Name Date Per. /Teacher. A2TH Common Core Review #1

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1 Name Date Per. /Teacher A2TH Common Core Review #

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9 Name Algebra 2 Regents Review Packet #2: #3 Units 6-7 Date DIRECTIONS: Show all work in the space provided. All work must be shown or no credit will be given. DUE: Thursday, 4/21 UNIT 6 QUADRATIC EQUATIONS 1) A homeowner wants to increase the size of a rectangular deck that now measures 14 feet by 22 feet. The building code allows for a deck to have a maximum area of 800 square feet. If the length and width are increased by the same number of feet, find the maximum number of whole feet each dimension can be increased and not exceed the building code. [3 points] 2) Solve for x and express your answer in simplest form: [2 points]

10 3) Which value of k will make a perfect square trinomial? [1 point] 1) 2) 3) 4) 4) Find the exact roots of by completing the square. [2 points] 5) Solve for x and express your answer in simplest radical form: 1 (x 6) [2 points]

11 UNIT 7 POLYNOMIAL FUNCTIONS 6) If a, b, and c are all positive real numbers, which graph could represent the sketch of the graph of ( ) ( )( )? [1 point] 7) Use an appropriate procedure to show that is a factor of the function ( ). Explain your answer. [2 points]

12 8) Solve algebraically for all values of x:. [3 points] 9) Solve algebraically for all values of x: [3 points] ) Find four roots of the following equation: 2x 3x 20 [3 points]

13 11) What are the zeros of the polynomial function graphed below? [1 point] 1) 2) 3) 4) 12) Use a graphing calculator to graph. Tell whether the function is odd, even, or neither. Explain your answer. [2 points] 13) Sketch the graph of a polynomial with the given characteristics [2 points] is increasing when. is decreasing when ( ) when and. ( ) when.

14 14) Find the value of so that has a remainder of 8. [2 points] 15) Write a polynomial function in standard form with least degree whose roots are given. [3 points],,,

15 16) Consider the polynomial function [4 points] ( ). a) Verify that ( ). Since ( ), what must one of the factors of be? b) Find the remaining two factors of and state the zeros of. d) Sketch the graph of.

16 17) Consider the graph of a degree 5 polynomial shown to the right, with x-intercepts,,,,, and [3 points] a) Write a formula for a possible polynomial function that the graph represents using as the constant factor. b) Suppose the -intercept is. Find the value of so that the graph of has -intercept. 18) Solve the following system of equations algebraically: [4 points]

17 Name Algebra 2 Regents Review Packet #4: Units 8-9 DUE: Friday, 4/29 Date DIRECTIONS: Show all work in the space provided. All work must be shown or no credit will be given. UNIT 8 RATIONAL EXPRESSIONS AND EQUATIONS 1) Solve for x: [2 points] 2) Write ( ) ( ) as an equivalent rational expression in lowest terms. [2 points] 3) A boat goes 240 miles downstream in the same time it can go 160 miles upstream. The speed of the current is 5 miles per hour. What is the speed of the boat in still water? [2 points]

18 4) What is the solution set of the equation? [1 point] 1) 2) 3) 4) 5) Working by herself, Mary requires 16 minutes more than Antoine to solve a mathematics problem. Working together, Mary and Antoine can solve the problem in 6 minutes. Using the equation he works by himself? [2 points] how many minutes will it take Antoine to solve the problem if 6) Which expression is in simplest form? [1 point] x (1) x (3) x x 2 (2) 9 2 x 9 (4) x 2 6 x 9 2 x x 6

19 UNIT 9 RATIONAL EXPONENTS AND RADICAL EXPRESSIONS /EQUATIONS 7) Use the properties of rational exponents to determine the value of y for the equation: [2 points] ( ) 8) Solve algebraically for x: [2 points] 3 2 9) The expression 2 (1) x 1 is equivalent to [1 point] (2) (3) (4)

20 10) Solve for b: ( b 3/ 4 b 1/ 2 ) 2 30 [2 points] 11) Rewrite the given expression in the form, where is a real number, is a positive real number, and is rational. ( ) [2 points] 12) Show that for any rational number, the expression ( ) is equal to [2 points]

21 5 378a b 13) Express 3 7a 3 b in simplest radical form. [2 points] 14) Simplify: [2 points] 15) Solve for all values of x: [2 points]

