Algebra I End of Course Review

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2 Algebra I End of Course Review Properties and PEMDAS 1. Name the property shown: a + b + c = b + a + c (Unit 1) 1. Name the property shown: a(b) = b(a). Name the property shown: m + 0 = m. Name the property shown: a(b + c) = ab + ac. Name the property shown: a 1 = a 4. Name the property shown: (a b) c = a (b c). Name the property shown: (a + b) + c = a + (b + c) 5. Name the property shown: a b = b a 6. Name the property shown: a + ( a) = 0 4. Name the property shown: a + 0 = a 7. Name the property shown: abc=cab 8. Name the property shown: a 0 = 0 5. Simplify using PEMDAS Simplify using PEMDAS (5 + 1) Simplify using PEMDAS (8 + 1) 6 6. Simplify using PEMDAS 0 (4 + 1) Simplify using PEMDAS (-) Simplify using PEMDAS () Solving Equations Review Together: (Unit ) Homework: p 6 10p 1. 6m 9m

3 Algebra I End of Course Review. 5 ( 4) ( ) ( 9) p 7 p

4 Algebra I End of Course Review Inequalities Review Together: 1. ( 8) 4 (Unit ) Homework: 1. ( 4). 4 ( 4) < 6 < < + < 8. 1 > + 1 > 5 Absolute Value Solve and graph and write the final answer: (Unit Continued)

5 Algebra I End of Course Review Recognizing Functions 1. Give the function rule of the table: f() (Unit 4) 1. Give the function rule of the table: y Give the function rule of the table: f() Is the graph a function?. Is the graph a function? 4. Is the graph a function?. Give the domain and range of the following set of points: (, 7) (-, 5) (-8, -1) (-, ) Domain: Range: Is the relation a function? 5. Give the domain and range of the following set of points: (, 7) (1, 7) (6, -) (-8, ) Domain: Range: Is the relation a function? 4 6. Give the domain and range of the following set of points: (6, -1) (-4, ) (-7, -) (6, -5) Domain: Range: Is the relation a function?

6 Algebra I End of Course Review Basic Linear Graphing Review Together: 1. Complete the table and graph from the equation: y = y (Unit 5) Homework: 1. Complete the table and graph from the equation: y = + 4 y. Complete the table and graph from the equation: y = 5 +4 y. Give the slope of the line:. Give the slope of the line: 4. Give the slope of the line:. Solve for y and name the slope and y-intercept: y = 6 m= b= 5. Solve for y and name the slope and y-intercept: + 4y = -8 m= b= 6. Solve for y and name the slope and y-intercept: 5 y = 15 m= b= 4. Graph the following line from its slope and y-intercept: y = 4 7. Graph the following line from its slope and y-intercept: y = Graph the following line from its slope and y-intercept: y = + 1 5

7 Algebra I End of Course Review 5. Graph the following line from its slope and y-intercept: y = 9. Graph the following line from its slope and y-intercept: y = Graph the following line from its slope and 1 y-intercept: y = + 6. Graph y = and = - and name their slopes: 11. Graph y = -4 and = 5 and name their slopes: 1. Graph y = 1 and = - and name their slopes: Algebra with Linear Equations: Review Together: 1. Is the point (, 1) a solution to the equation: y = 5 (Unit 5 Continued) Homework: 1. Is the point ( 1, ) a solution to the equation: y = 4 1. Is the point (, 0) a solution to the equation: y = + 4. Name the and y intercepts of the equation: + y = -1. Name the and y intercepts of the equation: 4 + y 8 = 0 4. Name the and y intercepts of the equation: 5 y = 15. Graph from the and y intercepts: 5 +y 10 = 0 5. Graph from the and y intercepts: = 6y Graph from the and y intercepts: 5 4y = 0 6

8 Algebra I End of Course Review Review Together: 4. Give the slope of the line that goes through the points: ( 4, 1) and ( 5, 7) Homework: 7. Give the slope of the line that goes through the points: (, 5) and ( 4, 7) 8. Give the slope of the line that goes through the points: (0, 8) and ( 1, ) 5. Give the slope of the line that goes through the points: (, 1) and (, 1) 9. Give the slope of the line that goes through the points: (5, ) and ( 5, 1) 10. Give the slope of the line that goes through the points: (5, ) and ( 4, ) 6. Give the equation of the line with a slope of that goes through the point (, 1 ) 11. Give the equation of the line with a slope of 1/ that goes through the point ( 4, ) 1. Give the equation of the line with a slope of that goes through the point ( 5, 7) 7. Give the equation of the line that goes through the points: (1, ) and (, 5) 1. Give the equation of the line that goes through the points: (, ) and (, 5) 14. Give the equation of the line that goes through the points: (6, ) and (8, -4) 8. Give the equation of the line that is parallel to the line y = +1 and goes through ( 5, 6). 15. Give the equation of the line that is parallel to the line y = 4 6 and goes through (1, 8). 16. Give the equation of the line that is parallel to the line y = 5 and goes through the point (, 9). 7

