Semester Final Exam Review Packet Name Algebra 1 Hour Final Exam Review Days Assigned on Assignment 6/1 Unit 5 and Unit 6, 1-39 Complete and On Time 5 points Complete and Late 4 points At Least 50% Complete.5 points Less Than 50% Complete 1 point 6/4 Unit 7 and Unit 8, 40-60 6/5 Practice Test, 61-81 Category Totals Homework Grade / 15 Points This sheet is due Thursday, June 7 th Other Things You Need to Know: There are 6 Multiple Choice and 5 Free Response questions on the exam. The Multiple Choice portion is an Illuminate bubble sheet You will be provided with a note sheet and you will use one of my calculators. You may use a calculator on the entire exam. If you would like to estimate your semester grade, use the formula below. Semester Grade = 0.8(S percentage) + 0.(Exam percentage take a guess) Your exam is on
Semester Final Success Criteria Unit 5-Exponents and Exponential Functions I can use the Product of Powers property to simplify exponential expressions I can use the Power of a Power property to simplify exponential expressions I can use the Power of a Product property to simplify exponential expressions I can use the Power of a Quotient property to simplify exponential expressions I can use the Quotient of Powers property to simplify exponential expressions I can use the properties of Negative Exponents to rewrite exponential expressions with positive exponents I can use the Properties of Exponents simultaneously to simplify exponential expressions I can recognize an exponential decay pattern I can recognize an exponential growth pattern I can distinguish between exponential and linear patterns and write write the corresponding equations I can graph exponential growth and decay equations I can write exponential equation given a context Unit 6-Polynomials and Factoring I can add or subtract polynomials. I can multiply polynomials. I can use the Zero Product Property to solve an equation. I can factor by factoring out a GCF. I can use a box to factor. Unit 7-Graphing and Solving Quadratics I can graph a parabola given in standard form. I can compare the transformation(s) of the graph of y = ax + c to y = x. I can graph a parabola given in intercept form. I can solve a quadratic equation by graphing. I can solve a quadratic equation by taking square roots. I can solve a quadratic equation by completing the square. I can use completing the square to rewrite a quadratic equation in vertex form. I can graph a parabola given in vertex form. I can solve a quadratic equation by using the quadratic formula. I can use the discriminant to determine the number of solutions to a quadratic equation. Given a pattern, I can determine whether a function is linear, exponential, or quadratic and I can write the corresponding equation. Unit 8-Radicals I can graph square root functions. I can simplify radical expressions. I can use properties of multiplication and division to simplify radicals. I can use properties of addition and subtraction to simplify radicals. I can solve radical equations
Algebra 1 Units 5-8 Exam Note Sheet Exponent Properties a a a m m n a n a a mn mn ( a m a b ) n m a a b mn m m ( m m ab) a 1 a n n a 1 b m n a 1 1 a 0 1 a n Exponential Growth and Decay Product Property: a = Initial Amount r = Rate t = Time Quotient Property of Radicals: a a a b a b b b 4 9 3 16 4 5 5 36 6 49 7 64 8 81 9 100 10 11 11 144 1 169 13 Function Models Linear y mx b Exponential x y a b Quadratic y ax bx c Square Root y x
Standard Form of a Quadratic y ax bx c Vertex Form of a Quadratic y x h k Quadratic Formula Discriminant b b b Axis of Symmetry: Vertex: b b 4ac x a 4ac 0 Two Solutions 4ac 0 One Solution 4ac 0 No Solution b x a h, k Axis of Symmetry: x h 1 3 4 5 6 7 8 9 10 11 1 1 1 3 4 5 6 7 8 9 10 11 1 4 6 8 10 1 14 16 18 0 4 3 3 6 9 1 15 18 1 4 7 30 33 36 4 4 8 1 16 0 4 8 3 36 40 44 48 5 5 10 15 0 5 30 35 40 45 50 55 60 6 6 1 18 4 30 36 4 48 54 60 66 7 7 7 14 1 8 35 4 49 56 63 70 77 84 8 8 16 4 3 40 48 56 64 7 80 88 96 9 9 18 7 36 45 54 63 7 81 90 99 108 10 10 0 30 40 50 60 70 80 90 100 110 10 11 11 33 44 55 66 77 88 99 110 11 13 1 1 4 36 48 60 7 84 96 108 10 13 144
Unit 5: Exponents and Exponential Functions In #1-4 simplify the expression. Write your answer using exponents. 1) ( ) ( )( ) 5 ) (6 3 ) 5 3) 4 4 11 7 4) 7 6 6 8 6 1 In #5-7 simplify the expression 5) 1 5 8 6) ( 4m n ) 7) 3 r 3 In #8-11, Simplify the expression. Write your answer using only positive exponents. 8) x yz 3 1 3ab 9) a c 10) 3 ( 6m) (m ) 4 (3mn) (m) 11) 4 4m n 3 1) In the following, use the function y = 3 x a) Complete the table for the function b) Graph the function c) Identify the domain and range. Domain: Range:
