Algebra II Honors Midterm Review

Transcription

1 Algebra II Honors Midterm Review Simplify the following expressions. 1. 5x { [ x ( x )]}. x( x y) y(x y) Give an example for each, or state that it is not possible.. An integer that is not a whole number 4. A real number that is irrational 5. A transcendental number that is a natural number 6. A rational number that is an integer 7. A digit that is not a natural number Solve in the given domain. 8. x ( x 5)(x 9) 0 {positive reals} 9. 1 x 10 {positive reals} x 16 {integers} x 1 {reals}

2 Plot the graph of the function in the indicated domain. Identify the range y { x 4} 1. x y x {non-positive reals} Identify the domain and range Domain Range Domain Range

3 Solve for x: 16. x x x x 6 5 Plot the graph and tell whether or not the relation is a function. 0. y x 1. y x

4 Write the equation of the line described in Standard Form.. Through (, -) and (, 9). x-intercept of (-, 0) and slope Through (, -1) and perpendicular to x y Through (-, 6) and parallel to x y Nick takes a Padiddle Cab from the airport to his home which is exactly six miles away. The cab costs him $7.70. Dylan takes a cab from his hotel to a golf club 10 miles away. His fare is $ Assume that miles and fares are linearly related. a. Write the equation for this function expressing cost in terms of distance. b. Sarah uses a Padiddle Cab as a delivery service vehicle. The distance driven one morning was 60 miles. What was the cost of the cab? c. The fare from the international airport to the local airport is $ What is the distance between the two places? d. Sketch a graph and identify the domain and range. e. What is the real-world meaning of the cost- intercept?

5 Solve the following systems of equations. 7. x 5 y 6 7 x y 4 8. x x y y 1 Solve the following systems using Cramer s Rule. Show each fraction and use the calculator to find the determinants. 9. x y 10 x 5 y 1 0. x y 5 z 1 x y z x 4 y z 11 Solve by hand. 1. x y z 0 x y 5 z 1 x y z 15

6 Graph the system.. x y 9 x y8 x. Amanda is president of Amanda s Corn Chips, Inc. Her company is divided into two departments which put out two types of corn chips, Extra Larges and Really Smalls. Each department has separate regulations concerning the number of bags produced per day. (A kilobag is 1000 bags.) i. No more than 45 kilobags total, can be manufactured each day. ii. No more than 0 kilobags of Extra Larges and no more than 0 kilobags of Really Smalls can be put out per day. iii. The number of Extra Larges must be no less than 4 the number of Really Smalls produced per day. iv. More than 150 hours of labor must be used each day to meet union requirements. It takes 10 hours to make a kilobag of Extra Larges and 15 hours to make a kilobag of Really Smalls. a. Select variables for the numbers of kilobags of each kind produced each day, then write inequalities for each of the above restrictions. b. On the graph paper provided, draw a graph of the feasible region. c. If Amanda s Corn Chips, Inc. makes a profit of $00 per kilobag of Extra Larges and $150 per kilobag of Really Smalls, show the region on your graph in which the daily profit would be at least $6,000. d. How many bags of each kind should be produced each day to give the greatest feasible profit? What is this profit?

7 Put the quadratic into vertex form and sketch the graph y x 1x 7 y x x Simplify completely.. 65 i. 00 i 4. 6 i 5. ( 4 i) ( 6 i) 6. ( 5 i)(6 10 i) 7. 48i 6i 8. Which of the following is equal to i i? A) i 1 B) C) 1 D) 4 i 5

8 Using any method, solve the equation x 0x x 4x x x x x 5 x 1 4. What is the positive difference between the roots of the equation y 6x x 18? Use the discriminant to determine and describe the roots x 7x x x 5 0

9 Find the axis of symmetry, vertex, x- and y-intercepts, symmetric point and graph. 46. y x 4x y x 4x 48. Given f ( x) x 6x 4 a. Find f () b. Find f (4) c. Find x, if f ( x) d. Find the x-intercepts

10 Find the particular equation of the quadratic function containing the given information. 49. Containing -,-10,-151, Vertex at 1,-7, containing point, Mrs. Payne begins cramming for her math test at 10:00 p.m. Wednesday evening. Her grade depends on the number of hours she studies. She figures that with no studying she earns only a 40. With one hour of studying she would earn a 75 and with hours she might earn a 90. Assume that her grade is a quadratic function of the number of hours. a. Find the particular equation for this function. b. Predict Mrs. Payne s grade is she studies for hours, 4 hours, or 5 hours. c. How long must Mrs. Payne study to earn a 100 d. How long must Mrs. Payne study to earn the highest grade she can?

11 Simplify the expression with no negative variables x y 9 6x y 7 z z a 1 b 4 a b 1 6 Evaluate the expressions Evaluate without a calculator Simplify. Write your answer in scientific notation (7 10 )(10 )

12 5 x If 9 6, what is the value of x 1? 4 Solve each equation. 4x x e x x4 e 64. e x x e 65. e x x 4e x 400

13 67. A researcher estimates that the population of Basbaville is increasing at an annual rate of.5%. If the current population is 17,000, which of the following expressions models the population of the city t years from now? A) 17,000( ) t B) 17, 000( t ) C) 17, t D) 17, 000(0.005 t ) Find the value of x log x 69. log 49 4 x log x log x 0 7. log 5x log( x1) 7. ln( x 5) ln( x 1) ln( x 1)

14 74. log x log ( x ) log ( x 6) 75. 4ln x log 4 xlog 4( x1) 77. 8ln x 7 Write as a single log. 78. log 5 log 5 8 log log 116 log 11 log x x40 x 5 log7 log 7( x 5) log( x 64) x ( x ) ln ln 4 ln x x 81. x

15 Rewrite as base 10 logs log log 0 Rewrite as the sum and difference of logarithms. 84. ln x x 1 ( x ) g h km log 9 8 Find the decimal approximation for each. Round to 4 decimal places log 86. log 8 16 Graph the following functions. 1 x 87. f( x) * f( x) 1* 5 x

16 89. f ( x) log 4( x ) f ( x) log ( x 1) 4 Find the inverse of the function. 91. f x x 5 9. g x x Draw the inverse of each function on the same graph

17 Using composite functions, TEST to see if the two functions are inverses. 95. p( x) 1 4x and 1 1 r ( x) x h x ( ) x 1 and k( x) x Graph the following function: x1 x f x x x x x 0 ( ) Graph the following function: x x 1 f( x) x x 1 x 1

18 99. Write the function of the graph You decide to plant asparagus in your kitchen garden. You first harvest 10 stalks in By 1988 you produce 0 stalks. Assume that the number of stalks you harvest varies exponentially with the number of years since you started harvesting the plants. a. Find the particular equation of this function expressing number of stalks in terms of the time since you harvested. b. You will need 100 stalks to enter the gardening contest at the local fair. When can you enter the contest? c. According to your model, when did you harvest the first stalk? d. What will be your production in the year 000? You are done! Now aren t you excited to take the midterm?????