9 Algebra I End of Course Review Review Together: 9. Give the equation of the line that is perpendicular to the line y = and goes through (6, 5). Homework: 17. Give the equation of the line that is perpendicular to the line y = ¼ - and goes through ( 1, ). 18. Give the equation of the line that is perpendicular to the line y = + 4 and goes through the point (4, ). Graphing Inequalities: 1. Graph the inequality: y > (Unit 5 Continued) 1. Graph the inequality: y < + 5. Graph the inequality: y > ½ 1. Graph the inequality: y Graph the inequality: y + 4. Graph the inequality: y + 8

10 Algebra I End of Course Review Solving Systems of Equations: Review Together: 1. Solve the following system of equations by graphing: y = 4 y = + 4 (Unit 6) Homework: 1. Solve the following system of equations by graphing: + y = y = 4. Solve the following system of equations by graphing: + y = 4 + y = 1. Solve the following system of equations by substitution: y = + 5 y = 10. Solve the following system of equations by substitution: = y y = 7 4. Solve the following system of equations by substitution: y = y =. Solve the following system of equations by substitution: + y = 7 + y = 1 5. Solve the following system of equations by substitution: + y = 4 + y = 1 6. Solve the following system of equations by substitution: + y = y = 1 9

11 Algebra I End of Course Review 4. Solve the following system of equations by elimination: + y = + y = 7. Solve the following system of equations by elimination: y = 1 + y = 4 8. Solve the following system of equations by elimination: + y = 1 y = 0 5. Solve the following system of equations by elimination: + y = 5 5 y = 9. Solve the following system of equations by elimination: 5y = y = Solve the following system of equations by elimination: + y = 1 5 4y = 6. Solve the following system of equations by elimination: + 5y = y = Solve the following system of equations by elimination: + 6y = 4 7y = 6 1. Solve the following system of equations by elimination: y = 0 y = 5 7. Solve the system of inequalities by graphing: y 4 and y > 1 1. Solve the system of inequalities by graphing: y and y > Solve the system of inequalities by graphing: y < + and y <

12 Algebra I End of Course Review Eponent Rules Review: Review Together: 1. Simplify: 4 4. Simplify: n n n 4 (Unit 7) Homework: 1. Simplify: 5 5. Simplify: g 5 g g 6. Simplify: Simplify: 5 4. Simplify: Simplify: m m - m 6 6. Simplify: b -4 b b Simplify: ( 4 y ) 6 7. Simplify: ( 4 y 5 ) 5 8. Simplify: ( y 5 ) 5. Simplify: 0 6. Simplify: 8 0 y 8 4 y 6 9. Simplify: p Simplify: m p -1 m p Simplify: (10p ) 0 1. Simplify: 5 a b 5 a 4 b 7. Simplify: ( y ) ( 4 y) 1. Simplify: (m 4 p 5 ) (5mp ) 14. Simplify: (a 5 b 4 ) (a b) 5 8. Simplify: ( ) Simplify: p m(p 5 ) Simplify: a 5 b (5a b 4 ) 9. Simplify with positive eponents: - y z Simplify with positive eponents: 5g 5 m g 4 m Simplify with positive eponents: -9a 6 b - c -8 a 4 b c 10. Simplify with positive 4 y eponents: 6 y 19. Simplify with positive 5 a b eponents: 8a b 0. Simplify with positive 4 0m p y eponents: 8 4m y 11. Simplify with positive eponents: 5 1. Simplify with positive m eponents: 4 m. Simplify with positive 6 m p eponents: m p 11

13 Algebra I End of Course Review Adding and Multiplying Polynomials.: Review Together: (Unit 8) Homework: y + y y m p 4m 4 + 6m p + m p 4 p ( 5 6 5) + (4 + +8) 7. (9 + ) + ( + 6) 8. ( + 6) + (8 + 9) 15. ( + 4 ) (5 + 5) 9. ( 5 1) ( + 1) 0. ( + 5) ( 4 + 8) Multiply: 16. ( + )( 5) 1. ( + 6)( ). ( 4)( + ) 17. ( 4)( + 5). ( )(4 ) 4. (5 + )( 1) 18. ( + )( 4 + 5) 5. ( )( + 6 4) 6. ( + 5)( 8) 19. ( + 5)( 5) 7. ( + 7)( 7) 8. ( + )( ) 0. ( + 4) 9. ( + ) 40. ( + 9) 1. ( 5) 41. ( ) 4. ( 6). ( + ) 4. ( + 4) 44. (5 + 1) 1

