Los Angeles Southwest College. Mathematics Department. Math 115 Common Final Exam. Study Guide SPRING 2010

Transcription

1 Los Angeles Southwest College Mathematics Department Math Common Final Eam Study Guide SPRING 00 Prepared by: Instr. B.Nash Dr. L.Saakian

2 Chapter.. Simplify:8 [ ( )]. Simplify: 8 [9 ( )]. Simplify:[( 9) ( )]. Simplify:[ ( 9)] [6 ( )]. Decide whether the statement is true or false: 6 ( ) 6. Decide whether the statement is true or false: Decide whether the statement is true or false: ( ) 8. Decide whether the statement is true or false: Perform indicated operation: ( ) () [ ( )] 0. Perform indicated operation: 0 8 ( ). Perform indicated operation: (0.6) (0.8) (.) ( 0.6). For the following word phrase write an epression using as the variable and simplify. less than the difference between 8 and -.. For the following word phrase write an epression using as the variable and simplify. The sum of and 0, increased by.. For the following word phrase write an epression using as the variable and simplify. 9 less than the difference between 9 and -.. For the following word phrase write an epression using as the variable and simplify. The sum of and -7,decreased by. 6. Otis neglects to keep up his checkbook balance. When he finally balanced his account, he found that the balance was -$.7, so he deposited $0.00. What is his new balance?

3 7. Mike O Hanian owed a friend $8. He repaid $, but than borrowed another $. What positive or negative amount represents his present financial status? 8. Peyton Manning of the Indianapolis Colts passed for a gain of 8 yd, was sacked for a loss of yd, and than threw a yd touchdown pass. What positive or negative number represents the total net yardage for the plays? 9. If the temperature drops temperature? 0 7 below its previous level of 0, what is the new 0. Evaluate 6 z, if and z. Evaluate y, if and y. Evaluate 6 z, if and z. Evaluate z ( 8 y), if, y, and z. Combine like terms: (y 9) ( y 6). Combine like terms: (r ) (6 r) r 6. Combine like terms: p p 8p 6p 7. Combine like terms: 6 z z z z Chapter.. Solve the equation and check your solution: 6 7. Solve the equation and check your solution: ( k 6) (k ). Solve the equation and check your solution: (y 6) ( y ) 0. Solve the equation and check your solution: ( r) ( r ). Solve the equation and check your solution: 6. Solve the equation and check your solution: m 6m m 6 7. Solve the equation and check your solution:r r 6r Solve the equation and check your solution: 9p p

4 9. Solve the equation and check your solution: (m ) m 8m 7 0. Solve the equation and check your solution: 6( ) ( ). Solve the equation and check your solution: ( ) 6( ). Solve the equation and check your solution: 7r r r r. The sum of three times a number and 7 more than the number is the same as the difference between and twice the number. What is the number?. During the 09 th Congress (00-006), the U.S. Senate had a total of 99 Democrats and Republicans. There were more Republicans than Democrats. How many Democrats and Republicans were there in the Senate?. In one day, a store sold 8 as many DVDs as CDs. The total number of DVDs and CDs sold that day was 7. How many DVDs were sold? 6. In her job as a mathematics tetbook editor, Lauren Morse works 7. hr a day. She spent a recent day making telephone calls, writing s, and attending meetings. On that day, she spent twice as much time attending meetings as making telephone calls and spent 0. hr longer writing s than making telephone calls. How many hours did she spend on each task? 7. The supplement of an angle measures 0 times the measure of its complement. What is the measure of the angle? 8. Find two consecutive odd integers such that when the lesser is added to twice the greater, the result is more than the greater integer. 9. The perimeter of a certain rectangle is 6 times the width. The length is cm more than the width. Find the width of the rectangle. 0. Two trains are 90 mi apart. They start at the same time and travel toward one another, meeting hr later. If the speed of one train is 0 mph more than the speed of the other train, find the speed of each train.. The perimeter of a triangle is 96 m. One side is twice as long as another and the third side is 0 m long. What is the length of the longest side?. The perimeter of a basketball court is 88 ft. The width of the court is ft less than the length. What are the dimensions of the court?. Solve the formula d rt for t

5 . Solve the formula P L W for W. Solve the formula M C( r) for r 6. Solve the formula C ( F ) for F 9 7. Solve the formula A h ( b B ) for h 8. Solve the equation Solve the equation y 6 y 0. If 6 gal of premium unleaded gasoline costs $9.6, how much would it cost to completely fill a - gal tank?. The distance between Singapore and Tokyo is 00 mi. On a certain wall map, this is represented by in. The actual distance between Meico City and Cairo is 7700 mi. How far apart are they on the same map?. Solve the inequality 6. Solve the inequality ( ) 6 ( ). Solve the inequality 9. Solve the inequality q 6 Chapter.. Find the -intercept and y -intercept: y. Find the -intercept and y -intercept: y 0. Find the -intercept and y -intercept: y. 0. Find the -intercept and y -intercept: 0. Find the slope of the line through pair of points: (, ) and (, 8)