13) A company is offering its employees a retirement benefit of $4,000 per year and guarantees an annual cost of living increase of % of the benefit. a) Write a function that models the retirement benefit over time. Assume that the retirement benefit only increases by the cost of living increase. y a 1 r t b) Use the function to find the amount of the retirement benefit after 6 years. 14) You buy a new car for $3,000. It depreciates at the rate of 1% per year. a) Write a function that models the value of your car over time. y a 1 r t b) Use the function to find the amount the car is wroth after 5 years. In 15 and 16, Tell whether the graph represents exponential growth or exponential decay. Then write a rule for the function. 15) 16)
Unit 6: Polynomials and Factoring In 17 and 18, find the sum of the polynomials. 3 3 17) (3x 7x 5x 3) ( x 3x) 18) (7a 3a 14) (9a 11a) In 19 and 0, find the difference of the polynomials. 3 3 19) (17y 6y 5) (11y y 8) 0) ( b b 6b 1) (3b 11b ) In #1-4, find the product of the polynomials. 1) ( 9r 3)(r 1) ) (7t )( t 5t 3) 3) ( 3 5b) a 4) ( 9z )(9z )
In #5-3, factor the polynomial. 5) x 10x 1 6) 4y 3y 6 7) 5x 0x 0 8) x 11 9) x 7x 30 30) 9y 66y 11 3 31) x x 5x 5 3) m 3 6m m 1 In #33-34, what are the x-intercepts? (Also called Zeros/Roots/Solutions) 33) ( x 7)( x 3) y 34) (5x )( x 11) y
In #35-38, solve the equation. 35) x x 56 0 36) z 169 6z 37) 1x 15 0 38) 4x 11x 3 5x 4 39) A rectangle has the length of (3x+) inches, a width of (x+4) inches, and an area of 153 square inches. Find the value of x. (hint: draw a picture!) Unit 7: Quadratic Equations and Functions Find the vertex of the following quadratics: 40) x 4x 1 41) x 8x 5
4) Given the following information about the parabola, answer the questions. y x 8x 3 a) a = b = c = b) Does the parabola open up or down? c) Does the parabola have a maximum or minimum? d) Find and draw the axis of symmetry ( Also known as the x coordinate of the vertex. e) Find more points on the graph and graph the parabola x y Vertex 43) Given the following information about the parabola, answer the questions. y x 4x 3 a) a = b = c = b) Does the parabola open up or down? c) Does the parabola have a maximum or minimum? d) Find and draw the axis of symmetry ( Also known as the x coordinate of the vertex) e) Find more points on the graph and graph the parabola x y Vertex
In 44-45 solve the equation. Round to the nearest hundredth, if necessary 44) x 5 0 45) 81x 18 7 46) Use the Quadratic Formula to solve. 7x x 5 Use the discriminant to tell whether the equation has two, one, or zero solutions. 47) 4x 1x 9 0 48) w 9w w 4 49) The discriminant of x 5x c is -7. What is the value of c? Unit 8: Radicals and Geometry Connections In # 50-57, simplify the expression 108 50) 4x 51) 18 x 3 x 5) 3 5 53) 75 np 4 m 54) 108 5 5 81k 55) 6 49d
56) 15 5 3 7 57) 3 5 500 In #58-60, solve for x. 58) 3x 6 4 59) x 4 x 1 60) 4x 3 x 0
Name: Date: Hour: Algebra Practice Exam Unit 5-8 Multiple Choice Please select the choice that best answers the question and mark your answer on the provided Scantron sheet. 61. What is the equation of the graph? a.) y = x b.) y = 3 x c.) d.) 6. Simplify 5a5 b 3a 3 b 6a- b 5 15a -5 b. a.) b.) c.) d.)
63. Which of the models below are exponential decay models? I. y = 1.19 x II. y = 0.1 x III. IV. a.) I and II b.) II and III c.) I and III d.) II and IV 64. You buy a used tractor for $55,10. It depreciates at the rate of 8.8% per year. What is the value of the tractor after 6 years? a.) $16,458.74 b.) $91,48.71 c.) $31,715.99 d.) $,433,639.8 y a 1- r t 65. You deposit $700 in an account that pays 8% interest compounded yearly. How much money is in the account after 10 years? a.) $13,000 b.) $589.10 c.) $117.84 d.) $964,06.15 y a 1 r t 4 66. Simplify a.) 4 8 b.) 4 16 c.) 4 10 d.) 4 1 4 4? 67. Which of the following is equal to? a.) b.) c.) d.)
68. Which of the following is equal to (6a 4b)? a.) b.) c.) d.) 69. Which of the following is equal to the expression 5x 4 + 30x 3 35x 4? a.) (3x 7)(6x + 5) b.) (5x 3 + 6)(x 7) c.) (6x + 7)(x + 5) d.) (5x 3 7)(5x + 6) 70. Which of the following is a solution of the equation 7x 11 = 4x +97? a.) 0 b.) -5 c.) -6 d.) -3 71. What is the x-coordinate of the vertex of the graph of the equation y = -x + 1x 7? a.) b.) - c.) 3 d.) 1 7. What are the zeros of the function y = 3x - 4x + 36? a.) - and 3 b.) c.) - and 6 d.) 6 and
73. What is the discriminant of the equation y = x x 1? a.) 0 b.) 9 c.) -7 d.) -8 74. Name the type of model that the graph suggests. a.) Quadratic b.) Exponential Decay c.) Exponential Growth d.) Linear 75. What is the correct factorization of -3x +16x + 35? (Factor the expression) a.) (3x + 5)(x 7) b.) -(3x + 5)(x 7) c.) -(3x 5)(x + 7) d.) (3x 5)(x 7) 76. What is the simplest form of (5x + )(5x )? a.) 5x -4 b.) 10x c.) 5x + 10x - 4 d.) 5x + 0x 4
77. What are the x-intercepts for the graph of y = (x 3)(x + ) a.) and 3 b.) - and 3 c.) -3 and d.) -3 and - 78. Which of the following is 7 6-1 + 4, in simplified form? a.) 5 9 b.) 9 6 4 3 c.) 6 18 d.) 3 3 6 79. Solve 8 x - 5 + 34 = 58. a.) b.) x 4 c.) x 14 d.) 7 x 710 80. Which expression is equivalent to 7? a.) 70 b.) 36 c.) d.) 6 81. Find the area of the rectangle. (A = l * w) 4 3 a.) 4 3 b.) 16 3 c.) 1 d.) 1 4 3 4