Algebra 2 Honors Final Exam StudyGuide

Transcription

1 Name: Score: 0 / 80 points (0%) Algebra 2 Honors Final Exam StudyGuide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Simplify. 2. D Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL method and the difference of squares to simplify the given expression. REF: Lesson B Multiply the numerator as well as the denominator by the conjugate of the denominator. Use the FOIL method and the difference of squares to simplify the given expression. REF: Lesson 5-4

2 C REF: Lesson Asume that all absolute value symbols are present 5. C Find the principal square root of each term of the radicand. REF: Lesson 7-4 C Multiply the real numbers and imaginary numbers separately. REF: Lesson Asume that all absolute value symbols are present 7. A Find the principal square root of each term of the radicand. REF: Lesson 7-4 Solve the given triangle. Round the measures of sides to the nearest tenth and measures of angles to the nearest degree.

3 ,, a.,, c.,, b.,, d.,, B Let be any triangle with a, b, and c representing the measures of sides opposite angles with measurements A, B, and C respectively. Then, REF: Lesson 13-4 Find the value of the given trigonometric function. 8. D First, find the reference angle. Then, find the value of the trigonometric function for. Then, using the quadrant in which the terminal side of θ lies, determine the sign of the trigonometric function value of θ. REF: Lesson C First, find the reference angle. Then, find the value of the trigonometric function for. Then, using the quadrant in which the terminal side of θ lies, determine the sign of the trigonometric function value of θ. REF: Lesson 13-3 Solve the given equation. 10. a. n = c. n = 1

4 b. n = d. n = A Eliminate the bases and use the Property of Equality for Exponential Functions to solve the equation. REF: Lesson a. The solution set is (, ). c. The solution set is (, ). b. The solution set is (, ). d. The solution set is (, ). B Obtain two linear equations using the definition of equal matrices. REF: Lesson a. n = 1 c. n = b. n = d. n = B Eliminate the bases and use the Property of Equality for Exponential Functions to solve the equation. REF: Lesson 8-2 Factor the polynomial completely C To find the coefficient of the x terms, find two numbers whose product is or 99 and whose sum is 20. REF: Lesson 6-5

5 B Find the GCF (greatest common factor) of the monomials in the given polynomial, and use it in grouping the polynomial. REF: Lesson 6-5 D To find the coefficient of the x terms, find two numbers such that their product is or 24 and their difference is 5. REF: Lesson Find for the following functions. a., c., b., d., A Divide f(x) by g(x) to obtain the required answer. REF: Lesson Use a calculator to approximate the value of to three decimal places. a c b d REF: Lesson 7-4 D Simplify the radical, and then use a calculator to find the approximate value of Solve the following system of equations by graphing.

6 18. Solve the following system of equations by graphing. a. (1, 18) c. (4, 17) b. (2, 18) d. (18, 2) B Graph the equations and find their point of intersection. REF: Lesson Write an equation for the parabola whose vertex is at and which passes through 20.. A If the vertex and another point on the graph of a parabola are known, the equation of the parabola can be written in vertex form. REF: Lesson 5-7 Simplify the given expression. Assume that no variable equals 0. D Multiply the constants and then multiply the powers using the Power of a Product Property. REF: Lesson

7 B Simplify each base using the properties of powers. Then, write all the fractions in the simplest terms and ensure there are no negative exponents. REF: Lesson A Multiply the constants and then multiply the powers using the Power of a Product Property. REF: Lesson 6-1 Evaluate the determinant using expansion by minors a. 2 c. 18 b. 58 d. 58 D To use expansion by minors with third-order determinants, each member of one row is multiplied by its minor and position sign, and the results are added together. The position signs alternate between positive and negative, beginning with a positive sign in the first row and first column. REF: Lesson 4-5 Estimate the x-coordinates at which the relative maxima and relative minima occur for the function. a. The relative maximum is at, and the relative minimum is at. b. The relative maximum is at, and the relative minimum is at. c. The relative maximum is at, and the relative minimum is at. d. The relative maximum is at, and the relative minimum is at.

8 D Make a table of values and graph the equation. REF: Lesson Write an equation in slope-intercept form for the line that satisfies the following condition. slope 8 and passes through (4, 29) a. y = c. y = b. y = d. y = A Substitute the values of the x- and y-coordinates in the equation. Manipulate the equation to get it in the slope-intercept 26. form. REF: Lesson 2-4 Simplify the given expression. a. b. c. d. 27. A Use the properties of real numbers to simplify the given expression. REF: Lesson D Group the similar terms and then combine them. REF: Lesson 6-1 Simplify the expression using long division. a. quotient and remainder 0 c. quotient and remainder 32 b. quotient and remainder 16 d. quotient and remainder 32 A Use the division algorithm. When dividing, you can add or subtract only similar terms.

