Part I : Multiple Choice.

Transcription

1 Math 1010 Final Exam Intermediate Algebra Spring Semester 013 Form A Instructor Name Student ID ID Verification Section Number Time Limit: 10 minutes All problems are weighted equally. Graphing/programmable calculators, notes, books, cell/head phones, or any devices that can connect to the Internet are not allowed. Scientific calculators with no more than a basic numeric store and recall memory may be used. This exam has three parts Part I - Ten multiple choice questions - answer all Part II - Ten open ended questions - answer all Part III - Ten open ended questions - choose FIVE INSTRUCTIONS PART I: Questions 1-10, Multiple Choice. Answer all TEN questions. Circle the correct answer. There will be no partial credit awarded on this part of the exam. Part I : Multiple Choice. 1) Perform the indicated operations and simplify if possible. 5 x x x x x 4 A) B) x x 10 ( x )( x ) x 4x 10 ( x )( x ) 5 C) ( x )( x )( x 4) D) xx ( 4) ( x )( x ) 1

2 ) A barge moves 10 mph in still water. It travels 87 miles upriver in the same time it takes to travel 153 miles downriver. Let x be the speed of the current in mph. Write an equation in x which could be solved to find the speed of the current. DO NOT SOLVE THE EQUATION. A) B) x 10 x x 10 x C) 10 x 10 x D) 10 x 10 x 3) Perform the indicated operation. Then, write your final answer using radical notation. A) 1 x x 1 4 x 3 B) 11 1 x C) 1 3 x D) 1 11 x

3 4) Use the graph to find f (). A) -3 B) 1 C) 3 D) 5) Find the domain of the function. f ( x) x 4. A) (,4) (4, ) B) (,0) (0, ) C) (4, ) D) [4, ) x 3 6) Find the domain of the function. f( x) x x. x x is a real number and x, x 1, x 3 A) B) x x is a real number and x, x 1 C) x x is a real number and x 1, x D) x x is a real number and x 0, x 3 3

4 7) Factor completely. 3 4r 3 A) B) C) D) 4( r )( r 4) 4( r )( r r 4) 4( r )( r r 4) 4( r ) 3 8) If a ball is thrown upward with an initial speed of 3 feet per second, then its height h in feet after t seconds is given by the equation h( t) 16t 3t. Find the maximum height of the ball. A) 1 foot B) 3 feet C) feet D) 16 feet 9) Find the midpoint of the line segment whose endpoints are (-1, 3) and (, -5). A) ( 1, -) B) (-3, 8) C) ( 3, -4) D) ( 1, -1) 4

5 10) Find the distance between the points (-5,-1) and (,4). A) 74 B) 3 C) 34 D) 58 INSTRUCTIONS PART II: Questions Answer all TEN questions carefully and completely, showing all appropriate work and clearly indicating your answer. Part II : 11) Becky bought some large frames for $5 each and some small frames for $3 each at a closeout sale. If she bought 11 frames for $41, find how many of each type she bought. a) Write down the system of equations which represents this situation. b) Solve the system that you wrote down in part (b). c) How many frames of each type did she buy? Please answer with a complete sentence. 5

6 1) Find the equation of the line passing through the two points. Write your answer in slopeintercept form. (-6, -5) and (1,-0). Answer: 13) Factor completely. 3 y 4y 9y 36 14) Simplify the complex fraction. 3 5 x x 3x 6

7 15) Rationalize the denominator. x 7 x 16) Solve the equation. x 1 x 5 17) Perform the operation and simplify. Write the result in the form a + bi i 7

8 18) Solve the following equation. x 7x ) Graph the function. Label the vertex and (at least) one other point on the graph, and draw the axis of symmetry. Write the equation of the axis of symmetry. f x ( ) ( x ) 1 Equation of the axis of symmetry: 8

9 0) Solve the equation. log 5( x 1) 3 INSTRUCTIONS PART III: Questions Answer FIVE questions only. Show all appropriate work carefully and completely, clearly indicating your answer. Put an X through the 5 problems you do not want graded. If you do not cross out any problems, the first 5 problems that show any work will be the ones that are graded. Part III : 1) Solve the following system. x y z 6 3x y z 4x 3y z 3 9

10 ) Solve the compound inequality. Graph the solution set. Write your answer using interval notation. 3 x 1 7 Interval Notation: 3) The Math department can copy all the Math 1010 final exams in 15 minutes by using a new photocopier. The old photocopier working alone would take 30 minutes to complete the job. How much time will it take to copy the exams if both photocopiers are used together? a) Write down an equation which models this situation. b) Solve the equation from part a). c) How long does it take to copy the exams using both machines at the same time? Please answer using a complete sentence. 10

11 4) Solve for t. s R 1 t 5) Solve the inequality. Graph the solution set. Write your answer using interval notation. 6 4x 10 Interval Notation: 11

12 6) Graph the system of inequalities. 6x 3y 1 y 7) Solve the equation. x

13 8) Given the equation of the circle in general form, answer the following questions. Do not use mixed numbers or decimals. x y x y a) Rewrite the equation in standard form by completing the square. b) Find the center of the circle. c) Find the radius of the circle. 13

14 9) Fill in the table and sketch the graph of f( x ) 3 x 1. Give exact values for y (no decimal approximations). x -1 y ) Perform the indicated operation and simplify if possible. x 3x 6 4x 4 x 1 14