review for finals 10. If f (x) = x 2 A If f (x) = x 0 + x x 1, find f (4). 13. If f (x) = (x 0 + x 1 2 ) 2, find f (9).

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1 Name: ate: 1. If g(x) = (ax 1 x) 2, express g(10) in simplest form. 2. The value of the x-intercept for the graph of x 5y = 0 is What is the inverse of the function y = 2x +? x = 1 2 y 2. y = 1 2 x 2. y = 2x x = 2y. function is defined by the equation y = 2x +. Which equation defines the inverse of this function? y = 1 2 x + 1. x = 1 2 y 2. y = 2x y = 1 2 x 2 5. If f (x) = x and g(x) = 7x 1, what is (f g)()? 6. If g(x) = x and h(x) = x 1, what is g(h())? 10. If f (x) = x 2, what is f ()? If f (x) = x 0 + x x 1, find f (). 12. Evaluate: If f (x) = (x 0 + x 1 2 ) 2, find f (9). 1. The value of ( 6) 2 is Meteorologists can determine how long a storm lasts by using the function t(d) = 0.07d 2, where d is the diameter of the storm, in miles, and t is the time, in hours. If the storm lasts.75 hours, find its diameter, to the nearest tenth of a mile. 16. Solve for x: x 2 = 2 x 17. Solve for x: = 2 x Solve for x: 2 x+ = 6 7. If f (x) = x and g(x) = x, then f (g()) is If f (x) = x and g(x) = x 2, find the value of f () g(2). 9. The value of ( 27 ) 2 is 19. The accompanying diagram shows the graph of the equation y = x. What is the equation of the graph obtained by reflecting y = x in the x-axis? y = log x. y = ( 1 )x. y = x x = y page 1

2 20. The graph of the equation y = ( 1 )x lies in Quadrants I and IV. I and II. III and IV II and III 21. The accompanying graph shows the relationship between a person s weight and the distance that the person must sit from the center of a seesaw to make it balanced. 2. The Franklins inherited $,500, which they want to invest for their child s future college expenses. If they invest it at.25% with interest compounded monthly, determine the value of the account, in dollars, after 5 years. Use the ( formula = P 1 + n) r nt, where = value of the investment after t years, P = principal invested, r = annual interest rate, and n = number of times compounded per year. 2. If log x =, what is the value of x? 25. If log 2 x =, then x is equal to If log x 1 = 1, find x. 27. If log 2 = log + log x, what is the value of x? Which equation best represents this graph? y = 12x 2. y = 120x. y = 2 log x y = 120 x 22. The accompanying graph represents the value of a bond over time. Which type of function does this graph best model? The value of (2i ) is 6. 6i. i 29. Express the product (2 + i)( i) in the form a + bi. 0. Expressed in a + bi form, 5 + i is equivalent to 15 5 i. 5 5i i 15 5i 1. The expression 2 + i + i is equivalent to trigonometric. logarithmic. quadratic exponential i 7 5i i 7 + i 10 page 2

3 2. The accompanying diagram shows the graph of the parabola y = ax 2 + bx + c. 7. The accompanying diagram shows a parabola. Which statement is not true? What must be one root of the equation ax 2 + bx + c = 0? The roots of the equation x 2 10x + 25 = 0 are imaginary. real and irrational. real, rational, and equal real, rational, and unequal. Find the positive root of the equation x 2 6 = What are the roots of the equation x 2 x + 1 = 0? The equation of the axis of symmetry is x = 2.. The parabola has a minimum point.. The turning point of the parabola is ( 2, 1). The parabola has two x-intercepts.. What is the minimum point of the graph of the equation y = 2x 2 + x + 9? (2, ). (2, 17). ( 2, 15) ( 2, 1) 9. If x = 0, the roots of the equation are 25 and , only. 5 and 5 5, only. 1 ± 2 1 ± i 2. 1 ± ± i Solve using the quadratic formula: x 2 + 5x 2 = 0 1. x x + 6 = 0 6. What are the coordinates of the minimum point of a parabola whose equation is y = x 2 + 2? (0, ). ( 1, 2). (, 0) (, 12) page

4 2. company produces x units of a product per month, where (x) represents the total cost and R(x) represents the total revenue for the month. The functions are modeled by (x) = 00x and R(x) = 0.5x x 100. The profit is the difference between revenue and cost where P(x) = R(x) (x). What is the total profit, P(x), for the month? = If x = and y = 1, what is the value of the expression below? 2x y P(x) = 0.5x x 150. P(x) = 0.5x x P(x) = 0.5x 2 500x + 50 P(x) = 0.5x x What is expressed in simplest radical form?. The square of a positive number decreased by times the number is 12. Find the positive number. [Only an algebraic solution will be accepted.]. The sum of 1 and 6 2 is The expression 200 is equivalent to In simplest form, 00 is equivalent to i 10. 5i i 12i Expressed in simplest form, x 1, 0, 1, is equivalent to 2x x x 2 x 2 1 x 1, x 2 x 2x x Perform the indicated operation and express in lowest terms: x x x 2 y subtracted from 7x 2 1 is 2x 2 y x 2 + y 1. 2x 2 + y 1 none of these 7. What is equal to 27? amille placed blocks on a table in rows and columns. ll the rows and columns had the same number of blocks in them and formed a square. Which could be the total number of blocks amille placed on the table?. If x = 100, what is the value of x? blocks. 121 blocks. 11 blocks 222 blocks page