9 REF: Lesson Find one angle with positive measure and one angle with negative measure coterminal with an angle of 158. a. 248, 68 c. 518, 68 b. 512, 22 d. 518, 202 D In degree measure, coterminal angles differ by an integral multiple of 360. REF: Lesson Use synthetic substitution to find and g ( 5) for the function. a. 475, 3,603 c. 479, 3,693 b. 547, 482 d. 151, 272 A Use synthetic substitution to obtain the required answer. REF: Lesson Find and for the function. a. 21; 1,383 c. 43; 1,405 b. 25; 53 d. 38; 1,410 C Replace the values of p(x) and simplify. REF: Lesson Find for the following functions. B Multiply f(x) and g(x) to obtain the required answer. REF: Lesson The workers in a factory earn $25 an hour. Every week, 20% of each worker s total pay is deducted for taxes. If each worker wants a take-home salary of at least $620 a week, solve the inequality to determine how many hours each worker must work. a. at the most 31 c. at least 31 b. at least 3.1 d. 31

10 C Solve the given inequality to determine the number of hours each worker must work. REF: Lesson Two boys are on opposite sides of a tower. They sight the top of the tower at 33 and 24 angles of elevation respectively. If the height of the tower is 100 m, find the distance between the two boys. a m c m b m d m D Write an equation using a trigonometric function. REF: Lesson 13-1 As a receptionist for a hospital, one of Elizabeth s tasks is to schedule appointments. She allots 60 minutes for the first visit and 30 minutes for a follow-up. The doctor cannot perform more than eight follow-ups per day. The hospital has eight hours available for appointments. The first visit costs $120 and the follow-up costs $70. Let x be the number of first visits and y be the number of follow-ups. 35. Write a system of inequalities to represent the number of first visits and the number of followups that can be performed. B Form the system of inequalities using the appropriate values. REF: Lesson What is the maximum income that the doctor receives per day? a. $1920 c. $970 b. $960 d. $1040 D Substitute the coordinates of the vertices of the feasible region into the required function. REF: Lesson Graph the system of inequalities showing the feasible region to represent the number of first visits and the number of follow-ups that can be performed.

11 visits and the number of follow-ups that can be performed. D Write the system of inequalities and then plot the graph. REF: Lesson Determine the number of first visits and follow-ups to be scheduled to make the maximum income. a. 4 first visits and 8 follow-ups c. 4 first visits and 7 follow-ups b. 16 first visits and 0 follow-ups d. 8 first visits and 0 follow-ups A Find out the vertices of the feasible region that represents the number of the first visits and the number of the follow-ups. Then, substitute the vertices in the required function. REF: Lesson Find and.

12 40. REF: Lesson 7-1 C If f and g are functions such that the range of g is a subset of the domain of f, then the composite function can be described as Find the coordinates of the vertices of the figure formed by each system of inequalities. 41. a. ( 2.5, 4.5), (8, 6), (34, 27) b. ( 2.5, 4.5), ( 24, 22), ( 34, 27) c. ( 2.5, 27), ( 34, 6), (8, 4.5) d. ( 2.5, 4.5), (8, 6), ( 34, 27) D Solve the system of inequalities by graphing the inequalities on the same coordinate plane. The solution set is represented by the intersection of the graphs. REF: Lesson 3-3 Rewrite the radian measure in degrees. C To rewrite the radian measure of an angle in degrees, multiply the number of radians by. REF: Lesson 13-2 Graph the quadratic inequality.

13 42. REF: Lesson 5-8 C Graph the related quadratic equation. Because the inequality symbol is >, the parabola should be dashed. Test a point inside the parabola. If is the solution of the inequality, shade the region inside the parabola. If is not a solution, shade the region outside the parabola. Find the value of the determinant. 43. a. 26 c. 34 b. 50 d. 29 C The value of the second-order determinant is obtained by calculating the difference of the products of the two diagonals.