6 6. Find the slope of the line through pair of points: ( 8,0) and (0, ) 7. Find the slope of the line through pair of points: ( 8,6) and ( 8, ) 8. Find the slope of the line through pair of points: (6, ) and (, ) 9. For the pair of equation, give the slopes of the lines and then determine whether the two lines are parallel, perpendicular, or neither parallel nor perpendicular. y 0y 0. For the pair of equation, give the slopes of the lines and then determine whether the two lines are parallel, perpendicular, or neither parallel nor perpendicular. y 6 y. For the pair of equation, give the slopes of the lines and then determine whether the two lines are parallel, perpendicular, or neither parallel nor perpendicular. 8 9y 6 8 6y. For the pair of equation, give the slopes of the lines and then determine whether the two lines are parallel, perpendicular, or neither parallel nor perpendicular. y y 0. Write an equation for the line passing through the given point and having the given slope. Give the final answer in slope-intercept form: (,), m. Write an equation for the line passing through the given point and having the given slope. Give the final answer in slope-intercept form: (,), m. Write an equation for the line passing through the given point and having the given slope. Give the final answer in slope-intercept form: (,), m 6. Write an equation for the line passing through the given point and having the given slope. Give the final answer in slope-intercept form: (,7), m 7. Write an equation for the line passing through the given pair of points. Give the final answer in slope-intercept form. (8,) and (9, 6) 6

7 8. Write an equation for the line passing through the given pair of points. Give the final answer in slope-intercept form. (,0) and (6,) 9. Write an equation for the line passing through the given pair of points. Give the final answer in slope-intercept form. (, ) and (, ) 0. Write an equation for the line passing through the given pair of points. Give the final answer in slope-intercept form. (, 0) and (0, ). Graph the linear inequality: y 9. Graph the linear inequality: y 6. Graph the linear inequality: y 0 Chapter.. Decide whether the given ordered pair is a solution of the given system. (,) y y 9. Decide whether the given ordered pair is a solution of the given system. (,) y y. Solve the system by graphing: y y y. Solve the system by graphing: y y y. Solve the system by the substitution method. y 9 y 8 7

8 6. Solve the system by the substitution method. y 0 y 7. Solve the system by the substitution method. y y 8. Solve the system by the substitution method. y 6 y 7 9. Solve the system by the elimination method. y y 0. Solve the system by the elimination method. y y. Solve the system by the elimination method. y y. Solve the system by the elimination method. y 0 y. Bill Kunz went to the post office to stock up on stamps. He spent $9. on 6 stamps, made up of a combination of 9-cent and -cent stamps. How many stamps of each denomination did he buy?. A 0% dye solution is to be mied with a 70% dye solution to get 0 L of a 0% solution. How many liters of the 0% and 70% solutions will be needed?. Two trains start from towns 9 mi apart and travel toward each other on parallel tracks. They pass each other. hr later. If one train travels 0 mph faster than the other, find the speed of each train. 6. If a plane can travel 0 mph into the wind and 00 mph with the wind, find the speed of the wind and the speed of the plane in still air. 8

9 7. Nancy Johnson invested $8,000. Part of it was invested at % annual simple interest, and the rest was invested at %. Her interest income for the first year was $60. How much did she invest at each rate? 8. Graph the solution set of the system of linear inequalities. y y 9. Graph the solution set of the system of linear inequalities. y y 6 Chapter.. Simplify: ( y z) ( yz ). Simplify: a b 6 c. Simplify: 6 y z 9. Simplify: ( r s) ( r s ). Simplify. Use only positive eponents: (6 z ) 6. Simplify. Use only positive eponents: ( y ) y 7. Simplify. Use only positive eponents: ( r s) ( r s ) 8. Simplify. Use only positive eponents: mn p mn p m np m np 9. Perform the operation: (9a a ) (a a ) ( a 6a ) 0. Perform the operation: (8m 7 m) (m 7m 6). Perform the operation: (6b c) ( b 8 c ) 9

10 . Perform the operation: ( y ) ( y ). Find the product: ( m 7)( m ). Find the product: (m n)( m n ). Find the product: 6. Find the product: p (p p)( p p ) (a ) 7. Find the product. Use special product formulas to simplify: ( a 8)( a 8) 8. Find the product. Use special product formulas to simplify: ( m ) 9. Find the product. Use special product formulas to simplify: (y )(y ) 0. Find the product. Use special product formulas to simplify: ( z ). Find the product. Use special product formulas to simplify: (r t ). Find the product. Use special product formulas to simplify: (6m )(6m ). Find the product. Use special product formulas to simplify: p(p 7)(p 7). Find the product. Use special product formulas to simplify:. Find the product. Use special product formulas to simplify: (r ) 6. Perform the division: 7. Perform the division: 8t t t t 0m 0m m m 8. Perform the division: ( 0m n m n 6 m n ) m n 9. Perform the division: r r 6r r 0

