7) (2 + 3i) + (9 + 4i) 8) (3 + 4i) + (7 2i) 9) (9 + 2i) (12 i) 14) 2 + 3i 15) 5 2i

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1 Advanced Algebra EOC Study Guide Unit 1: Quadratics Revisited Simplify each of the following expressions. 1) i 45 ) i 7 3) i 130 4) i 453 5) i 480 6) i 141 7) ( + 3i) + (9 + 4i) 8) (3 + 4i) + (7 i) 9) (9 + i) (1 i) 10) (5 3i)(3 + 7i) 11) (7 i)(3 5i) 1) 5 6i 3 5i 13) 7 i 5 9i 14) + 3i 15) 5 i Solve the following by factoring. 16) x + 8x + 16 = 0 17) x 6x = 9 18) x + 8x = 1 19) x 7x + 10 = 0 Solve the following by completing the square and the square root method. 0) x + 4x + 1 = 0 1) x 6x + = 0 Solve each of the following using the quadratic formula. ) x + 3x 5 = 0 3) x + 5x 3 = 0 Factor and solve the following. 4) x 9 5) x + 9 6) x + 16 Simplify the following completely. 7) 8x 8) 4 4x y 3 9) ( 5)( 5)

2 Advanced Algebra EOC Study Guide Unit : Operations with Polynomials Find the sum or difference of the following. 1) (4y - y + 7) - (3y - y + 6) 3) (4x - 6x -9) + (-5x + x +11) ) (1x x 3 +4) + (x 8x ) 4) ( y - y ) - (y - y ) Use long division or synthetic division to divide the following polynomials. 5x 5x 18 x 7) (8x 4 + x 3) (x 5) 5) 6) 3x 3 5x x x 1 8) (8x 3 7) (x 3) Multiply the following expressions. Write your answer in standard form. 9) (x + 5) 3 10) ( 5x + 7)(6x + 4) Classify the following polynomials by degree and number of terms. Degree Number of terms 11) -7 1) x y + x 13) 3v 5 + 5v v + 3 Use Pascal s triangle in order to answer #14-15: 14) (x + 3) 5 15) (x )³ State if the given functions are inverses. Show or explain how you determined the answer. 16) f(x) = 6x 8 g(x) = x Find the inverse of the function. 17) f(x) = 5x ) y = 4x + 6

3 Advanced Algebra EOC Study Guide Given the following functions m(x) = 4x 3 and t(x) = x + 5, find: 19. m(t(5)) 0. t(m(x)) 1. m(x) + t(x). 3t(x) m(x) Use the graph to answer f(g(-1)) 4. g(f(-1)) 5. g(g(0)) Unit 3: Polynomial Functions Find all roots of the following. 1) F(x) = x 3 + 3x 4x 1 ) G(x) = x 3 + 4x + x 6 3) H(x) = x 3 + 4x + x + 4 4) J(x) = x 4 1x 64 5) For the following find each of the roots, classify them and show the factors. 3 a. f ( x) x 5x 4x 0 Possible rational roots: Show work for Synthetic Division and Quadratic Formula (or Factoring): Complete Factorization: Roots and Classification:

4 Advanced Algebra EOC Study Guide 6) For the following find each of the roots, classify them and show the factors. 4 3 f ( x) x x 9x x 8 Possible rational roots: Show work for Synthetic Division and Quadratic Formula (or Factoring): Complete Factorization: Roots and Classification: Find the equation, in standard form, for each of the following functions using the given information. 7) x-intercepts: ( 3, 0), ( 1, 0), (1, 0), and (, 0) y-intercept: (0, 3) Find the 4 th degree equation 8) x-intercepts: ( 5, 0), ( 1, 0), and (1, 0) y-intercept: (0, 5) Find the 3 rd degree equation 9) x-intercepts: (, 0) Mult., (1, 0), and (3, 0) y-intercept: (0, 1) Find the 4 th degree equation 10) Using the provided graph, answer all of the following questions. A) x-intercepts: B) y-intercept: C) 3 rd degree equation: D) Relative Maximum(s): E) Relative Minimum(s): E) Absolute Maximum: F) Absolute Minimum(s): F) Domain: G) Range: H) Odd, even, or neither: I) Intervals of increase: J) Intervals of decrease: J) Multiplicities:

5 Solve, show all work: 1) Advanced Algebra EOC Study Guide Unit 4: Rational and Radical Relationships 7 3 = 1 ) 3x x = 7 4x x x 3 Simplify: 3) x 5 x 13x+40 4) 4 x+1 x+ 5) + 4 x 9 x+3 6) 1x(x 7) (x 6)(x+8) (x 7)(x+3) x+3 7) 10 x+10 x 3 x+5 8) x+7 x+9 x +0x 1 6 Solve (Remember to check your answers!): 3 3 9) 18 3x = x 6 10) x 5 = x ) Nancy takes hours to spread mulch. Jessica takes 1 hour and 30 minutes to complete the same job. If they work together, how long, in minutes, will it take them? Identify all aspects of the graph that we have discussed in this unit. (Vertical asymptotes, horizontal asymptotes, holes in the graph, solutions, domain, and range.) Then graph. 1) y = x +x 8 x x 3 x 13) y x x x

6 Advanced Algebra EOC Study Guide Unit 5: Exponential & Logarithmic Functions A new solar system was discovered far from the Milky Way in After much preparation, NASA decided to send a group of astronauts to explore Exponentia, one of the planets in the system. Upon landing on the planet, the astronauts discovered life on the planet. Scientists named the creatures Viètians (vee-et-ee-ans), after the French mathematician François Viète who led the way in developing our present system of notating exponents. After observing the species for a number of years, NASA biologists determined that the population was growing by 10% each year. 1. The estimated number of Viètians was 1 million in 1999 and their population increases 10% a year. Complete the table to show the population for the next 4 years after Years since Population in millions 1. Write an equation for the population of Exponentia, P, as a function of the number of years, t, since How can you express the population as an expression in the table rather than as a computed value to help you see patterns to create the function? 3. What was the population in 005? What will the population be in 015 if the population growth rate remains the same? 4. Suppose you want to know when the population reached million. Write an equation that could be solved to answer this question. Determine the answer graphically and algebraically. 5. Expand log ab c d 6. Write the following using one log: loga + 3logB ½logC Solve the following x = logx8 = t = e 3t = log 3X = 5 1. log 19X = log(n + 3) = log(5n 1) 14.log 4 (3x ) log 4 (4x + 1) = 15. ln(6x 5) = log 3 (x 6x) = log8 x + log8(x + 6) = log8 (5x + 1) 18. log6 x + log6 (x -9) =

7 Advanced Algebra EOC Study Guide Unit 6: Mathematical Modeling Write the following series in summation notation and find the sum of the first 10 terms. 1 1) ) Isolate the designated variable (3 points each). ) E = mc for c 3) E = F q for q 4) Ten years ago, Josh put money into an account paying 5.5% compounded quarterly. If the account has $1,000 now, how much money did he deposit? 5) Your favorite neighbor, Mr. Nelson, needs your advice. He has $50,000 that he received as an inheritance from his late father. He would like to invest it into a savings account. He has the following two options: Option A: This is a continuously compounding account that has a 4% interest rate. Option B: This a monthly compounding account that bears a 4.5% interest rate. If Mr. Nelson is planning to invest for 5 years, which account would you suggest? Determine the degree type, leading coefficient, and function type (i.e. even, odd, or neither) for each of the following. 6) Degree: 7) x 3 + x Leading coefficient: Degree: Even, Odd, or Neither: Leading coefficient: Even, Odd, or Neither: 8) You and your family are away on vacation. Instead of eating out every night, it is decided that you will buy groceries and store them in the fridge in the condo. You buy $37.44 worth of groceries (before tax). If the sales tax in your current location is 6%, how much were your groceries after tax? (5 points) Using the graph to the left find each of the following. 9) f(3) 10) f(0) 11) f(-) 1) Is f(x) a function? 13) f(g(3))

8 Advanced Algebra EOC Study Guide Unit 7: Inferences & Conclusions from Data Use the data below to answer questions ) Find the 5-number summary of the data. ) Draw a box-and-whiskers graph of the data. 3) Draw a histogram of the data. 4) Find the mean median and mode. 5) Is the data skewed left or right? 6) What is the IQR? Identify any outliers. 7) Use the data set {8,, 30, 0}. Find: MAD Variance Standard Deviation Use the data below to answer questions freshmen at ELHS took an algebra test. The scores were distributed normally with a mean of 75 and a standard deviation of 7. Label the mean and three standard deviations from the mean. 8) What percentage of scores are between scores 61 and 89? 9) What percentage of scores is less than a score of 61? 10) What percentage of scores is greater than a score of 96? 11) Approximately how many algebra students scored between 61 and 89? 1) Approximately how many algebra students scored between 68 and 8? 13) A freshman scored a 65 on this test. Find the z-score associated with this test score. 14) Based on your answer for #1, what percent of students scored less than a 65? 15) Based on your answer for #1, what percent of students scored greater than a 65?