Algebra II Honors. Midterm Review

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1 Algebra II Honors Midterm Review Simplify the following epressions { [ ( )]}. ( y) y( y) Solve in the given domain.. ( 5)( 9) 0 {positive reals} {positive reals} {integers} 5a. 6 1 {reals} Plot the graph of the function in the indicated domain. Identify the range y { } 7. y {non-positive reals}

2 Identify the domain and range Domain Range Domain Range Plot the graph and tell whether or not the relation is a function. 10. y 11. y

3 Write the equation of the line described in Standard Form. 1. Through (, -) and (, 9) 1. -intercept of (-, 0) and slope Through (, -1) and perpendicular to - y = Through ( -, 6) and parallel to + y = Nick takes a Padiddle Cab from the airport to his home which is eactly si 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 epressing 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 $1.5. 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 costintercept?

4 Solve the following systems of equations y = = y 7 y = + y = 1 Solve the following systems using Cramer s Rule. Show each fraction and use the calculator to find the determinants. 19. y = y 5z = y = 1 + y z = - y z = 11 Solve by hand. 1. y + z = 0 + y 5z = -1 y + z = 15

5 Graph the system.. + y > 9 y -8. Amanda is president of Amanda s Corn Chips, Inc. Her company is divided into two departments which put out two types of corn chips, Etra 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 5 kilobags total, can be manufactured each day. ii. No more than 0 kilobags of Etra Larges and no more than 0 kilobags of Really Smalls can be put out per day. iii. The number of Etra Larges must be no less than 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 Etra 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 Etra 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?

6 Put the quadratic into verte form and sketch the graph y 1 7 y Simplify completely i i 8. 6 i 8. ( i) ( 6 i) 9. ( 5 i)(6 10 i) 0. 8i 6i

7 Using any method, solve the equation Use the determinant to determine and describe the roots

8 Find the ais of symmetry, verte, - and y-intercepts, symmetric point and graph. 7. y 7 8. y 9. Given f ( ) 6 a. Find f () b. Find f () c. Find, if f ( ) d. Find the -intercepts

9 Find the particular equation of the quadratic function containing the given information. 0. Containing (-, -10) (, -15) (, -) 1. Verte at (1, -7), containing point (, -7). 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 0. 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, 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?

10 Simplify the epression with no negative variables.. 5 y 9 6 y 7 z z. a 1 b a b 1 6 Evaluate the epressions Evaluate without a calculator Simplify. Write your answer in scientific notation (7 10 )(10 )

11 Solve each equation Find the value of log 5. log log log 0 Write as a single log. 57. log 5 log 5 8 log log 116 log 11 log 11

12 Find the decimal approimation for each log 60. log 8 16 Graph the following functions f( ) * 6. 1 f( ) 1* 5 6. f ( ) log ( ) 1 6. f ( ) log ( 1)

13 Find the inverse of the function. 65. f() = g() = + Draw the inverse of each function on the same graph Using composite functions, test to see if the two functions are inverses. 69. p( ) 1 and 1 1 r ( ) 70. h ( ) 1 and k( ) 1

14 Assume that f is an eponential function. 71. f ( 6) 15 and f ( 1) 5 a. f (15) b. f ( 1) 7. 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 eponentially with the number of years since you started harvesting the plants. a. Find the particular equation of this function epressing 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? Factor each completely

15 75. ( a c c) ( a ) b 6g Use long division to divide Use synthetic division to divide. 78. ( 1 7 6) ( 1) 79. ( 6) ( ) Use the Factor Theorem to factor completely

16 Perform the indicated operation

17 88. What is the positive difference between the roots of the equation y 6 18? 89. If , what is the value 1?

18 90. 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 epressions 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 ) 91. If 1 1, find a possible value for. 9. Which of the following is equal to i i? A) i 1 B) 5 C) 1 i D) 5

19 Solve for : Give an eample for each, or state that it is not possible. 96. An integer that is not a whole number 97. A real number that is irrational 98. A transcendental number that is a natural number 99. A rational number that is an integer 100. A digit that is not a natural number You are done! Now aren t you ecited to take the midterm?????

Algebra II Honors Midterm Review

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