14 Algebra I End of Course Review Factoring Review: Review Together: 1. Factor by GCF: 9 (Unit 8) Homework: 1. Factor by GCF: Factor by GCF: 8 7. Factor by GCF: Factor by GCF: Factor by GCF: Factor by GCF: Factor by GCF: Factor by GCF: 4 4. Factor by GCF: Factor by GCF: Factor by GCF: Factor: 4 9. Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor: Factor:

15 Algebra I End of Course Review Simplifying Radical Epressions: Review Together: 1. Simplify: 6. Simplify: 40 From here on use only principal roots:. Simplify: 8 50 p (Unit 9) Practice: 1. Simplify: 81. Simplify: 18 From here on use only principal roots: 5. Simplify: m. Simplify: Simplify: 75 From here on use only principal roots: 6. Simplify: p 4. Multiply: Multiply: 5 8. Multiply: Multiply: Multiply: Multiply: Multiply: Multiply: 6 1. Multiply: Multiply: Multiply: Multiply: Simplify: Simplify: Rationalize: Simplify: Simplify: Simplify: Rationalize: 7 1. Simplify: Simplify: Simplify: 6 00 p p 0. Rationalize: Simplify: Simplify: Simplify: Simplify:

16 Algebra I End of Course Review 1. Solve: Solve: 8 6. Solve: Solve: 5 7. Solve: 4 8. Solve: Solve: Solve: Solve: Quadratic Functions Review Together: 1. Make a table and graph for: y = for the domain {- 4} (Unit 10) Practice: 1. Make a table and graph for: y = 4 5 for the domain {-1 5}. Make a table and graph for: y = for the domain {0 6}. Identify the verte of the graph above.. Identify the roots of the : graph above.. Identify the verte of the graph above. 5. Identify the roots of the : graph above. 4. Identify the verte of the graph above. 6. Identify the roots of the : graph above. 15

17 Algebra I End of Course Review 4. Use the parent graph pattern to graph: y = Use the parent graph pattern to graph: y = 7 8. Use the parent graph pattern to graph: y = 5. Double the parent graph pattern to graph: y = Triple the parent graph pattern to graph: y = Double the parent graph pattern to graph: y = 5 6. Find the verte of: y = Find the verte of: y = Find the verte of: y = Now make a graph for the quadratic from # 6 1. Now make a graph for the quadratic from # Now make a graph for the quadratic from # 1 Is the verte a maimum or minimum value? Give the domain: Give the range: Is the verte a maimum or minimum value? Give the domain: Give the range: 16 Is the verte a maimum or minimum value? Give the domain: Give the range:

18 Algebra I End of Course Review 8. Graph the quadratic inequality: y > Graph the quadratic inequality: y < Graph the quadratic inequality: y + 6 Solving for Roots: 1. 5 = 1 Solving for Roots: = 58 Solving for Roots: = = = 4. 4 = = = = = = = = = = = = = = = = 0 17

19 Algebra I End of Course Review 8. How many solutions are there for the quadratic: y = How many roots are there for the quadratic: y = How many times does the graph of this quadratic cross the -ais: y = Review of Rational Epressions Review Together: Simplify: (Unit 11) Practice: Simplify: 4m 1. m 1 Simplify:. t 5 4t 0. 1m m 6. 7 p 14 p m m p 4 p 1 Multiply: 5. 4 m m m 6m Multiply: m 5 6m 14 Multiply: 10w w 4 1w 5w ( 4 5 6) 1. v 4m 4 ( v v 15) 14. ( m 1) v m 1 18

20 Algebra I End of Course Review 19 Divide: m m m m 9. Add: Subtract: 15. Divide: Add: Subtract: 9. Divide: Add: Subtract: 0. ) ( y y y p p ) ( y m m 5 10) 7 (

21 Algebra I End of Course Review Word Problems Review: Review Together: 1. Five less than twice a number is 9. Find the number. (All Chapters) Practice: 1. Seven more than three times a number is 19. Find the number.. Four less than half a number is 7. Find the number.. Four times the sum of a number and two is 8. Find the number.. Twice the sum of a number and si is 18. Find the number. 4. Three times the difference of a number and four is 9. Find the number.. Five more than a number is the same as twice the number decreased by two. Find the number. 5. Si less than twice a number Is the same as the number increased by seven. Find the number. 6. Two more than three times a number is the same eight less than twice the number. Find the number. 4. Three consecutive numbers have a sum of 18. What are the numbers? 7. Three consecutive numbers have a sum of 159. What are the numbers? 8. Three consecutive numbers have a sum of 7. What are the numbers? 5. Three consecutive odd numbers have a sum of 7. What are the numbers? 9. Four consecutive odd numbers have a sum of 51. What are the numbers? 10. Three consecutive even numbers have a sum of -60. What are the numbers? 6. A larger number is three less than four times a smaller number. If their sum is, find the numbers. 11. A greater number is seven less than five times a smaller number. If their sum is 41, find the numbers. 1. A larger number is five more than twice a smaller number. If their sum is, find the numbers. 0

