Algebra 2 CP Semester 1 PRACTICE Exam January 2015

Transcription

1 Algebra 2 CP Semester 1 PRACTICE Exam January 2015 NAME DATE HR You may use a calculator. Please show all work directly on this test. You may write on the test. GOOD LUCK! THIS IS JUST PRACTICE GIVE YOURSELF 67 MINUTES TO DO THE TEST CHECK YOUR ANSWERS AFTER. Once you ve checked, go back and redo any problem that s incorrect it should probably then go on your notecard! 1. Find the y-intercept of: y = 2x 2 + 8x 10 A. (0, 2) B. (0, -2) C. (0, 8) D. (0, -10) 2. Find the Axis of Symmetry of: y = 2x 2 + 8x 10 A. x = 2 B. x = -2 C. x = 8 D. x = -10. Which of the following is equivalent to: (6 5i)(6 + 5i) A. 61 B. 6 25i C i D i 4. Which of the following is equivalent to: 5+ 2 A B C D

2 5. Solve the following equation: x 2 4x + 6 = 0 A. 4 ± 10 B. 2 ± 10 C. 4 ± 2 D. 2 ± 2 6. Which of the following expressions is equivalent to: ( 2x y 4 ) 2 (x 9 y ) A. 12x 18 y 12 B. 12x 15 y 12 C. 12x 15 y 5 D. 6x 15 y 5 7. Which of the following expressions is equivalent to: 125a7 b 4 5a 4 b A. 25a b B. 25a b C. a 625b D. a 10b 8. Which of the following expressions is equivalent to: (x + 2)(x 1)(x + ) A. x 6 B. x + x 2 2x 6 C. x + 4x 2 + x 6 D. x + 2x 2 2x 6

3 9. Which graph has the following End Behavior: as x, f(x) as x, f(x) A. B. C. D. 10. Identify one of the factors of: 2x 4 x 2 A. (2x 2 ) B. (2x 2 1) C. (x 2 ) D. (x 2 1) 11. Identify all of the factors of: 125x + 1

4 A. (5x + 1) B. (5x + 1)(5x 6 25x + 1) C. (5x + 1)(25x 2 5x + 1) D. (5x 1)(5x 2 + 5x + 1) 12. One factor of x 5x 2 x + 5 is (x 5). Find the remaining factors. A. (x + 2)(x 2) B. (x 2)(x 2) C. (x 1)(x 1) D. (x 1)(x + 1) 1. Identify all of the zeros of the following polynomial: x + x 2 2x 6 A., ± 2 B., ± 2 C., ±2 D., ±2 14. Based on the figure, determine the number of real zeros. A. B. 4 C. 5 D. 6

5 15. Express in simplest radical form: (81x 2 ) 4 A. 27x 2 x B. 81 x 2 C. 81x 2 x D. 27x x 16. Express in simplest radical form: a 2 7 a A. a a 2 B. a a C. a 2 a 2 D. a 2 a 17. Which of the following expressions is equivalent to: A B. 7 8 C D Which of the following expressions is equivalent to: 2 5x 7 4 2x 2 A. 8x 10 B. 8x 4 10x C. 8x 4 10x 2 D. 8x 10x

6 19. If f(x) = 2x + 5 and g(x) = x 6 find f(x) g(x). A. x 1 B. x + 11 C. x 11 D. x Find the domain of: f(x) = 5x A (4, ) B ( 4, ) C (, 0) (0, ) D (, 4) ( 4, ) x Describe the transformations of the function f(x) = 2 x to g(x) = 2 x+1 4 A. Reflect Over x-axis, Left 1, Down 4 B. Reflect Over x-axis, Right 1, Down 4 C. Reflect Over x-axis, Left 1, Up 4 D. Reflect Over x-axis, Right 1, Up Use the Change of Base Theorem to find the value of: log 5 10 A. 2 B C D Identify the expression that is not equivalent to log A. log log 6 2 B. 2log 6 10 C. log log 6 2 D. log

7 24. Find the solution to the equation: ln(x + 2) = 4 A B. 8 C D Find the solution to the equation: 2x+1 = 9 2 A. B. C. x = 1 2 x = 2 x = 4 D. x = Find the solution to the equation: 2e x + 1 = 2 A B C D You deposit $200 in an account that pays % annual interest compounded monthly. What is the balance after 4 years? A. $ B. $ C. D. $ $826.45

8 28. You buy a baseball card for $100. It appreciates in value 5% per year. In how many years will it be triple its value? A years B. 2.2 years C. 2.9 years D years 29. A recent survey of 500 shows that 75% of students don t study for their Algebra 2 CP Midterm. Find the interval likely to contain the exact percent. A. 70.5% % B. 6.5% % C. 71.6% % D. 0% - 100% For number 0-1, use the box-and-whisker plots below to answer the questions What is the Lower Fence? A B. - C D What percent of the data lies between 7 and 8? A. 7.1% B. 6.% C. 14% D. 25%

9 Algebra 2 CP Semester 1 PRACTICE EXAM January 2015 Part 2 NAME DATE HR For #1: Find the indicated values and graph the equation as well as the Axis of Symmetry. You must show all work for credit. y = 2x 2 4x + 1 Graph the equation as well as the axis of symmetry Vertex, Axis of Symmetry Does this graph have a maximum or minimum? (circle one) Maximum/ Minimum Value For #2, Find the Discriminant and Describe the Nature of the Zeros: x 2 4x + 9 = 0 Discriminant: Nature of Zeros: For #, Your University Book Store sells 200 freshmen math text books at $175 each. The store estimates that for every $5 decrease in price, the store will sell 10 more text books. Find the number of text books and cost of textbooks that will maximize profit, and the maximum profit. Cost of Book: Number of Books Sold: Max Profit:

10 For #4, Find all of the zeros of the function. All work must be shown to receive full credit. f(x) = x 4 + x + 7x 2 + 9x 18 x = For #5, if f(x) = x + 2x 2 and g(x) = 5x 2 + 1; then find the following: f(x) + g(x) f(x) g(x) f(x) + g(x): f(x) g(x): For #6, find the solution(s) to the following equation: (x) 4 = 81 x = For #7, find the solution(s) to the following equation: x + 1 = x x =

11 For #8, You bought a new phone for $580. It depreciates at a rate of 6.5% annually. If the phone is now worth $20, how long ago did you buy it? Answer = For #9, fill in each of the missing pieces of information and graph the logarithmic function. You must graph the parent and the transformed graph. You may make a table if you would like, but it will not be graded. y = log 2 (x + 4) Transformations: Parent Rewrite Exponentially: Domain: Range: ANSWERS 1. D 2. B.. A. 4. B 5. B 6. C 7. B 8. C 9. D 10. A 11. C 12. D 1. B 14. C 15. D 16. A 17. C 18. A 19. B 20. D 21. A 22. D 2. D 24. D 25. B 26. C 27. B 28. D 29. A 0. C 1. D FREE RESPONSE ANSWERS 1. Vertex: (-1, ) AoS: x = Discriminant: -92 Nature of Zeros: 2 imaginary roots. Cost: $17.50; 275 Books Sold; Profit: $ Zeros: x = -2, 1, ±i 5. f(x) + g(x) = x 2 6. x = ±9 7. x = 4 8. x = 8.8 years ago + x + 1 f(x) - g(x) = 7 x 2 + x Transformations: Left 4; Parent: 2 y = x ; Domain : (-4, ) ; Range : (-, ) Log Graph Shifted Left 4