Honors Algebra II Final Exam Order - Fall 2018 For the Final Exam for Algebra II, students will be given the opportunity to re-take any of their Fall 2018 Assessments. To do so they will need to place an order for the assessments they want to retake so that their individualized final exam can be prepared. Students grades will not be lowered if they earn a grade lower than their original assessment grade. Students Current Overall %: Current Letter Grade: # Topic Current Score ReDo YES Required if score is less than 18 Ex This is an example of how 20/25 to fill out this sheet x 20 Simplifying complex numbers (i) ReDo - NO 21 Add, Subtract and Multiply Complex Numbers 22 Finding zeros, completing the square 23 Solving quadratic equations and using the quadratic formula 50 Finding zeros, writing a polynomial function from zeros, using synthetic division 51 Graphing Polynomials 52 Add, Subtract and Multiply Polynomials 53 Use pascals triangle to expand a binomial. 80** Solve systems of equations in two variables 81** Solve absolute value equations and solve multivariable equations 82 Find the vertex, find the axis of symmetry and graph a parabola 83 Graph polynomial equations on coordinate axes with labels and scales 84 Find the center, radius and diameter of a circle. Graph the circle. **To improve your grade on Test 1 (from Mr. Ben Rudy s time as the substitute) you will sign up to take #80 AND #81 and your grade will be averaged. If you do not plan to re-take any of the assessments for the final exam, you must complete the attached Final Exam Review packet AND return this paper, signed by your parent/guardian no later than Thursday, December 13 th at 1pm indicating that they approve of your current Algebra II course grade and will not require you to re-do any assessments. Parent Signature: Parent Name: Student Period:
Unit 3 Algebra II FINAL REVIEW #20 HSN-CN.A.1 (Chapter 3.2, IXL H1, J4) 5 questions Know there is a complex number i such that i 2 = -1, and every complex number has the form a + bi with a and b real. 1) Use imaginary number i to re-write the expression below as a complex number. Simplify all radicals. (IXL H1) 9 2) Use imaginary number I to re-write the expression below as a complex number. Simplify all radicals. (IXL H1) 18 3) Use imaginary number I to re-write the expression below as a complex number. Simplify all radicals. (IXL H1) 7 + 20
4) Find the complex conjugate of the number. Write your answer in a + bi format. (IXL H1) 3 + 5i 5) Solve for the given variable. Write your answer in simplified, rationalized form. (IXL J4) -8v 2 128 = 0 ANSWER KEY B - HSN-CN.A.1 #20 1 2 3 4 5 Period:
Unit 3 Algebra II FINAL REVIEW #21 HSN-CN.A.2 (Chapter 3.2, IXL H2-H6) 5 questions Use the relation i 2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 6) Add/subtract: Simplify and write your answers in the form a + bi (H2-H3) a) 9i + 7i b) (13 8i) + ( 12i + 14) c) 9i 5i 7) Complex Conjugate: Simplify and write your answers in the form a + bi (H3) Find the sum of 3 + 6i and its complex conjugate. 8) Multiply: Simplify and write your answers in the form a + bi (H4) a) ( 7i) 4 b) 3i 6 4 6 c) (8 + i)(8 i)
9) Divide: Simplify and write your answers in the form a + bi (H5) 8i 4i 10) One complex problem: Simplify and write your answers in the form a + bi (H6) 5 2 + 6i ANSWER KEY B - HSN-CN.A.2 #21 6 7 8 9 10 a) b) c) a) b) c) Period:
