In #8-11, Simplify the expression. Write your answer using only positive exponents. 11) 4

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1 Algebra 1 Summer Review Name Directions: Do your best, this is a refresher from what you learned in Algebra 1. The more you review now, the easier it will be for you to jump back into Algebra Chapter 8: Exponents and Exponential Functions In #1-4 simplify the expression. Write your answer using exponents. 1) ( 5 ) ( )( ) ) ( 6 ) ) ) In #5-7 simplify the expression 1 5) 6) 8 5 ( 4 n m ) 7) r In #8-11, Simplify the expression. Write your answer using only positive exponents. 8) x yz 1 ab 9) a c 10) ( 6m) (m ) 4 (mn) (m) 11) 4 4m n 1) In the following, use the function y = x a) Complete the table for the function b) Graph the function c) Identify the domain and range. Domain: Range:

2 1) Write in scientific notation 14) Write 1,08,000 in scientific notation 15) 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. 16) You buy a new car for $,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 17 and 18, Tell whether the graph represents exponential growth or exponential decay. Then write a rule for the function. 17) 18)

3 In 19 and 0, simplify the expression. 19) x when x = 5 0) 1 x when x = Chapter 9: Polynomials and Factoring In 1 and, find the sum of the polynomials. 1) (x 7x 5x ) ( x x) ) (7a a 14) (9a 11a) In and 4, find the difference of the polynomials. ) (17y 6y 5) (11y y 8) 4) ( b b 6b 1) (b 11b ) In #5-8, find the product of the polynomials. (double-distribute/foil) 5) ( 9r )(r 1) 6) (7t )( t 5t ) 7) ( b a 5 ) 8) ( 9z )(9z )

4 In #9-4, factor the polynomial. 9) x 10x 1 0) 4y y 6 1) 5x 0x 0 ) x 11 ) x 7x 0 4) 9y 66y 11 In #5-6, what are the x-intercepts? (Also called Zeros/Roots/Solutions) 5) ( x 7)( x ) y 6) (5x )( x 11) y In #7-4, solve the equation. 7) x x ) z 169 6z 9) 1x ) 4x 11x 5x 4 41) x x 5x 5 0 4) m 6m m 1 0

5 4) A rectangle has the length of (x+) inches, a width of (x+4) inches, and an area of 15 square inches. Find the value of x. (hint: draw a picture!) Chapter 10: Quadratic Equations and Functions Find the vertex of the following quadratics: 44) x 4x 1 45) x 8x 5 46) Given the following information about the parabola, answer the questions. y x 8x 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 and plot the vertex. Find more points on the graph and graph the parabola x y Vertex

6 47) Given the following information about the parabola, answer the questions. y x 4x 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 and plot the vertex Find more points on the graph and graph the parabola x y Vertex In solve the equation. Round to the nearest hundredth, if necessary 48) x ) 81x ) Use the Quadratic Formula to solve. 7x x 5 Use the discriminant to tell whether the equation has two, one, or zero solutions. 51) 4x 1x 9 0 5) w 9w w 4

7 5) The discriminant of x 5x c is -7. What is the value of c? Chapter 11: Radicals and Geometry Connections In # 54-61, simplify the expression ) 4x 55) 18 x x 56) 5 57) 75 np 4 m 58) k 59) 6 49d 60) ) In #6-64, solve for x. 6) x 6 4 6) x 4 x 1 64) 4x x 0

8 Chapter 1: Rational Equations and Functions 65) Given that y varies inversely with x, use the specified values to write an inverse variation equation that relates x and y. Then find y when x = 6. x = 4, y = 66) Given that y varies inversely with x, use the specified values to write an inverse variation equation that relates x and y. Then find y when x = 18. x = 6, y = 9 Graph the function. 67) y x x y Und. 68) Use the stem-and-leaf plot to find the mean, median, mode, and range. a) Mean: b) Median: c) Mode: d) Range:

69) Use the histogram to answer the following questions. a) What salary level had the highest number of employees? b) Roughly, how many employees were surveyed?

9 69) Use the histogram to answer the following questions. a) What salary level had the highest number of employees? b) Roughly, how many employees were surveyed? c) How many emplyees make $77,000 - $87,000? 70) Solve the system using substitution: y = x - 4 y + x = -. Check your answer by graphing the two equations. 71) Solve the system using elimination: y = x - y = -x + 4. Check your answer by graphing the two equations.