14 REF: Lesson 4-5 Find the exact solution of the following quadratic equation by using the Quadratic Formula. 44. B The solution of a quadratic equation of the form, where, is obtained by using the formula. REF: Lesson Find for the following functions. D Subtract g(x) from f(x) to obtain the required answer. REF: Lesson 7-1 Write a quadratic equation with the given roots. Write the equation in the form, where a, b, and c are integers and 4 C A quadratic equation with roots p and q can be written as, which can be further simplified. REF: Lesson 5-3 Evaluate the expression. Express the result in scientific notation.

15 47. D Use the Properties of Powers to divide numbers in scientific notation. REF: Lesson 6-1 Rewrite the degree measure in radians A To rewrite the degree measure of an angle in radians, multiply the number of degrees by. REF: Lesson 13-2 Given a polynomial and one of its factors, find the remaining factors of the polynomial. Some of the factors may not be binomials. 49. ; a. ( )( ) c. ( ) b. ( )( ) d. ( ) A Use the Factor Theorem. REF: Lesson Find and. a. b.

16 c. d. REF: Lesson 7-1 C If f and g are functions such that the range of g is a subset of the domain of f, then the composite function can be described as Perform the indicated matrix operation. 51. B The order of operations for matrices is similar to that of real numbers. Perform scalar multiplication before matrix addition and subtraction. REF: Lesson The formula to calculate the volume of a cylinder is. Write an expression to represent the volume of the cylinder. a. b. c. d.

17 A Substitute each given value into the formula. Then, evaluate the expression using the order of operations. REF: Lesson Find all of the zeros of the function. a., 2, 12 c., 2, 12 b., 2, 12 d., 12 B Use synthetic substitution to obtain the required answer. REF: Lesson 6-7 Find the exact values of the remaining five trigonometric functions of θ. 54. Suppose θ is an angle in the standard position whose terminal side is in Quadrant II and. a.,,,, b.,,,, c.,,,, d.,,,, A If the quadrant that contains the terminal side of θ in the standard position and the exact value of one trigonometric function of θ are known, then the values of the other trigonometric functions of θ can be obtained using the function definitions. REF: Lesson Suppose θ is an angle in the standard position whose terminal side is in Quadrant I and. a.,,,,

18 b.,,,, c.,,,, d.,,,, B If the quadrant that contains the terminal side of θ in the standard position and the exact value of one trigonometric function of θ are known, then the values of the other trigonometric functions of θ can be obtained using the function definitions. REF: Lesson Solve by using the measurements,, and. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. a.,, c.,, b.,, d.,, A If the measures of one side and one acute angle are known, you can determine the measures of all sides and angles of the triangle by using trigonometric functions. REF: Lesson 13-1 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.

19 57. a. The end behavior of the graph is as and as. It is an even-degree polynomial function. The function has four real zeros. b. The end behavior of the graph is as and as. It is an even-degree polynomial function. The function has five real zeros. c. The end behavior of the graph is as and as. It is an odd-degree polynomial function. The function has four real zeros. d. The end behavior of the graph is as and as. It is an even-degree polynomial function. The function has four real zeros. A The end behavior is the behavior of the graph as x approaches positive infinity or negative infinity. The x-coordinate of the point at which the graph intersects the x-axis is called the zero of the function. REF: Lesson Find the value of f( 9) and g(9) if and. a. f( 9) = 11 g(9) = b. f( 9) = 29 g(9) = c. f( 9) = 43 g(9) = d. f( 9) = 36 g(9) = B Substitute x = 9 in the equation f(x) and x = 9 in the equation g(x). REF: Lesson Simplify.

20 A Factor into squares where possible. Use the Product Property of Radicals to simplify. REF: Lesson 7-5 Solve the given equation. Check your solution. 60. a. {1.98, 3.03} b. { 1.98, 3.03} c. { 1.98, 3.03} d. {39.5, 3.03} C For any real numbers a and b, where, if, then, or. REF: Lesson Solve C Use the definition of logarithms with base b to solve the logarithmic equation. REF: Lesson Find for the following functions. a., c., b., d., C Divide f(x) by g(x) to obtain the required answer. REF: Lesson 7-1 Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.