Unit 3 Algebra II FINAL REVIEW #22 HSF-IF.C.8a (Chapter 3.1 and 3.3, J5, J7 and J8) Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. HSN-CN.C.7 (Chapter 3.2 and 3.3 and 3.4, IXL J7 and J8) Solve quadratic equations with real coefficients that have complex solutions. 11) Find zeros: Solve for the given variable. Write your answers as integers or as proper or improper fractions in simplest form. (J5) (d - 3)(d + 7) = 0 12) Find zeros: Solve for the given variable. Write your answers as integers or as proper or improper fractions in simplest form. (J5) (2s + 7)(5s + 10) = 0 13) Find zeros: Solve for the given variable. Write your answers as integers or as proper or improper fractions in simplest form. (J5) -9y (4y + 14) = 0
14) Complete the Square when a = 1: Solve by completing the square. Write your answers as integers, proper or improper fractions in simplest form, or rounded to the nearest hundredth OR as a radical in simplest form. (J8) d 4 + 4d 15 = 0 15) Complete the Square when a 1: Solve by completing the square. Write your answers as integers, proper or improper fractions in simplest form, or rounded to the nearest hundredth OR as a radical in simplest form. (J8) 5g 4 + 120g = 225 ANSWER KEY B - HSF-IF.C.8a and HSN-CN.C.7 #22 11 12 13 14 15 Period: Unit 3 Algebra II FINAL REVIEW
HSA-REI.B.4b (Chapter 3.1, 3.3 and 3.4, J4, J5, J9) 5 questions #23 Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. 16) Inspection: solve for p. Write your answer(s) in simplified, rationalized form. (J4) p 2 = 49 17) Taking the Square Root: solve for v. Write your answer(s) in simplified, rationalized form. (J4) v 2 + 144 = 0 18) Taking the Square Root (Complex): solve for v. Write your answer(s) in simplified, rationalized form. (J4) -150v 2 3 = 0
19) Completing the Square: Complete the square. Hint: your answer should be a whole number. (J7) p 2 18p + 20) Quadratic Formula: Solve for h. Write your answer(s) in simplified, rationalized form. (J9) 5h 2-8h - 6 = 0 ANSWER KEY B - HSA-REI.B.4b #23 16 17 18 19 20 Period:
Unit 4 Algebra II Final Review #50 9.12.A-APR.2 IXL K.6, K.9 and K.8 Know and apply the remainder theorem for a polynomial p(x) and a number a. 16) Find the zeros of the function f(x) (K8) f(x) = (x - 9)(3x + 24) 17) Find the zeros of the function f(x) (K8) f(x) = x(x + 5)(5x - 45) 18) Write a polynomial function of the least degree with zeros 8 and -4 (K9)
19) Write a polynomial function of the least degree with zeros 6, -3 and 0 (K9) 20) Use synthetic division to find h(2) if h(x) = 5x 2 4x 2 7x + 3 (K6) ANSWER KEY B #50 1 2 3 4 5 Period:
Unit 4 Algebra II Final Review #51 9.12.A-APR.3 (IXL J11, K12 and K14) Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function by the polynomial For #6 to #10: In the list of graphs below, identify the graph of the equation by writing the letter of your corresponding graph in your answer key. (J11/J12/K14) 21) f(x) = x 3-1 7) f(x) = x 4-3x 2-1 8) f(x) = -x 4 + 2x 2 1 9) f(x) = x 2-5x + 4 = (x - 4 )(x - 1) 10) f(x) = x 2 + 4 A) B) C) D) E) F) G) H) J) NONE OF THE ABOVE ANSWER KEY B #51 6 7 8 9 10 Period:
Unit 4 Algebra II Final Review #52 9.12.A-APR.4 (K2 and K3) Prove polynomial identities and use them to describe numerical relationships 10) Simplify the following equation by adding and subtracting polynomials (K2) (-6a + 9) + (3a 2 a + 11) 11) Simplify the following equation by adding and subtracting polynomials (K2) (5a 4 + a 12) (3a 4 + a 3 7a + 9) 12) Simplify the following equation by multiplying polynomials (K3) -3x(x 3 2x 2 + 7x)
