Algebra II: Chapter 4 Semester Review Multiple Choice: Select the letter that best answers the question. D. Vertex: ( 1, 3.5) Max. Value: 1.

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1 Algebra II: Chapter Semester Review Name Multiple Choice: Select the letter that best answers the question. 1. Determine the vertex and axis of symmetry of the. Determine the vertex and the maximum or minimum following quadratic: value of the following quadratic: y = ( x + 6) y = x + x. A. Vertex: ( 6, 1) B. Vertex: ( 6, 1) A. Vertex: ( 1, 1.) B. Vertex: ( 1, ) Axis: x = 6 Axis: x = 1 Max. Value: 1. Max. Value: C. Vertex: ( 6, 1) D. Vertex: ( 6, 1) C. Vertex: ( 1,.) D. Vertex: ( 1,.) Axis: x = 6 Axis: x = 6 Min. Value:. Min. Value:. Determine whether the equation is in Vertex, Intercept, or Standard form. Then, find the indicated values and graph each equation. Don t forget to draw the axis of symmetry!. y = x + 1x. y = x + 10x Vertex or Intercept or Standard Vertex or Intercept or Standard Opens Opens Vertex (, ) Vertex (, ) Axis of Symmetry Axis of Symmetry Maximum or Minimum Maximum or Minimum Value Value

2 Determine whether the given equation is in Vertex, Intercept, or Standard Form.. y = ( x + )( x + 1) 1 6. ( x) = x + x 1 + f. y = ( x + ) Vertex or Intercept or Standard Vertex or Intercept or Standard Vertex or Intercept or Standard Multiple Choice: Select the letter that best answers the question. 8. Simplify 6 x 8x A. 8 x x B. 96 x x C. 96 x x D. 19x x Simplify ( 1)( 6 + ) 9. A B C D Simplify ( 1 i) ( 6 i) A. i B. 1+19i C. 9i D. + i Simplify i i 1. A. i B. i + i i C. D. i + Use what you know about simplifying square roots and the properties of i to answer the following questions. Make sure that all denominators are rationalized and each root is completely simplified. 1. ( i) ( 6 i) + 1. ( 11 )( 11+ ) i 1i Answer: Answer: Answer: Answer:

3 18. Find the value of the discriminant and describe the zeros of: x + x = A. D = 100 real zeros B. D = double zero/root C. D = 9 imaginary zeros D. D = 96 real zeros 19. Find the solutions/zeros of: x x + = A. ± i B. 1 ± i C. ± i Which value of c makes the trinomial x + 16x + c a perfect square trinomial? D. 1± i A. B. 18 C. 6 D. 6 Write the quadratic equation in vertex form: y = x 16x y = Write the quadratic equation in vertex form: y = x + 0x y =

Algebra II: Chapter Semester Review Evaluate or simplify the expression completely. 1.. 0 h e h e ( )( ) a 0 6 b d Name. 6 c 16c d d Answer: Answer: Answer:. ( ) x y. 11 8 1 ( 10w x)( w x ) 6.

a b Which of the following expressions is equivalent to: ( a + a 6) ( a a + ) D. a bc 8. 9. A. a a + 8 a B. a + a + a + C. a + a 8 D.

4 Algebra II: Chapter Semester Review Evaluate or simplify the expression completely h e h e ( )( ) a 0 6 b d Name. 6 c 16c d d Answer: Answer: Answer:. ( ) x y ( 10w x)( w x ) 6. 9b 1b c c 0 Answer: Answer: Answer:. Which of the following expressions is equivalent to: 1 8a bc 1ab c. 8. A. ab c B. a b c C. a b Which of the following expressions is equivalent to: ( a + a 6) ( a a + ) D. a bc A. a a + 8 a B. a + a + a + C. a + a 8 D. a + a + a 8 Which of the following expressions is equivalent to: ( x + 1)( x 9x ) 9. A. B. C. D. Use the graph to describe the end behavior, determine the number of real zeros, and estimate the indicated value As x, f ( x) As x, f ( x) As x +, f ( x) As x +, f ( x) Number of real zeros: Local Maximum: (, ) Number of real zeros: Local Minimum: (, )

5 Identify all of the factors of each polynomial. 1. 8y x x Factors: Factors: x 1. x 1x + 10x 1. x 8 Factors: Factors: Use synthetic division to divide the following polynomials. 16. ( x 11x + 1x ) ( x ) 1. ( x + x 1x + 10) ( x + ) Answer: Given polynomial f ( x) and a factor of f ( x), factor ( x) 18. One factor of f ( x) = x x x + is ( x + ). Find the remaining factors. Answer: f completely. 19. One factor of f ( x) = x x + 6 is ( x 1) remaining factors.. Find the Remaining Factors: Remaining Factors:

0. Find two of the zeros of the function: f ( x) = x x + x x 6 0. 1. A., B., 1 C. i, D. i, Find two of the zeros of the function: f ( x) = x + x + x + x 1. A. 6, B. 1,. C. 6, i D.