5 56. What is the value of the expression below? What is the value of the expression? 6x 16 y The total area of laska is 591,000 square miles. Which of the following is 591,000 expressed in scientific notation? What is written in standard form? x y 2. x y 2. 2x y 2 2x y 2 6. What is the complete factorization of the polynomial shown? 5x 20x 2 25x x(5x 2 20) 25. 5x(x + 5)(x 1). 5x(x 5)(x + 1) x(5x 2 20x 25) ,000 72,900, What is the standard notation for the following expression? Which polynomial represents (x 2 + x )(2x 5)? 6x 1x 2 1x 20. 6x 1x 2 1x x + 1x 2 + x 20 6x + 1x 2 + x ( 2x 2 + 6x + 1) 2(x 2 x + 1) 60. garden snail travels at approximately miles per second. Which of these is written in scientific notation? 6x x x x 1 10x x Which of the following expressions is equivalent to (6xy) 2? 12x 2 y 2. 6xy 2. 6x 2 y 2 6x 2 y If a = and b = 2, what is the value of the expression a 2 b? page 5

6 67. What is the volume of the figure below? 7. What is the common ratio of the geometric sequence whose first term is 27 and fourth term is 6? What is the common difference of the arithmetic sequence 5,, 11, 1? x + 10x 2 + x + 2. x + 11x 2 + x + 2. x + 10x 2 + 2x + 2 x + 11x 2 + 2x Look at the pattern below:, 1,, 11,... What is the 7 th term in this pattern? The area of a rectangle in square inches is represented by the expression x 2 + 2x. The length of the rectangle is x + inches. What is an expression for the width of the rectangle in inches? 77. Study the number sequence below. 16, 19, 2, 1,... What is the seventh term in the sequence? 69. Expressed as a single fraction, equivalent to x 1 2 x is x(x 1). x 2 x(x 1) 7. Look at the sequence. 15,, 0.6, 0.12,.... x + 2 x(x 1) x 2 x(x 1) What is the next number in the sequence? 70. Solve for n: n 5n + 7 = Kara formed a pattern using the following steps. 71. Solve for x: 2x = Solve for x: x = 5 7. What is a formula for the nth term of sequence shown below? = 10, 12, 1, 16,... b n = + 2n. b n = n. b n = 10(2) n b n = 10(2) n 1 She chose 1 as the first term. Each term after the first was two more than the immediately previous term. What are the first five terms of Kara s sequence? 1, 2,,, 10. 1, 0, 2,, 6. 1, 1,, 5, 7 1, 0,, 5, 7 page 6

7 0. Sandra wrote the sequence below. 2, 5, 10, 17,... Which equation represents the rule for finding the n th term of this sequence? 5. Which is the factored form of a 2 2ab + b 2? (a b)(a 6b). (a 16b)(a b). (a b)(a b) (a b)(a b) a n = n + 1. a n = 2n 2. a n = n a n = 2n Which function describes the sequence, 6, 12, 2,... for n = 1, 2,,...? f (n) = n. f (n) = n f (n) = (2 n 1 ) f (n) = (n 1) Use the table below to answer the question n a n If the pattern in the table continues, which of the following expressions represents a n? 2 n 1. (n 1) 2. (n 1) n 2 1. n auditorium has 0 rows of seats. The first row has 0 seats. The second row has 2 seats. The third row has seats. Each successive row has two more seats than the row before it. How many seats are there in the 0th row? 6. Which is a factor of x 2 11x + 2? x +. x. x + x 7. Which of the following shows 9t t + factored completely? (t + 2) 2. (t + )(t + 1). (9t + )(t + 1) 9t t. What are the solutions for the quadratic equation x 2 x = 9?.,. 1, 9 1, 9 9. What are the solutions to the equation x 2 + 2x + 2 = 0? x = 0; x = 2. x = 0; x = 2i. x = 1 + i; x = 1 i x = ; x = seats. 7 seats. 9 seats 100 seats. Look at the pattern below. 16, 21, 26, 1, 6, 1,... If the pattern continues, what will be the tenth term? 90. Which of the following is one of the factors of the expression below? x 2 25 (x 5). (2x + 1). (x 1) (2x 5) page 7

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