13) Simplify the following equation by multiplying polynomials (K3) (x - 5) 2 14) Simplify the following equation by multiplying polynomials (K3) (x - 2)(x 2 + 6x - 3) ANSWER KEY B #52 11 12 13 14 15 Period:
Unit 4 Algebra II Final Review HONORS ONLY #53 9.12.A-APR.4 (K16, K17, K18) Know and apply the binomial theorem [ and apply ] Pascal s Triangle. 15) In pascals triangle below, what value belongs in the box with the # sign? Row 0, (a + b) 0 Row 1, (a + b) 1 Row 2, (a + b) 2 Row 3, (a + b) 3 Row 4, (a + b) 4 Row 5, (a + b) 5 Row 6, (a + b) 6 Row 7, (a + b) 7 Row 8, (a + b) 8 Row 9, (a + b) 9 # #17 18 Use pascals triangle to complete the expansion of (y + z) 7 to fill in the below blanks y 7 + 7y 6 z + 21y z 2 + 35y 4 z 3 + 35y 3 z 4 + 21y 2 z 5 + yz 6 + z 7 17 18 #19 20 Use pascals triangle to complete the expansion of (y + z) 4 #19 make sure all variables and exponents are correct #20 make sure all coefficients are correct ANSWER KEY B #53 16 17 18 19/20 Period:
Unit 5 Algebra II Final Review #80 Rudy Review Part 1 E.10 Solve a system of equations using any method (to include substitute and elimination) #1-5 solve the system of equations using any method (E6, E8 and E10) 1) 4x + 6y = 12 x = -3 2) 2x 3y = -11 y = 4 3) y = x + 6 2x y = 8
4) 2x 3y = 12 4x + 3y = 24 5) 5x + 2y = 8 2x + 3y = -4 ANSWER KEY Final Review #80 1 2 3 4 5 Period:
Unit 5 Algebra II Final Review #81 Rudy Review Part 2 B.4 Solve absolute value equations B.6 Solve multi-variable equations 6) How many solutions does each equation have? (B4) a) -2 x = 14 b) 2 x + 3 = 9 c) -6 x 3 = -15 7) Solve for the given variable: (B4) 2 3x = 72 8) Solve for the given variable: (B4) -12 + 3x - 2 = 22
9) Solve for c in the equation (B6) ½ c = a 2 b 10) Solve for x in the equation (B6) y = 2zw 2 x 5 ANSWER KEY Practice #81 6 7 8 9 10 a) b) c) Period:
Unit 5 Algebra II Final Review #82 9-12.A-CED.2 T.2 Find the vertex of a parabola T.4 Find the axis of symmetry of a parabola T.9 Graph parabolas Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. For #11-12 use the following graph: 11) What are the coordinates of the vertex of the graph? 12) What is the axis of symmetry of the graph?
For #13-15 use the following equation: y = (x + 1) 2 + 2 13) Sketch the graph of the equation: 14) What are the coordinates of the vertex of the graph of the equation 15) What is the axis of symmetry of the graph of the equation ANSWER KEY Practice #82 11 12 13 14 15 SEE GRAPH Period:
Graphing Activity Final Review #83 9-12.A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. When given an equation, be able to graph a parabola by doing the following (5pts each): Draw a graph, label the x and y axis and create a scale that is appropriate for graphing the equation (ie, is each unit 1, 5, 10, etc) Plot and label the vertex Plot and label the x intercept Plot and label the y-intercept Draw and label the axis of symmetry EQUATION: y = (x + 2) 2-25 Period:
Unit 5 Algebra II Final Review (HONORS ONLY!) #84 9-12.F-IF.7.c U.1 Find the center of a circle U.2 Find the radius or diameter of a circle U.7 Graph circles For #16 and #17 use the following graph: 16) Find the center of the circle 17) Find the radius and diameter of the circle using the graph above. 18) Find the radius diameter of the circle given the equation x 2 + y 2 = 81
19) graph x 2 + y 2 = 4 20) graph (x + 1) 2 + (y - 2) 2 = 64 ANSWER KEY Practice #84 16 17 18 19 20 r = d = r = d = See graph See graph Period: