Alg. II Final Review 2013

Transcription

1 Name: Class: Date: ID: A Alg. II Final Review 201 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which function matches the graph? a. y = x c. y = x b. y = x 5 5 d. y = x Short Answer 2. The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 ln(9t + 4), where y is the number of mowers sold. How many mowers will be sold years after a model is introduced? Round the answer to the nearest whole number.. A particular sound wave can be graphed using the function y = 1 sin 6x. Find the amplitude and period of the function. Evaluate the logarithm. 4. log Write the equation in logarithmic form = Solve 16 6x = 68. Round to the nearest ten-thousandth. 7. Find the exact value of csc 15º. If the expression is undefined, write undefined. 1

2 Name: ID: A 8. Suppose you invest $800 at an annual interest rate of 2.1% compounded continuously. How much will you have in the account after 2 years? Find the mean and standard deviation of the of data. Round to the nearest tenth , 22, 18, 8, 15, 20, Use a graphing calculator to solve the equation tan 1 θ = 8 in the interval from 0 to 2π. Round your answers to the nearest hundredth. 11. In how many ways can 2 singers be selected from 8 who came to an audition? 12. Two urns contain white balls and yellow balls. The first urn contains 7 white balls and 5 yellow balls and the second urn contains 5 white balls and 8 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white? 1. An initial population of 280 quail increases at an annual rate of 22%. Write an exponential function to model the quail population. 14. The bar graph shows the rents paid per month for apartments in an urban neighborhood. The curve shows that the rents are normally distributed. Estimate the percent of apartment residents who pay from $600 to $749 per month. 15. Solve log 2x = 4. Round to the nearest ten-thousandth. 2

3 Name: ID: A Rationalize the denominator of the expression. Assume that all variables are positive Use the Law of Cosines. Find m A to the nearest tenth of a degree. 18. Find the length x. Round to the nearest tenth. Multiply. Ê ˆ ËÁ 2

4 Name: ID: A Use a unit circle and triangles to find the degree measures of the angle. 20. angles whose cosine is 2 Simplify the trigonometric expression. 21. secθ cosθ 22. Find the measure of an angle between 0º and 60º coterminal with an angle of 156º in standard position. Solve. Check for extraneous solutions. 2. 2x = x 24. The table shows the results of a survey of college students. Find the probability that a student is taking a humanities class, given the student is male. Round to the nearest thousandth. First Class of the Day for College Students Male Female Humanities Science Other Use the Law of Sines. Find b to the nearest tenth. 26. Graph y = 4x 2 2 and its inverse. 4

5 Name: ID: A 27. The formula for the volume of a sphere is V = 4 πr. Find the radius, to the nearest hundredth, of a sphere with a volume of 17 in The half-life of a certain radioactive material is 41 hours. An initial amount of the material has a mass of 616 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 hours. Round your answer to the nearest thousandth. Solve the equation. 29. x 5 8 = ( x) 5 = Let f(x) = 4x 2 and g(x) = x + 5. Find (f û g)( 5). 2. Use the frequency table. Find the probability that a person goes to the movies at least 5 times a month. Round to the nearest thousandth. Trips to the Movies Number of Movies Number of Moviegoers More than 7 movies per month movies per month movies per month 225 Less than 2 movies per month 244 Total 768. A garden has width 7 and length 8 7. What is the perimeter of the garden in simplest radical form? 5

6 Name: ID: A 4. Find the cosine and sine of 270º. Round your answers to the nearest hundredth if necessary Write the exponential expression 4x in radical form. Simplify Solve ln(5x + 7) = 5. Round to the nearest thousandth. 8. Write the equation for the sine function shown below. 9. A Ferris wheel has a radius of 45 feet. Two particular cars are located such that the central angle between them is 100º. To the nearest tenth, what is the measure of the intercepted arc between those two cars on the Ferris wheel? 6

7 Name: ID: A Solve the equation for 0 θ < 2π. Write your answer as a multiple of π, if possible. 40. cosθ 1 = Write Ê ËÁ 27a ˆ 2 in simplest form. Use a table to solve. Round to the nearest hundredth x = This is a spinner used in a board game. What is the probability that the spinner will land on a multiple of and 4? Use natural logarithms to solve the equation. Round to the nearest thousandth. 44. e x = Find the measure of x in the right triangle. 46. Write an equation for the translation 4 units right of y = cos x. 7

8 Name: ID: A 47. Use the graph below. Determine the period of this function º Write the measure in radians. Express the answer in terms of π. Write the measure in degrees. 49. π 2 radians 50. Let f(x) = x 6 and g(x) = x 2. Find f and its domain. g 8

