOPE.PERPENDICULAR LINES HAVESLOPES.Given the equation of a line, write the slope of a parallel line and the slope of a perpendicular line.16. y 3x 4 m 215. y x 1m 3Slope of a parallel line:Slope of a parallel line:Slope of a perpendicular line:Slope of a perpendicular line:Write an equation of a parallel line.17. passes through (7, 4), parallel to the line y 3x 118. passes through (2, 5), parallel to the line y 2 x 1EquationEquation

Write an equation of a perpendicular line.19.passes through (4, 16), perpendicular to the line2y x 8320. passes through (1, 1), perpendicular to the liney 2 x 5EquationEquationDraw a scatter plot of the data. Determine whether the data has positive, negative, or no correlation.21.Match each inequality on the left with its graph on the right.A.22. x y 323. x y 3B.24. x y 3C.

Graph the inequality in a coordinate plane.25. y x 426. y 5x 1CHAPTER 5 Midterm ReviewSTANDARD FORM:Write each quadratic equation in standard form.21. y x 5 x 7 2. y x 3 27. 2 x 2 y 7VERTEX FORM:3. y x 6 22

For #4-5, Given the quadratic in STANDARD FORM, y ax 2 bx c : find all the information and then graph it.Use the formula x bto help.2a4. y x 2 6 x 5a b c 5. y x 2 6 x 8a b c Y-interceptY-interceptVertex ( , )Vertex ( , )Axis of Symmetry x Axis of Symmetry x Opens Upor Opens DownOpens Upor Opens DownMaximumor MinimumMaximumor MinimumMax/Min ValueMax/Min ValueFor #6-7, Given the quadratic equation in VERTEX FORM, y a( x h) 2 k , find all the information and then graph.6. y x 3 42a h k Vertex ( , )Axis of Symmetry x Opens Upor Opens DownMaximumor MinimumMax/Min ValueY-intercept:

7. y 2 x 4 32a h k Vertex ( , )Axis of Symmetry x Opens Upor Opens DownMaximumor MinimumMax/Min ValueY-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!2A.B.C.8. y x 1 9. y x 1 9210. y 2 x 1 32Factor the following expressions completely.11. x 2 12 x12. 3x 2 9 x13. x 2 2 x 4814. x 2 9 x 52

15. 9 x 2 9 x 216. 8x 2 10 x 317. x 2 14 x 4918. 4 x 2 12 x 919. x 2 2520. 9 x 2 144Solve the quadratic equation by factoring. Don’t forget to set the equation equal to 0 first!21. x 2 5x 14 022. x 2 56 15x

23. 4 x 2 11x 3 024. 3x 2 16 x 5 025. 6 x 2 11x 026. 2 x 2 10 xSimplify the following radical expressions.27.2428.30. 9931. 12 507529. 3632. 5 10 30

Rationalize the denominators.33.2334.7535.22 i36.53 i37. 3 i 2 4i 38. 4 6i 2 3i 39. 3 2i 2 5i 40. 4 6i 1 i

Find the solutions of each equation using square roots.41. x 2 4942. x 2 8143. x 5 2044. x 2 1822Solve the quadratic equations using the Quadratic Formula.45. 3x 2 8x 10 0x (b) (b) 2 ( 4)(a)(c)2(a)46. x 2 3x 9 0

Find the discriminant and describe the nature of the roots for each quadratic equation.47. x 2 12 x 36 048. 2 x 2 x 17 0Discriminant:Discriminant:Nature of the roots:Nature of the roots:CHAPTER 6 Midterm ReviewEXPONENT PROPERTIESSimplify the expressions.1. 2 4 2 25. x 4 5x4 2. 2 46.x2x 32 3 3. 4 37. 2 x 3 y 24. 7 0 7 x 5 y 3 8. 4 x y 2