6 0. Find two of the zeros of the function: f ( x) = x x + x x A., B., 1 C. i, D. i, Find two of the zeros of the function: f ( x) = x + x + x + x 1. A. 6, B. 1,. C. 6, i D. 1, i Write an equation in standard form with the following zeros:. x 9 and x = i =. x = i and x = Equation: Equation:. The function whose graph is shown has.. A. two local maximums B. no local maximums C. two local minimums D. one local minimum

7 Algebra II: Chapter 6 Semester Review Evaluate the expression. 1. ( ). ( ) Name Use the properties of rational exponents to simplify. Express in simplest radical form.. 8. m m x x. x 8. x b b 8 9. Which of the following expressions is equivalent to: B C D. 1 8 A. 9 Which of the following expressions is equivalent to: x y z 10. A. xyz B. x xyz C. x xyz D. 9 x xyz 9x

8 Simplify the expression using the properties of radicals x x y 10 y 1. If h ( x) = x 9 and m ( x) = x + x, find: ( x) m( x) h? A. x 9 x B. + x + 9 x C. If h ( x) = x 9 and m ( x) = x + x, find: ( x) h( x) m? x + 6x D. x 9 1. A. x 9 x B. + x + 9 x C. Let f ( x) = x 9, g( x) = x. Perform the indicated operation. 1. f ( g( x) ) 16. g ( f ( x) ) x + 6x D. x 9 Find the inverse of the function. 1. f ( x) = x f ( x) = x 9

9 Let f ( x) = x, g( x) = x, j ( x) = x, and m ( x) = x 11 g( x) 19. f (x) 1. Find only the domain of each. 0. j m ( x) ( x) Domain: Find the solution(s) to the equation: Domain: 1. = x x. x 8 = 18x. x = x 1

10 Algebra II: Chapter Semester Review Name Determine whether each function represents exponential growth, decay, or neither. x y = ( ) x x. y = 10 y = Match the function with the graph. x A. B. C.. y =. y = x + x+ 6. y = Match the function with the graph. A. B. C. x +. y = 8. 1 y = 1 + x x1 9. y = Convert each of the following. 10. = 9 to logarithmic form 11. e = 1 to logarithmic form 1 = 1. x ln 0 x to exponential form 1. ln10x = to exponential form Use the Change of Base Theorem to evaluate the following expressions. 1. log 1. log 1

11 Use the rules of logs to condense the expression log ( x ) log x 1. log x log log y 19. log log Solve each logarithmic equation. 0. log x = 1 1. log 6 ( x + 1) =. ln ( x + ) = 1. x + log ( x + ). x + log ( x 6) log = log = Solve each exponential equation. Round all decimals to two decimal places. z +. = 8 n + 1 = 9 n 1 6. ( ). 6x 1 = x + x 8. = 9. x e 1 = 1

12 Use the formulas to solve the following story problems. You will need to have these on your notecard for the exam. rt A= Pe y = a( 1 ± r) t A = P 1 + r n nt 0. A computer system depreciates at a rate of 1% per year. If the computer system originally cost $000, how long would it take for it to be worth half its value? 1. A car depreciates in value 1% per year. After approximately how long will a $0,000 car be worth half its original value?. Suppose you deposit $1,000 in an account paying 6.% annual interest compounded continuously. What is the balance after 6 years?. You deposit $10,000 in an account paying 6.% annual interest compounded continuously. What is the balance after 6 years? Find the inverse of the function. y. y = ln ( x + ). = ( x 1) log

13 Algebra II: Chapter 11 Semester Review Name A recent survey of 000 people showed that 8% returned a purchase during the month of December. Find the margin of error for the survey. 1. MOE: Calculate the following values for each data set. Round decimals to the nearest tenth Mean: Median: Range: Mean: Median: Range: Mode: Standard Deviation: Mode: Standard Deviation: Use the box and whisker plot to answer the following questions.. Find the range:. Find the median: 6. Find the Greatest Value:. Find the Lower Quartile: 8. Find the Interquartile Range:

2015 2nd Semester Exam Review

Algebra 2 2015 2nd Semester Exam Review 1. Write a function whose graph is a translation of the graph of the function in two directions. Describe the translation. 2. What are the solutions to the equation?