Algebra II Honors @ Name Period Date REVIEW FOR THE FIRST SEMESTER EXAM You must NEATLY show ALL of your work ON SEPARATE PAPER in order to receive full credit! All graphs must be done on GRAPH PAPER! This review is due on exam day. Chapter 1 1. Find the next two numbers in each pattern. a. 5,, 1,, b. 144, 7, 6,,. Name all subsets of real numbers to which each number belongs: a. 5 b. 5 c. 5 d. 5. Name the property that is illustrated in each example. 5 4 a. 5 5 0 b. 1 1 c. 1 d. 4 4 x 4 x 4 5 4. Write an inequality that represents the sentence, the difference of a number and is at least 15. 5. Evaluate a a for a 6. Solve: 8w 56 7. The expression 0 6h models the cost in dollars of renting scuba gear from the water sports store. In the expression, h represents the number of hours the scuba gear is rented for. What is the cost of renting scuba gear for 4 hours? Include units in your answer! 8. Solve the equation for x. x 6 10a 9. Solve each inequality and graph the solution(s) on a number line. 1 a. c 6c 7 b. 8 x 1 and x 10. Solve the equation and graph the solution(s) on a number line. x 1 11. Solve the inequality and graph the solution(s) on a number line. x 5 9 1. Solve x 5 4x 9. Check for extraneous solutions. 1. Determine whether each equation is always, sometimes, or never true. 1 m 6 m 6 b. d 5 6 a. 14. Avin and Anuj are identical twins. Their brother Rohan is five years older than the twins. The sum of the three brothers ages is 5. Write a single equation to determine how old Avin and Anuj are, then determine their ages.
Chapter 1. Find the domain and range of each relation. Then determine if the relation is a function. a. {(, 5), (, ), ( 5,0), (4, )} b. c.. Evaluate the function f x x 6 for x 4. 8. Write an equation in slope-intercept form for the line shown in the graph at right. 4. For x 10 y : a. Write the equation in slope-intercept form. b. Find the slope and y-intercept of the line. Write the y-intercept as an ordered pair. 1 5. Graph y x 5. 6. Find the x- and y-intercepts of x y 1. Then graph the equation. 7. Write the point-slope form equation of the line that passes through 4, and 6,1 8. Write 4 5 y x in standard form with integer coefficients. 9. Write an equation of a line that has a slope that is undefined. 10. Write an equation of a line that has a slope that is zero. 11. Write the slope-intercept form of the line that passes through (4, 1) and is perpendicular to 1 y x 5. 1. Write the slope-intercept form of the line that passes through, x 4y 16. and is parallel to 1. Describe the transformation from the parent function f x for f x 8 y. 14. Write the equation of the transformed graph for the parent function f x x that has been shifted right, reflected over the x-axis, and vertically stretched by a factor of. 15. The graph of f x is shown on the grid below and a table of values of the key points of f x has been provided. Identify the values of h, and k. Apply the transformations to the table, then use the points from the new table to sketch the transformed graph. Key points of f x: x 6 4 4 y 4 0 5 y f x a = h = k = x + h ay + k
16. Describe each transformation from the parent function. a. y x 4 b. y x 5 17. Evaluate the piecewise function x 6 if x f for the given value. x 4 if x a. f 4= b. f = c. f 18. Graph the piecewise function. m x x x 1 if if x 1 x 1 Chapter 1. Classify the system of two equations as independent, dependent, or inconsistent. a. The system has no solutions. b. A system has exactly one solution. c. The system has infinitely many solutions. d. The graph of the system is two lines that intersect at one point. e. The graph of the system is two parallel lines. f. The graph of the system is one line.. Solve each system of equations. a. x y 14 x y 6-9x + y 6. Solve the system of equations by graphing. x + y > -1 x y 4 4. Solve the system of equations by substitution. y 4x 9 4x 5y 1 5. Solve the system of equations by elimination. x y x y z 8 6. Solve the system of equations. x y z 5 5x y z 6 b. y x 5 1 5 y x Chapter 4 1. Write a quadratic equation in vertex form that opens down, has a vertex of (4, -5), and which has been vertically compressed by a factor of 0.5.. What is the y-intercept of the function y x 1 5?. What is the equation of the axis of symmetry of the function 1 y x 5 x? 4. What is the domain and range of the function y 0.5x 8? 5. What is the vertex form of y x 4x? 6. What are the solutions of x 1x 11 0?
7. Find the minimum/maximum value of each function. State whether it is a minimum or maximum. a. y x 5 1 b. y = x - +6 8. Write the equation of the parabola in vertex form whose graph has a vertex at, 5 passes through the point 0,. 1 1 9. Solve x x 0 using a graphing calculator. 4 4 10. Factor each expression completely. a. m m b. 5k 70k 49 11. Solve each equation by factoring. a. x 4x 1 b. x 5x 0 1. Use the function x 5 y to find the following: a. vertex b. axis of symmetry c. opens up or down? d. max/min and its value e. y-intercept f. domain g. range h. describe the transformation(s) from the parent function 1. Find the sum. 4i 7i 14. Find the difference. 9 i 6i 15. Find each product. a. 6i 5i b. 4 8i i 4 7i 6 16. Simplify each expression. a. b. i 1 i 17. Find the absolute value of the complex number: 8 5i 18. Factor over the imaginary numbers. 9x 16 19. Find the value of the discriminant of x x 5 0. 0. What value of the discriminant will indicate that a quadratic equations has a. imaginary solutions b. 1 real solution c. real solutions and You may use imaginary numbers for problems 1,, and. 1. Solve each equation by finding square roots. a. x 8 0 b. 4x 48 0. Solve by completing the square. a. x 6x 1 0 b. x 8x 6. Solve by using the quadratic formula. a. x 4x 6 b. 4x x 0
Chapter 5 4 1. For the function y x 6x x 1 : a. Identify the degree and leading coefficient. b. Determine the end behavior. c. Determine the maximum number of turning points the graph could have.. For the graph given at the right a. Describe the end behavior. b. Determine whether the degree is even or odd. c. Determine whether the leading coefficient is positive or negative. d. Give the least possible degree of the polynomial.. Write a cubic function in standard form with zeros 1, 4, and. 4. Write a quartic function in standard form whose only real zeros are 1 and -5 and has an imaginary zero of i. 5. For the function y xx x : a. Find the zeros of each function. b. State the multiplicity of each zero. c. Sketch the graph using the zeros, y-intercept, and end behavior. 6. Find all solutions, Real and imaginary, by factoring. x 4 + 14x = 0 7. Find all solutions by factoring. 7x 64 = 0 SETS and MATRICES 1. Given U = {0, 1,,, 4, 5,, 0}, A = {0, 1,,, 4, 5, 6, 7, 8, 9, 10} and B = {0,, 4, 6, 8, 10, 1, 14, 16, 18, 0}, find a) A B b) A B c) A. Given A = -1-7 and B = - -1 4, find a. A + B b. AB c. the determinant of B d. A -1