11 0. Perform the division:. Perform the division: 6 r r r Chapter 6.. Factor completely: 8m n m n. Factor completely:. Factor completely:. Factor completely:. Factor completely: 6. Factor completely: 7. Factor completely: 8. Factor completely: 9. Factor completely: 0. Factor completely:. Factor completely:. Factor completely: m mp mr 6pr 6m m p mp p 6 6 p q p q 8p q r ra a y y 0 m n m n mn ( a b) ( a b) ( a b ) 6 7 t t 8 s st t Factor completely:. Factor completely: a 8. Factor completely: 0 6. Factor completely: a 7 7. Factor completely: 7t 6s 6

12 8. Factor completely: t 8s 6 9. Factor completely: 6r a 0. Factor completely:. Solve the equation: 8w 6 ( 7)( ) 0. Solve the equation:. Solve the equation:. Solve the equation: ( ) ( ) 6r 9r 0. A certain triangle has its base equal in measure to its height. The area of the triangle is 7 m. Find the base and height measure. 6. The product of the second and third of three consecutive integers is more than0 times the first integer. Find the integers. 7. A ladder is leaning against a building. The distance from the bottom of the ladder to the building is ft less than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is ft less than the length of the ladder. 8. An object projected from a height of 8 ft with an initial velocity of ft per sec after t seconds has height h 6t t 8 ( a ) After how many seconds is the height 6 ft? ( b ) After how many seconds does the object hit the ground? Chapter 7.. Write the rational epression in lowest terms: 7t t 0 7t. Write the rational epression in lowest terms: 6. Write the rational epression in lowest terms: k k 6 k

13 . Write the rational epression in lowest terms: 7. Multiply: 6. Multiply: k k k k 6k 7k k k 7. Divide: 8. Divide: m mp p m mp p m mp p m mp 8p ( q ) ( q ) q 6q 9 q q q q m m 9. Add: m m m 6m a a 0. Add: a a a 7a z z. Perform indicated operation: z 0z z 6. Perform indicated operation: k k k k k k. Simplify: 8. Simplify: m m. Simplify: m m m m

14 6. Simplify: p 7. Solve the equation and check your solutions: p p p 8. Solve the equation and check your solutions: k k k 0 9. Solve the equation and check your solutions: z z z 0. Solve the equation and check your solutions: 6. One-third of a number is more than one-sith of the same number. What is the number?. A boat can go 0 mi against a current in the same time that it can go 60 mi with the current. The current is mph. Find the speed of the boat in still water.. Working alone, Jorge can paint a room in 8 hr. Caterina can paint the same room working alone in 6 hr. How long will it take them if they work together?. One pipe can fill a swimming pool in 6 hr, and another pipe can do it in 9 hr. How long will it take the two pipes working together to fill the pool full? Chapter 8.. Find the square root:. Find the square root:. Find the distance between the pair of points: (,7) and (,). Find the distance between the pair of points: (, 6) and (, 0). Simplify: 8m n

15 6. Simplify: 7. Simplify: 8. Simplify: 6 y 69 wz 00 9 n Simplify and combine like terms where possible: 8 0. Simplify and combine like terms where possible: 7 7. Simplify and combine like terms where possible: 6. Simplify and combine like terms where possible: 0m m. Simplify and combine like terms where possible: k 8k n k n. Perform indicated operation: ( 6) ( ). Simplify the radical: 0 6 y 6. Simplify the radical: 7. Simplify the radical: a b 6 0 y 8. Simplify the radical: 9. Simplify the radical: mn z y 0. Rationalize the denominator: 7. Rationalize the denominator:

16 . Rationalize the denominator:. Rationalize the denominator: 8 y. Solve the equation:. Solve the equation: 6. Solve the equation: 7. Solve the equation: 8. Simplify: 9. Simplify: 7 ( pq ) 0. Simplify: q q q 6 6. Simplify: ( mn ) Chapter 9.. Solve the equation by using square root property:. Solve the equation by using square root property:. Solve the equation by using square root property:. Solve the equation by using square root property:. Solve the equation by completing the square: (z 6) 7 ( ) 9 (k ) 8 0 ( m ) 7 6. Remove parentheses and solve the equation by completing the square: ( r )( r ) 7. Solve the equation by completing the square: k 7k 8. Solve the equation by completing the square: ( k )( k 7) 6

17 9. Use the quadratic formula to solve the equation: r r Use the quadratic formula to solve the equation: ( )( ) 7. Use the quadratic formula to solve the equation:. Use the quadratic formula to solve the equation: 0 7. A farmer has a rectangular cattle pen with perimeter 0 ft and area 700 What are the dimensions of the pen? ft.. The base of a triangle measures m more than three times the height of the triangle. The area of the triangle is m. Find the lengths of the base and the height.. If an object is projected vertically into the air from ground level on Earth with an initial velocity of 6 ft per sec. Its altitude (height) s in feet after t seconds is given by the formula: s 6t 6t. At what time will the object be at a height of 6 ft? 6. In a right triangle, the lengths of the sides are consecutive integers. Use the Pythagorean formula to find these lengths. 7