22 Name Algebra 2 Regents Review Packet #5: Unit 10 Parts 1 and 2 DUE: May 10 th Date DIRECTIONS: Show all work in the space provided. All work must be shown or no credit will be given. UNIT 10 Part 1 Exponential and Logarithmic Functions 1) 2) What is the inverse of the function y = log 3 x (1) 3 y = x (3) x 3 = y (2) 3 x = y (4) y = x 3 [2 points] [2 points] 3) If and, the expression is equivalent to 1) 3) 2) 4) [2 points] 4) Which expression is not equivalent to log 36 b? (1) 6log b 2 (3) 2log b 6 (2) log 9 log 4 (4) log 72 log 2 b b b b [2 points] 5) The expression (1) log x 3 y 1 2log x log y is equivalent to: 3 (2) 2 log x 3 y 3 (3) log xy (4) 3 log( x y ) [2 points]

23 ab 6) If d 2 c 2, then log d is equal to: 1 (1) log a (log b log c) 2 (3) log a 2(log b log c) (2) log a log b log c 1 1 (4) log a log b log c 2 2 [2 points] 7) Solve for x: [2 points] rt 8) Todd invests $7,000 at an annual interest rate of 4.2% compounded continuously. Use the formula A Pe to determine how many years, to the nearest tenth of a year, it will take for Todd s investment to triple. [4 points] 9) Use the change of base rule to solve for x: log 25(2x 2) log 5( x 3) [4 points]

24 10) Solve for x: log ( x 3) (2x 3) log ( x 3) ( x 5) 2 11) Solve for x to the nearest hundredth: 5 x 3 5 x 100 [4 points] [4 points] UNIT 10 Part 2 Exponential and Logarithmic Functions 12) [2 points]

25 13) A savings account initially has a balance of $500. The number of years, t, that the money must be in the account for it to grow to a balance of b dollars is shown in the accompanying table. Balance 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 (b) Years (t) (a) Determine a logarithmic regression equation that models this data. Round coefficients to the nearest hundredth. (b) Use the regression equation found in part a to predict, to the nearest tenth of a year, the number of years the money must be left in the account for it to grow to a balance of $7,500. [4 points] 14) Find the inverse of the following function and state the domain and range of the original function and inverse function. 2 f ( x) e x [4 points]

26 15) Suppose that you would like to buy a home priced at 220,000. You plan to make a payment of of the purchase price and pay of the purchase price into an escrow account annually. Compute the total monthly payment of the loan for a -year mortgage at 4.6% annual interest. [4 points] 16) [4 points]

27 17) [4 points]

28 Name Algebra 2 Regents Review Packet #6: Units DUE: May 20, 2016 Date DIRECTIONS: Show all work in the space provided. All work must be shown or no credit will be given. UNIT 11 Sequences and Series 1) Write an explicit formula for the nth term of the recursively defined sequence below. For what values would when 2) What is the common ratio of the sequence? {4 points} 1) 2) 3) 4) {1 point}

29 3) Write the sum without using summation notation, and find the sum. {2 points} 4) Find the sum of the following geometric series: 5) Write a rule for the nth term of sequence 57, 48, 39, 30, {2 points} {2 points} Unit 12 Intro to Trig 6) Find the degree measure of an angle of 2.75 radians to the nearest tenth. {2 points}

30 7) Use the Pythagorean identity, where is any real number, to find the following:, given for. 8) Simplify the expression: {2 points} 9) In which quadrant does the terminal side of lie when {1 point} 10) Find the exact value of sec(-120 ) {1 point} {2 points}

31 11) Point Q( 5, 1) is on a circle of radius r whose center is at the origin. If is an angle in standard position whose terminal ray passes through point Q, find the value of: f) cos b) sin c) csc d) cot e) tan f) sec {4 points}

32 Unit 13 Trig Graphs 12) Which statement is incorrect for the graph of the function [ ]? (1) The period is 8. (2) The amplitude is 6. (3) The range is [-6, 6] (4) The midline is {1 point} 13) Write an equation to represent the graph below. 14) Which of the following functions has a maximum value of 25? (1) (3) (2) (4) {2 points} {1 point}

33 15) Suppose that a Ferris wheel is feet in diameter and rotates counterclockwise. When a passenger car is at the bottom of the wheel, it is located feet above the ground. It takes 6 minutes to go around the Ferris wheel one time. a. Sketch a graph of a function that represents the height of a passenger car that starts at the top of the wheel for one turn. b. The sketch you created in part (a) represents a graph of a function. What is the domain of the function? What is the range? c. Find the equation for the function in part (a). {6 points}