9 ID: A Alg. II Final Review 201 Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: L2 REF: 7-8 Graphing Radical Functions OBJ: Radical Functions STA: NM 2.B. NM 2.B.10 NM 2.D.1 TOP: 7-8 Example KEY: domain graphing range radical function translation SHORT ANSWER 2. ANS: 18,886 mowers PTS: 1 DIF: L REF: 8-6 Natural Logarithms OBJ: Natural Logarithms STA: NM 2.C.11 TOP: 8-6 Example 2 KEY: simplifying a natural logarithm logarithmic function problem solving. ANS: amplitude = 1, period = 1 π PTS: 1 DIF: L REF: 1-4 The Sine Function OBJ: Interpreting Sine Functions TOP: 1-4 Example 4 KEY: amplitude period sine function problem solving word problem 4. ANS: PTS: 1 DIF: L REF: 8- Logarithmic Functions as Inverses OBJ: 8-.1 Writing and Evaluating Logarithmic Expressions STA: NM 2.B.10 NM 2.D.1 TOP: 8- Example KEY: evaluating logarithms 5. ANS: log = PTS: 1 DIF: L REF: 8- Logarithmic Functions as Inverses OBJ: 8-.1 Writing and Evaluating Logarithmic Expressions STA: NM 2.B.10 NM 2.D.1 TOP: 8- Example 2 KEY: logarithm logarithmic form 6. ANS: PTS: 1 DIF: L REF: 8-5 Exponential and Logarithmic Equations OBJ: Solving Exponential Equations STA: NM 2.C.8 NM 2.C.11 TOP: 8-5 Example 1 KEY: exponential equation 1

10 ID: A 7. ANS: 2 PTS: 1 DIF: L2 REF: 1-8 Reciprocal Trigonometric Functions OBJ: Evaluating Reciprocal Trigonometric Functions TOP: 1-8 Example 2 KEY: reciprocal trigonometric functions cosecant 8. ANS: $84.2 PTS: 1 DIF: L REF: 8-2 Properties of Exponential Functions OBJ: The Number e STA: NM 2.B.10 NM 2.D.1 TOP: 8-2 Example 5 KEY: exponential function exponential growth interest rates problem solving the number e compounding continuously percent 9. ANS: mean = 17.; standard deviation = 4.6 PTS: 1 DIF: L2 REF: 12-4 Standard Deviation OBJ: Finding Standard Deviation STA: NM 5.B. TOP: 12-4 Example 2 KEY: mean standard deviation 10. ANS:.64 PTS: 1 DIF: L REF: 1-6 The Tangent Function OBJ: Graphing the Tangent Function TOP: 1-6 Example KEY: graphing calculator graphing tangent function 11. ANS: 28 PTS: 1 DIF: L REF: 6-7 Permutations and Combinations OBJ: Combinations STA: NM 5.D TOP: 6-7 Example 4 KEY: permutation 12. ANS: PTS: 1 DIF: L2 REF: 9-7 Probability of Multiple Events OBJ: Finding P(A and B) STA: NM 5.D.4 NM 5.D.5 TOP: 9-7 Example 2 KEY: probability problem solving word problem 1. ANS: f(x) = 280(1.22) x PTS: 1 DIF: L REF: 8-1 Exploring Exponential Models OBJ: Exponential Growth STA: NM 2.B.10 TOP: 8-1 Example 2 KEY: exponential function growth factor 2

11 ID: A 14. ANS: 9% PTS: 1 DIF: L2 REF: 12-7 Normal Distributions OBJ: Using a Normal Distribution STA: NM 5.B. TOP: 12-7 Example 1 KEY: normal distribution 15. ANS: PTS: 1 DIF: L REF: 8-5 Exponential and Logarithmic Equations OBJ: Solving Logarithmic Equations STA: NM 2.C.8 NM 2.C.11 TOP: 8-5 Example 6 KEY: logarithmic equation properties of logarithms 16. ANS: PTS: 1 DIF: L2 REF: 7- Binomial Radical Expressions OBJ: 7-.2 Multiplying and Dividing Binomial Radical Expressions STA: NM 2.A.12 NM 2.C.11 TOP: 7- Example 6 KEY: binomial radical expressions conjugates multiplying binomial radical expressions simplifying a radical expression 17. ANS:.9 PTS: 1 DIF: L2 REF: 14-5 The Law of Cosines OBJ: The Law of Cosines STA: NM.D.5 TOP: 14-5 Example 2 KEY: Law of Cosines 18. ANS: 17.0 PTS: 1 DIF: L2 REF: 14- Right Triangles and Trigonometric Ratios OBJ: Finding the Lengths of Sides in a Right Triangle STA: NM.D.5 NM.D.6 TOP: 14- Example KEY: angle measure trigonometric ratios sine function 19. ANS: PTS: 1 DIF: L2 REF: 7- Binomial Radical Expressions OBJ: 7-.2 Multiplying and Dividing Binomial Radical Expressions STA: NM 2.A.12 NM 2.C.11 TOP: 7- Example 4 KEY: binomial radical expressions multiplying binomial radical expressions simplifying a radical expression 20. ANS: 0 + n 60 and 0 + n 60 PTS: 1 DIF: L2 REF: 14-2 Solving Trigonometric Equations Using Inverses OBJ: Inverses of Trigonometric Functions STA: NM.D.5 TOP: 14-2 Example 2 KEY: unit circle triangles cosine function angle measure inverse of a trigonometric equation

12 ID: A 21. ANS: 1 PTS: 1 DIF: L2 REF: 14-1 Trigonometric Identities OBJ: Verifying Trigonometric Identities STA: NM.D.5 TOP: 14-1 Example KEY: trigonometric identities simplifying trigonometric expressions 22. ANS: 204º PTS: 1 DIF: L REF: 1-2 Angles and the Unit Circle OBJ: Working With Angles in Standard Position TOP: 1-2 Example KEY: initial side of an angle measure of an angle in standard position standard position of an angle terminal side of an angle 2. ANS: PTS: 1 DIF: L2 REF: 7-5 Solving Radical Equations OBJ: Solving Radical Equations STA: NM 2.A.2 NM 2.A.1 TOP: 7-5 Example 4 KEY: radical equation extraneous solutions 24. ANS: 0. PTS: 1 DIF: L2 REF: 12-2 Conditional Probability OBJ: Finding Conditional Probabilities STA: NM 5.D.5 TOP: 12-2 Example 2 KEY: conditional probability 25. ANS: 9.7 PTS: 1 DIF: L2 REF: 14-4 Area and the Law of Sines OBJ: Area and the Law of Sines STA: NM.D. TOP: 14-4 Example 2 KEY: Law of Sines 4

13 ID: A 26. ANS: PTS: 1 DIF: L2 REF: 7-7 Inverse Relations and Functions OBJ: The Inverse of a Function STA: NM 2.B NM 2.B.11 TOP: 7-7 Example KEY: graphing inverse relations and functions 27. ANS: 1.6 in. PTS: 1 DIF: L REF: 7-1 Roots and Radical Expressions OBJ: Roots and Radical Expressions STA: NM 2.A.11 NM 2.A.12 NM 2.C.11 TOP: 7-1 Example 4 KEY: real roots problem solving 28. ANS: 1 Ê y = ˆ 41 x ; kg ËÁ 2 PTS: 1 DIF: L REF: 8-2 Properties of Exponential Functions OBJ: Comparing Graphs STA: NM 2.B.10 NM 2.D.1 TOP: 8-2 Example KEY: exponential decay exponential function 29. ANS: 21 PTS: 1 DIF: L2 REF: 7-5 Solving Radical Equations OBJ: Solving Radical Equations STA: NM 2.A.2 NM 2.A.1 TOP: 7-5 Example 1 KEY: radical equation 0. ANS: 5, 11 PTS: 1 DIF: L REF: 7-5 Solving Radical Equations OBJ: Solving Radical Equations STA: NM 2.A.2 NM 2.A.1 TOP: 7-5 Example 2 KEY: radical equation rational exponent 5