21 63. nearest degree. 64.,, a. one solution; ; ; b. one solution; ; ; c. no solution d. one solution; ; ; A Determine whether the given triangle has zero, one or two solutions. Find the measure of angle C and the value of c. REF: Lesson 13-4 Write the following quadratic function in vertex form. Then, identify the axis of symmetry. a. The vertex form of the function is The equation of the axis of symmetry is. b. The vertex form of the function is The equation of the axis of symmetry is. c. The vertex form of the function is The equation of the axis of symmetry is. d. The vertex form of the function is The equation of the axis of symmetry is. D The vertex form of a quadratic function is. The equation of the axis of symmetry of a parabola is. REF: Lesson 5-7 Write a verbal expression to represent the given equation. 65. a. The quotient of a number and 25 is 3. b. The difference of a number and 25 is 3. c. The sum of a given number and 25 is 3. d. The difference of 25 and a number is 3. B Read the algebraic expression and represent it verbally.

22 REF: Lesson Write an equation in slope-intercept form for the line that satisfies the following condition. passes through (18, 5), perpendicular to the graph of y = x + 15 a. y = x + c. y = x + ( ) b. y = x + d. y = x + D The point-slope form of the equation of a line is, where are the coordinates of a point on the line and m is the slope of the line. The slopes of perpendicular lines are opposite reciprocals. REF: Lesson 2-4 Solve the given inequality. Graph the solution set on a number line. 67. or a. b. c. d. C Solve the given inequality and then plot the graph. REF: Lesson A 15-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? a m c. 7.5 m

23 b. 30 m d m C Write an equation using a trigonometric function that involves the ratio of length and 15. REF: Lesson 13-1 Find the inverse of the given function C The inverse function can be found by exchanging the domain and range of the function. REF: Lesson 7-2 Simplify the expression using synthetic division. a. quotient and remainder 93,170 b. quotient and remainder 0 c. quotient and remainder 102,487 d. quotient and remainder 18,282 B To use synthetic division, the divisor must be of the form. REF: Lesson 6-2 Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

24 71. a. The c. solution set is. The solution set is. b. Thed. solution set is. The solution set is. REF: Lesson 5-2 D The zeros of the function are the x-intercepts of its graph. These are the solutions of the related quadratic equation because at those points. 72. The formula for the surface area A of a sphere with diameter d is c = 4. Write an expression to represent the surface area of the sphere. a. b. c. d.

25 B Substitute the value of d in the given equation to find the expression. REF: Lesson 1-1 Solve the system of inequalities by graphing. 73. x > 3 y > 7 B Both the inequalities should be plotted and the region common to both should be shaded. REF: Lesson Graph the given function. State its domain and range.

26 a. c. The domain is x and the range is y The domain is x and the range is y b. 1. d. 1. The domain is x and the range is The domain is x and the range is y 1. y 1. D Write the expression inside the radicand as function. REF: Lesson 7-3. Solve for x and graph the 75. Find the value of if n = 4, b = 4, and a = 40,000. a b c. 10,000 d B Find the value of 4 raised to the power of 4. Then, divide a with the value obtained. REF: Lesson Find the values of the six trigonometric functions for angle θ, when and.

27 a. sin θ =, cos θ =, csc θ =, sec θ =, tan θ =, and cot θ =. b. sin θ =, cos θ =, csc θ =, sec θ =, tan θ =, and cot θ =. c. sin θ =, cos θ =, csc θ =, secθ =, tan θ =, and cot θ =. d. sin θ =, cos θ =, csc θ =, secθ =, tan θ =, and cot θ =. D If θ is the measure of an acute angle of a right triangle, opp is the measure of the leg opposite θ, adj is the measure of the leg adjacent to θ, and hyp is the measure of the hypotenuse, then the following are true. REF: Lesson List all of the possible rational zeros of the following function. a.,,,,,,, b.,,,,,,, c. 1, 2, 4, 5, 10, 20, 25, 50 d. 1, 2, 4, 5, 10, 20, 25, 50, 100 B Use the Rational Zero Theorem. REF: Lesson Graph the inequality.

28 78. Graph the inequality. A Graph the related equation. Because the boundary should not be included, the graph should be dashed. REF: Lesson Consider the quadratic function. Find the y-intercept and the equation of the axis of symmetry. a. The y-intercept is + 2. The equation of the axis of symmetry is x =. b. The y-intercept is. The equation of the axis of symmetry is x = 2. c. The y-intercept is. The equation of the axis of symmetry is x = 2. d. The y-intercept is 2. The equation of the axis of symmetry is x =. A For the quadratic equation, the y-intercept is c and the equation of

29 80. axis of symmetry is. REF: Lesson 5-1 Evaluate the logarithmic expression. 49 B Use the Property of Equality for Exponential Functions to evaluate the logarithmic expression. REF: Lesson 8-3

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