Algebra 2 with Trigonometry Final Exam Review

Transcription

1 Algebra with Trigonometry Final Exam Review Name: Find the value of the given expression. 1. [ + (0( ))]. Evaluate the given expression if x =, y = 10, w = 11, and z = 18. (x y) + 10wz Solve the given equation. Check your solution.. 7p 1p + 61p p = 18. 9(6x + ) 6(1x + 7) = 19. m 1 = 6. 0 s + = Solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the solution set on a number line Solve the given inequality. Graph the solution set on a number line. 9. m < or 6m m 1< 7 and m m p 9 1. Graph the function f(x) = x +. Identify its domain and range. 1. Graph the function f(x) = [[x + ]]. Identify its domain and range. 1. Graph the function f(x) = x +. Identify its domain and range. 16. Graph the function f(x) =. Identify the domain and range. 17. Graph the given relation or equation and find the domain and range. Then determine whether the relation or equation is a function. (.,.), ( 1.8,.), (.8,.), (.8,.8) 18. Graph the given relation or equation and find the domain and range. Then determine whether the relation or equation is a function.

2 y = x 19. Find the value of f( 10) and g() if f(x) = 10x 9 and g(x) = x + 7x. 0. Find the slope of the line that passes through the pair of points (6, 7) and (9, ). 1. Graph the line that passes through (, 1), parallel to a line whose slope is 0... Write an equation in slope-intercept form for the line that satisfies the following condition. slope, and passes through (, 0). Write an equation in slope-intercept form for the line that satisfies the following condition. passes through (1, 0) and (18, ). Write an equation in slope-intercept form for the line that satisfies the following condition. 0 passes through (9, 9), parallel to the graph of y = x + 10 Identify the function below as S for step, C for constant, A for absolute value, I for identity, or P for piecewise.. 6. y y x x 1 7. y 8. y x x 1

3 9. Graph the given inequality. Solve the given system of equations. 0. 8a = 1 a + 8c = 0 7b + 1c = 18 Solve each system of equations by using substitution. 1. 6x + y = 10 7x y =.. Solve each system of equations by using elimination.. Simplify the given expression. Assume that no variable equals Simplify the given expression

4 Factor the polynomial completely Simplify Use a calculator to approximate the value of to three decimal places. 61. Use a calculator to approximate the value of to three decimal places. 6. Simplify. 6. Write the given radical using rational exponents. 6. Solve the given inequality. Solve the given equation y y + = Simplify. 7. Simplify 7. Consider the quadratic function + +. Find the y-intercept and the equation of the axis of symmetry. 7. Graph the quadratic function. Determine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value of the function Solve the equation by factoring

5 Write a quadratic equation with the given roots. Write the equation in the form, where a, b, and c are integers and Solve the equation by using the Square Root Property Solve the equation by completing the square Find the exact solution of the following quadratic equation by using the Quadratic Formula Find the value of the discriminant. Then describe the number and type of roots for the equation Write the following quadratic function in the vertex form. Then, identify the axis of symmetry Find the coordinates of the vertex of the quadratic function. 86. Write an equation for the parabola whose vertex is at and which passes through. 87. Find and for the function. For the given graph, a. describe the end behavior, b. determine whether it represents an odd-degree or even-degree polynomial function, and c. state the number of real zeros.

6 f(x) f(x) x x Write the expression in quadratic form. 91. List all of the possible rational zeros of the following function. 9. Find for the following functions. 9. Find for the following functions. 9. Find for the following functions. 9. Find and. 96. Find the values of the six trigonometric functions for angle, when AC = 10 and BC = Solve ABC by using the measurements,, and. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.

7 98. Solve ABC by using the measurements,, and. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. 99. A 1-m long ladder rests against a wall at an angle of with the ground. How far is the foot of the ladder from the wall? 100. In a tourist bus near the base of Eiffel Tower at Paris, a passenger estimates the angle of elevation to the top of the tower to be 60. If the height of Eiffel Tower is about 98 feet, what is the distance from the bus to the base of the tower? Rewrite the radian measure in degrees Rewrite the degree measure in radians Find one angle with positive measure and one angle with negative measure coterminal with an angle of 17. Find the value of the given trigonometric function sin cos sec 100 Find the exact values of the remaining five trigonometric functions of Suppose is an angle in the standard position whose terminal side is in Quadrant III and Suppose is an angle in the standard position whose terminal side is in Quadrant IV and Suppose is an angle in the standard position whose terminal side is in Quadrant II and. 11. Suppose is an angle in the standard position whose terminal side is in Quadrant IV and.

8 11. Suppose is an angle in the standard position whose terminal side is in Quadrant IV and. 11. Suppose is an angle in the standard position whose terminal side is in Quadrant II and. Solve the given triangle. Round the measures of sides to the nearest tenth and measures of angles to the nearest degree. 11. c = 9.0, B = 0, C = Q =, p = 8, q = The given point P is located on the unit circle. Find sin and cos P(0.8, 0.6) 118. P 119. Solve x = Sin by finding the value of x to the nearest degree. 6 Find the amplitude, if it exists, and period of the function. Then, graph the function. 10. y = sin 11. y = cos State the amplitude, period, and phase shift for the function. Then, graph the function. 1. y = cos ( 90 ) 1. Find the value of cos, if sec = ; 0 90.

9 1. Find the value of csc, if cos = ; 180 < < Simplify