14 ID: A 1. ANS: 8 PTS: 1 DIF: L2 REF: 7-6 Function Operations OBJ: Composition of Functions STA: NM 2.A.17 NM 2.B.11 TOP: 7-6 Example KEY: composition of functions operations with functions 2. ANS: 0.89 PTS: 1 DIF: L2 REF: 12-1 Probability Distributions OBJ: Making a Probability Distribution STA: NM 5.B NM 5.B. NM 5.C. TOP: 12-1 Example 2 KEY: frequency table cumulative probability. ANS: 18 7 units PTS: 1 DIF: L2 REF: 7- Binomial Radical Expressions OBJ: 7-.1 Adding and Subtracting Radical Expressions STA: NM 2.A.12 NM 2.C.11 TOP: 7- Example 2 KEY: adding radical expressions problem solving 4. ANS: 0, 1 PTS: 1 DIF: L2 REF: 1-2 Angles and the Unit Circle OBJ: Using the Unit Circle TOP: 1-2 Example 4 KEY: unit circle cosine of an angle sine of an angle 5. ANS: 5 4 x 4 PTS: 1 DIF: L2 REF: 7-4 Rational Exponents OBJ: Simplifying Expressions with Rational Exponents STA: NM 2.A.4 NM 2.A.12 NM 2.A.16 NM 2.C.11 TOP: 7-4 Example 2 KEY: rational exponent radical form 6. ANS: 2 PTS: 1 DIF: L2 REF: 7-4 Rational Exponents OBJ: Simplifying Expressions with Rational Exponents STA: NM 2.A.4 NM 2.A.12 NM 2.A.16 NM 2.C.11 TOP: 7-4 Example 1 KEY: rational exponent 7. ANS: PTS: 1 DIF: L REF: 8-6 Natural Logarithms OBJ: Natural Logarithmic and Exponential Equations STA: NM 2.C.11 TOP: 8-6 Example KEY: natural logarithmic equation properties of logarithms 6

15 ID: A 8. ANS: y = sin 2θ PTS: 1 DIF: L2 REF: 1-4 The Sine Function OBJ: Graphing Sine Functions TOP: 1-4 Example 7 KEY: amplitude graphing period 9. ANS: 78.5 feet PTS: 1 DIF: L REF: 1- Radian Measure OBJ: 1-.2 Finding the Length of an Arc TOP: 1- Example 5 KEY: central angle problem solving radian measure 40. ANS: π 6, 11π 6 PTS: 1 DIF: L2 REF: 14-2 Solving Trigonometric Equations Using Inverses OBJ: Solving Trigonometric Equations STA: NM.D.5 TOP: 14-2 Example 5 KEY: trigonometric equation radian measure 41. ANS: a 2 9 PTS: 1 DIF: L2 REF: 7-4 Rational Exponents OBJ: Simplifying Expressions with Rational Exponents STA: NM 2.A.4 NM 2.A.12 NM 2.A.16 NM 2.C.11 TOP: 7-4 Example 5 KEY: rational exponent 42. ANS: 0.62 PTS: 1 DIF: L REF: 8-5 Exponential and Logarithmic Equations OBJ: Solving Exponential Equations STA: NM 2.C.8 NM 2.C.11 TOP: 8-5 Example KEY: exponential equation 4. ANS: 8 PTS: 1 DIF: L2 REF: 1-6 Probability OBJ: Theoretical Probability STA: NM 5.D NM 5.D. TOP: 1-6 Example KEY: theoretical probability 44. ANS: PTS: 1 DIF: L REF: 8-6 Natural Logarithms OBJ: Natural Logarithmic and Exponential Equations STA: NM 2.C.11 TOP: 8-6 Example 4 KEY: exponential equation properties of logarithms 7

16 ID: A 45. ANS: 67.6 PTS: 1 DIF: L2 REF: 14- Right Triangles and Trigonometric Ratios OBJ: Finding the Measures of Angles in a Right Triangle STA: NM.D.5 NM.D.6 TOP: 14- Example 4 KEY: angle measure trigonometric ratios cosine function 46. ANS: y = cos (x 4) PTS: 1 DIF: L2 REF: 1-7 Translating Sine and Cosine Functions OBJ: Writing Equations of Translations TOP: 1-7 Example 5 KEY: amplitude sine function period translation of a trigonometric function 47. ANS: 4 PTS: 1 DIF: L2 REF: 1-1 Exploring Periodic Data OBJ: Identifying Periodic Functions STA: NM 2.B TOP: 1-1 Example 1 KEY: periodic function cycle period 48. ANS: 7π 18 PTS: 1 DIF: L2 REF: 1- Radian Measure OBJ: 1-.1 Using Radian Measure TOP: 1- Example 1 KEY: radian measure measure of an angle in standard position 49. ANS: 90º PTS: 1 DIF: L2 REF: 1- Radian Measure OBJ: 1-.1 Using Radian Measure TOP: 1- Example 2 KEY: radian measure measure of an angle in standard position 50. ANS: ; all real numbers except x = 2 PTS: 1 DIF: L2 REF: 7-6 Function Operations OBJ: Operations with Functions STA: NM 2.A.17 NM 2.B.11 TOP: 7-6 Example 2 KEY: multiplication and division of functions operations with functions domain 8