Algebra 2 Semester Test Review

Transcription

1 Algebra 2 Semester Test Review Name This semester review covers everything from Semester 1. It is due. You will have a semester test that covers everything from the semester on. This packet is meant as a starting point to see what you need to study. Everything we have done in the semester is fair game for the test. There will NOT be an answer key posted. You may get help, but do not just copy another s work. Random questions will be graded for accuracy for a 20 point quiz grade. The packet will be accepted one day late for a maximum of 10 points (assuming you got the graded questions correct). After that, your grade will be a zero. You must show all of your work neatly with answers boxed. Completion of the packet is worth 4 points. Feel free to use additional lined paper to show your work. Please write the statement below and sign your name. This is worth 2 points. I have done all of my own work on this Algebra 2 Semester Test Review packet. I have not copied anyone else s work. I understand the due date and that it will be graded as a quiz grade.

2 Algebra 2 Semester Test Review 1. Place these numbers in increasing order: Name , 10, 4,, Circle all that apply for 15 : rational integer whole number irrational know your definitions 3. Name the property illustrated: a + 0 = a, 0 + a = a review all the properties 4. Evaluate when x = 2 and y = 2 1 : x 3 + x y (if x = 4, what is x 2?) 5. Simplify: 8x (7y + 3x) + 2y 6. Solve for x: 1 2 x + 3 = 2 + x multiply by lcm Solve the inequality for x: 3x + 2 > If f(x) = 2x 2 5, find f(3) Select the linear equation graph which does NOT represent a function. A. B. C. D. 10. Choose the equation whose graph is a horizontal line. A. x = 2 B. y = 5 C. y = x D. x = 2y 11. Which equation s graph will be parallel to the graph of 2x + y = 8? Parallel lines have What about perpendicular? A. 2x y = 8 B. y = 2x + 8 C. y = 2x + 3 D. 2x = y Name the slope and y-intercept of the line represented by this equation: 8x + 2y = 3

3 13. Write the equation of a line that passes through (5,2) and has a slope of Graph this equation: 4x + 2y = 6 Since this is in standard for, use xy intercepts!!! 15. Graph this equation: 1 y = x Get y by itself. How do you cancel that 2 1? 16. Graph the inequality: y > 3 2 x Solve for y: xy + 5x = 15 Solve for x: xy + 5x = Celsuis to Fahrenheit: C (F 32) Solve for F x 5 = x = 8

4 Solve and graph the solution x Solve and graph the solution. 2x Find the curve of best fit. (Make 1955 Year 0.) Black and white TV s Sold (in thousands) Year Model: Equation: Predict the # TVs sold in The table below shows the hourly temperatures, for a city in Virginia on July 21, Time, x am 12 pm 1 pm 2 pm 3 pm 4 pm 5 pm am Temp, y (degrees) a) What model best represents the data? b) Write an equation for the curve of best fit. c) Predict the temperature at 6:15 pm. Graph. x 1, if x f (x) 26. x 2, if x 3 1, if 3 x 0 g (x) 4, if 0 x 3

5 Write the equation of each absolute value function. Use y = a x h + k form f(x) = 2 1 x Solve. 30. x(x 9) = x 2 + 2x = 8 Draw a parabola whose related equation has the specified discriminant. Explain why you chose each graph. 32. Discriminant < Discriminant = Discriminant > 0 How many and what type solutions? 35. 3x 2 + 3x 1 = x x = x 2 2x + 1 = 0 Solve using the quadratic formula. Show exact answers. Put in simplest form x 2 10x + 9 = x 2 5x = 4 Solve using square roots. 40. Solve 5x 2 = Solve (2x 1) 2 = Use completing the square to rewrite this equation. x x = 8 What is the Vertex?

6 43. What are the factors of the quadratic whose graph is shown? 44. What are the zeros of this function? f(x) = 3x 2 7x What is the vertex of this quadratic function? y = 5x x Name the vertex of this equation: y = 3x x Graph this inequality: y (x + 3) i (1 + 3i) (4 2i) 50. 3i(i + 5) 51. (5 + 4i)(2 i) 52. 2i 3 5i 53.Complete the square and solve by square roots. 4x 2 8x + 3 = Given: f(x) = 4x 2 8x + 3 Name the vertex Axis of symmetry: Increasing Interval: Decreasing Interval: End behavior: As x, f(x) As x, f(x)

7 55. A volleyball is hit upward by a player in a game. The height ht ( ) in feet of the volleyaball after t seconds is given by the function: 2 h t = - 16t + 29t + 4. ( ) 56. Simplify. (x + 2)(3x 8)(x 2 + 7) a) What is the maximum height of the ball? b) After how many seconds does the ball reach its maximum height? c) The ball is not returned, so it hits the ground after how many seconds? 57. For each function, identify the requested information and graph the function. a) f(x) = 2(x 4) Function family: Domain: Range: Vertex: Complex Zeros: Increasing interval: Decreasing interval: End behavior: x, f ( x) x, f ( x)

8 b) f(x) = ½ x (x 4) 2 (x + 5) Function: Domain: Range: Vertex: Complex Zeros: Increasing interval: Decreasing interval: End behavior: x, f ( x) x, f ( x) 58. Factor completely. (Always look for GCF first)! x n 5 48n x x 9x 3 2x - 2x - 24x Find all zeros. x 3 6x 2 4x x 216 0

9 Factor 3x 4x 28x 16 completely given ( x 2) is a factor. Find all of the zeros of the polynomial when given one of the zeros. 61. Given f (3) = 0, find the other zeros f x x x x 3 2 ( ) = Find all of the possible rational zeros of the function: f(x) = 3x 4 7x 3 + 8x 2 6x + 30 Write a polynomial function with a leading coefficient of 1 and the following zeros. Write in factored form and standard form , 3 + i Factored form: Standard form:.