9. x 2 y 3 2 x 2 y 5 8x 3 y13.10ab 4 1 5 10. xy 4 14. 5xy 315a 2b 6 17. 8 x 3 2 22 5 11. 2 2 x 2 y 215.312. 42 x 316. xy 219. 5 x 218. 2 2y2z3y4z620.0 36a 2 b 6 c 218a 3b 1c 4Tell whether the function is a polynomial function, if it is write it in standard form, find the degree, determine theleading coefficient, determine the constant and determine the type.21. f ( x) 3x 5x 3 722. f ( x) 2 x5 7 x 2 4 x 1223. f ( x) 2 x 4 7 xPolynomial?Yes or NoPolynomial?Yes or NoPolynomial?Yes or NoStandard form:Standard form:Standard form:Degree Degree Degree Leading coefficient Leading coefficient Leading coefficient Constant Constant Constant Type of function:Type of function:Type of function:

24. 3x 3 2 4 x 3 25. 3x 4 2 x 2 1 2 x 3 2 x 2 5 26. x 5 2 x 3 2 x 5 x 4 3x 3 9 27. 4 x 3 2 x 3 x 5x 2 7 x 2Multiply.28. x 7 2 x 2 3x 1129. 2 x 1 3x 2 8x 130. x 3 31. x 7 x 1 x 4 3

Divide using synthetic division.32. 3x 2 8x 6 x 3 33. 2 x 3 x 2 2 x 9 x 3 34. x 2 2 x 35 x 5 35. x 3 8x 2 38x 15 x 3 Factor the polynomial in quadratic form.36. x 4 12137. x 4 4 x 2 538. x 4 11x 2 1839. x 4 5x 2 14

Find ALL of the solutions for each polynomial. Don’t forget to use the degree to help determine how many TOTALsolutions/roots there should be!40. 2 x x 1 x 2 10 0**This is factored already!41. x 4 9 x 2 0 42. x 4 3x 2 2843. x 4 81 0Match the following equation with its graph. Use the solutions/roots to help match! Think about where thesolutions/roots are on the graph. 44. y x 2 x 3 45. y x x 2 x 1 46. y x 2 1 x 2

Use the following graph to answer each question.47.How many turning points does the polynomial graphed have?How many real zeros does the polynomial have?Describe the end behavior of the graph:x y x y 48.How many turning points does the polynomial graphed have?How many real zeros does the polynomial have?Describe the end behavior of the graph:x y x y 49.How many turning points does the polynomial graphed have?How many real zeros does the polynomial have?Describe the end behavior of the graph:x y x y

CHAPTER 9 Midterm ReviewDetermine the asymptotes of each function.1. y 1 4xx 2. y y 1 2x 3x 3. y y Determine the domain and the range of each function.1 94. y 5. y 6x 2x 45 6x 2x 6. y y 8 2x 5Domain:Domain:Domain:Range:Range:Range:Match each graph to its equation. Use the asymptotes to help!A.B.37. y x 28. y 4 2x 19. y 3x 2Simplify.14 x 210.50 x 4Find the product.x2 9x 1 13.2x 2x 1 x 3a 4C.211.a 5a 62x2 4x 2 2 x 24 14. 2x 12 x 36 x 2 2 x 812.7 x 427 x 42x 2 11x 28 x 2 4 x 21 15. 2x 9 x 18 x 2 6 x 7

Find the quotient.2x4x216. x 4 3x 12Simplify each expression.x 319. x 6x 3x 1Simplify the following expressions.1 3 21.2x 523.x7 x 2 x 217.7 x 2 14 x 5 x 10 x3x518.x2 x 63x 320.3x 6x 2 4x 322.2 3 3x 224.42 2x 5 x 25x 2 2 x 35x 5 22x3x 12 x

Solve the equations.4825. 2x 3 2x27.2 x 3x 28 x 1 x 1x 126.x x 2 4228.35 2 x 4x 4Make sure everything is on your note card for the exam! Just a little more studying and youare going to ROCK this exam.

Algebra II Midterm Exam Review Packet Name:_ Hour:_ CHAPTER 1 Midterm Review Evaluate the power. 1. 34 2. 55 3. 63 4. 74 Find the value of each expression given the value of each variable. 5. 10 2x when x 5 6 6. 10 2 2 whenx 7. x 2 5x 4 when x 2 8. .

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