Name: Date: Hour: Algebra Practice Exam Chapters 8-1 Multiple Choice Please select the choice that best answers the question and mark your answer on the provided Scantron sheet. 7.

10 Name: Date: Hour: Algebra Practice Exam Chapters 8-1 Multiple Choice Please select the choice that best answers the question and mark your answer on the provided Scantron sheet. 7. What is the equation of the graph? a.) y = x b.) y = x c.) d.) 7. Rewrite 6.5 x 10 6 in standard form. a.) b.) c.) 65,000,000 d.) 6,500, 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

11 75. 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, b.) $91,48.71 c.) $1, d.) $,4,69.8 y a 1- r t 76. You deposit $700 in an account that pays 8% interest compounded yearly. How much money is in the account after 10 years? a.) $1,000 b.) $ c.) $ d.) $964,06.15 y a 1 r t Simplify a.) 4 8 b.) 4 16 c.) 4 10 d.) ? 78. Which number represents 65,006,000 in scientific notation? a.) x 10-7 b.) x 10 7 c.) x 10-6 d.) x Which of the following is equal to ( 8x -1x + 5x -1) - ( 4x -14x - 40)? a.) 7x + x - x - 8 b.) 8x -16x -11x - 5 c.) 8x -16x + 9x + 7 d.) 1x + x - x - 8

12 80. Which of the following is equal to (6a 4b)? a.) 6a - 48ab +16b b.) 6b + 48ab -16a c.) 6a +16b d.) 16b + 49a Which of the following is equal to the expression 5x 4 + 0x 5x 4? a.) (x 7)(6x + 5) b.) (5x + 6)(x 7) c.) (6x + 7)(x + 5) d.) (5x 7)(5x + 6) 8. Which of the following is a solution of the equation 7x 11 = 4x +97? a.) 0 b.) -5 c.) -6 d.) - 8. What is the x-coordinate of the vertex of the graph of the equation y = -x + 1x 7? a.) b.) - c.) d.) What are the zeros of the function y = x - 4x + 6? a.) - and b.) and c.) - and 6 d.) 6 and

85. What is the discriminant of the equation y = x x 1? a.) 0 b.) 9 c.) -7 d.) -8 86. Name the type of model that the graph suggests. a.) Quadratic b.) Exponential Decay c.) Exponential Growth d.

13 85. What is the discriminant of the equation y = x x 1? a.) 0 b.) 9 c.) -7 d.) Name the type of model that the graph suggests. a.) Quadratic b.) Exponential Decay c.) Exponential Growth d.) Linear 87. What is the correct factorization of -x +16x + 5? (Factor the expression) a.) (x + 5)(x 7) b.) -(x + 5)(x 7) c.) -(x 5)(x + 7) d.) (x 5)(x 7) 88. What is the simplest form of (5x + )(5x )? a.) 5x -4 b.) 10x c.) 5x + 10x - 4 d.) 5x + 0x 4

89. What are the x-intercepts for the graph of y = (x )(x + ) a.) and b.) - and c.) - and d.) - and - 90. Which of the following is 7 6-1 + 4, in simplified form? a.) 5 9 b.) 9 6 4 c.) 6 18 d.

14 89. What are the x-intercepts for the graph of y = (x )(x + ) a.) and b.) - and c.) - and d.) - and Which of the following is , in simplified form? a.) 5 9 b.) c.) 6 18 d.) Solve 8 x = 58. a.) x 710 b.) x 4 c.) x 14 d.) x = Which function is graphed? a.) xy = 0 x b.) y 1 c.) x x d.) xy = 9. Which expression is equivalent to 7? a.) 70 b.) 6 c.) 6 d.)

15 94. Find the area of the rectangle. (A = l * w) 4 a.) 4 b.) 16 c.) 1 d.) Which of the following equations models inverse variation?? a.) y = x b.) y = x c.) y = x + d.) xy =

In #8-11, Simplify the expression. Write your answer using only positive exponents. 11) 4

In #8-11, Simplify the expression. Write your answer using only positive exponents. 11) 4 Semester Final Eam Review Packet Name Chapter 8: Eponents and Eponential Functions In #1-4 simplify the epression. Write your answer using eponents. 1) ( ) ( )( ) 5 ) ( 6 ) 5 4 ) 7 4 11 7 6 6 4) 8 6 1