MATH 103 Sample Final Exam Review

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1 MATH 0 Sample Final Eam Review This review is a collection of sample questions used b instructors of this course at Missouri State Universit. It contains a sampling of problems representing the material covered throughout the semester and ma not contain ever tpe of question on the final eam. An material listed on the lecture schedule and/or the assignment sheet ma be on the final eam. Please also be aware that a few questions on the final eam, while requiring knowledge and understanding of the content covered in the course, ma be presented in a form different than the problems in the tet. Problems. Evaluate. Assume all variables are nonzero Problems. Simplif. Write answers with onl positive eponents. Assume all variables are positive..... w w m m 0. a c d.. a a a. 0 Problems. Simplif. Assume all variables are positive a b c Problems 9 0. Factor completel. If the epression cannot be factored, write prime p.. p 0 p p. m m a a 0. m 7n 9. 0.

2 Problems. Perform the indicated operation and simplif.. 7. zz.. 9 a. a 9 a m m m m a. a a a.. p 7 p p 7 p 7. 7 a0 a. m mn m n m Problems. Solve.. a a m m m 7 m q q 79. z z t 7 9 t. z z 9. k 7 p p p m m m 7m.

3 Problems 7. Solve b substitution Problems Solve b completing the square Problems Solve for the indicated variable. p p for 9. p p for p 9. for 9. I a b for b 9. for r R E R 9. m 9. for m n b for Problems Solve and graph on a numberline. Write our solution in interval notation n n m m 0. Use the formula for slope to find the slope of the line through the points, and,. 09. Given the line, find the slope and describe the line. 0. Find the -intercept and -intercept of 7. Write them as ordered pairs.. Write in slope-intercept form, then state the slope and -intercept.. Given f and g, find the following: a. f 7 b. g 7 c. g Problems Determine whether the pairs of lines are parallel or perpendicular to each other, or neither.. 0..

4 Problems 0. Write the equation of the line. When possible, write the equation in slope-intercept form.. Slope is and passes through, 7. Passes through,. Slope is and, and passes through 0, 9. Horizontal line that passes through, 0. Undefined slope that passes through, Problems. Give the domain and range of each relation. Determine whether the relation is a function..,0,,, 9,,,.... Problems 9. Determine where each function is undefined.. h 7. g k f Problems 0. For each parabola, identif a) the verte b) the ais of smmetr c) determine whether the parabola is wider, narrower, or the same width as Problems. Graph each of the following. Label at least ke points on the graph Line with slope. and passes through 0,

5 Problems 0. Applications. Define a variable, write an appropriate equation using the variable, solve.. A bookstore sells a college algebra book for $90. If the bookstore makes a profit of % on each sale, what does the bookstore pa the publisher for each book?. The perimeter of a garden is meters. The length is meters less than twice the width. Find the dimensions of the garden.. Ran can paint a room in hours when working alone. If Stephanie helps him, the total job takes hours. How long would it take Stephanie if she worked alone? 7. A certain airplane flies 0 mph in still air. On a wind da, this plane flew miles into the wind in the same amount of time that it flew miles with a tailwind. Find the speed of the wind.. Suppose that Bod s Hardware just announced a 0% decrease in the price of their snowblower. If one particular snowblower model sells for $9.99 after the decrease, find the original price of the snowblower. 9. A west-bound jet leaves an airport traveling 00 miles an hour. At the same time, an east-bound plane departs at 0 miles an hour. In how man hours will the planes be 900 miles apart? 0. Joe drives from cit A to cit B at an average speed of 7 mph. Once he arrives at cit B, he immediatel turns around and heads back to cit A. On the trip back to cit A from cit B, he has car trouble and drives an average speed of mph. If the total round trip takes Joe hours, what is the distance between cit A and cit B?. The hpotenuse of a right triangle is centimeter more than twice the length of the shorter leg, and the longer leg is 9 centimeters shorter than three times the length of the shorter leg. Find the length of the three sides of the triangle.. Bob can paint a room in hours working alone. It takes Barbara hours to paint the same room. How long would it take them to paint the room together?. Natalie can ride her bike mph faster than her husband, Chuck. If Natalie can ride miles in the same time that Chuck can ride miles, what are their speeds?. When Sarah takes the bus to work, the trip takes 0 minutes. When she takes the train to work, the trip takes 0 minutes. The average speed of the train is mph more than the average speed of the bus. Find the distance to work.. After t seconds, the height ht of a model rocket launched from the ground into the air is given b the function ht t 0t. Find how long it takes the rocket to reach a height of 9 feet.. Mar put some mone in a certificate of deposit earning.% simple interest. She deposited twice that amount in a mone market account paing % simple interest. After ear her total interest was $. How much did Mar deposit in her mone market account? 7. Two cars leave towns miles apart at the same time traveling toward each other. One car travels mph faster than the other car. The meet hours later. What is the speed of the faster car?. How man liters of a 0% alcohol solution should be mied with liters of a 0% alcohol solution to obtain a % alcohol solution? 9. A coffee merchant combines coffee A costing $ per pound with coffee B costing $.0 per pound. How man pounds of each should be used to make pounds of a blend costing $. per pound? 0. The proportion of males to females at a certain college is :. If the total population of the college is 90 students, how man of these are female?

6 w m 0. a d c.. a.. i. 9i. 7.. ab c abc 9. SOLUTIONS 0... pp. 0. p p. m m 0. prime 7. a. m nm mn 9n z a 7 aa m m m a aa 9 p p 7 0 a. m n m m a.,.,., 0,., 7.,. m 7 9. no solution 70., , 7., 7., ,, i 7, i 7 7. q 79. z 0..,. 7 t,. no solution. k,. z. m 7 7.,

7 7., 9., 90. i, i 9. p 9. p a b or b a 9. I Er I R or R r E E 9. m n b, , 00., 0., 0. no solution 0. 9, 0. 7,, 0.,,, , 0. slope is 09. The slope is undefined. vertical line passing 0. through 9, 0 7 intercept is,0 7 intercept is 0,. slope is intercept is 0,. a) b) c) 9. perpendicular. neither. parallel Domain,,,9. Range 0,,, Is a function Domain,. Range, Is a function Domain,,,,0,. Range, Not a function Domain,. Range, Is a function Domain,. Range, Not a function , 7. undefined nowhere 9. a) verte is 0,0 0. b) 0 c) wider. a) verte is 0,7 b) 0 c) same width a) verte is,. b) c) narrower. a) verte is, b) c) wider

8 $7. length is meters width is meters. hours 7. 0 mph. $ hours 0. miles. cm, cm, 7 cm 7. hours.7 hours. Chuck's speed is mph Natalie's speed is mph. miles. seconds. $ mph. liters lbs of coffee A 7. lbs of coffee B 0. female students.

1. Simplify each expression and write all answers without negative exponents. for variable L.

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