22 Algebra I End of Course Review 7. The length of a rectangle is two centimeters more than three times the width. If the perimeter is 6cm, find the width and length. 1. The length of a rectangle is five centimeters less than four times the width. If the perimeter is 50cm, find the width and length. 14. The length of a rectangle is si centimeters more than the width. If the perimeter is 60cm, find the width and length. 8. Three more than si times a number is at least 1. Find the smallest possible answer that makes this true. 15. Si less than five times a number is at least 9. Find the largest possible answer that makes this true. 16. One more than twice a number is at least 15. Find the smallest possible answer that makes this true. 9. Nine less than twice a number is at most 19. Find the largest possible answer that makes this true. 17. Four more than twice a number is at most 14. Find the largest possible answer that makes this true. 18. Seven less than half a number is at most. Find the largest possible answer that makes this true. 10. Amanda opens a bank account with dollars and saves $5 dollars a week. Her brother gets 100 dollars for his birthday, but spends 6 dollars a week. How many weeks until they have the same amount of money and how much will that be? 19. One wrestler weighed 106 pounds at the start of the season and had to gain pounds a week. Another wrestler weighed 160 pounds and had lose 4 pounds a week. How many weeks until the wrestlers weigh the same and what will that weight be? 0. A plane flying at an altitude of 400 feet starts to descend at a rate of 50 feet per second. A second plan starts at an altitude of 700 feet and starts to ascend at a rate of 15 feet per second. How many seconds until the planes are flying at the same altitude and what altitude will that be? 1

23 Algebra I End of Course Review 11. Adult tickets to a play are $1, student tickets are only $8. If a theater sells 90 tickets to a play for a total of $980, how many of each kind of ticket did the theater sell? 1. Lisa is selling candles and soap for a fundraiser. She sells a total of 4 items for a total of $11. If the candles sold for $4 each and the soap sold for $5 each, how many of each did she sell?. Gizmos cost $ to ship and widgets cost $ to ship. If a company is shipping 50 gizmos and widgets for $1, how many are gizmos and how many are widgets? 1. Jessica had 15 coins in her piggy bank, all dimes and quarters. If they totaled $.60, how many were dimes and how many were quarters?. Dylan looked in the couch for loose change. He found nickels and quarters totaling $4.0. How many were nickels and how many were quarters? 4. The tooth fairy left little Jenny 1 coins, all nickels and dimes totaling.95. How many coins were nickels and how many were dimes? *For the net two problems use: h = 16t + vt + c 1. If a ball is kicked up at a velocity of miles per second from a height of 4 feet, how many seconds until the ball reaches maimum height and what will that height be? *For the net four problems use: h = 16t + vt + c 5. If a cannonball is fired at a velocity of 160 miles per second from a height of feet, how many seconds until the ball reaches maimum height and what will that height be? 6. If a rocket is launched at a velocity of 96 miles per second from a 10 foot platform, how many seconds until the rocket reaches maimum height and what will that height be?

24 Algebra I End of Course Review 14. If an egg is thrown up and off the roof of a 100 foot building with an initial upward velocity of 10 feet per second, how long until it hits the ground? 7. If a model rocket is launched from a 0 foot high platform at an initial upward velocity of 0 feet per second, how long until it crashes back to earth? 8. If a cannon ball is fired from a 40 foot cliff at an initial upward velocity of 0 feet per second, how long until it falls into the ocean? 15. A clerk mied $ a pound almonds with $5 a pound cashews to make 10 pounds of a miture worth $4.50 a pound. How many pounds of each nut did he use? 8. A scientist mied some 10% acid solution with some 40% acid solution to make 600ml of 0% acid solution. How much of each did she use? 0. *Challenge: If 4 gallons of 10% salt solution is added to 6 gallons of 0% salt solution what percent salt will the miture be? 16. If Jasmine can wash the car in 0 minutes and Amanda can wash the car in 0 minutes. How long will it take them working together? 1. If Michael can load a truck in 10 hours and Daniel can load the truck in 8 hours. How long will it take them working together? 4. If Jesse can paint a house in seven hours and Billy can paint the house in nine hours. How long will it take them working together?

25 Algebra I End of Course Review 17. Plane A leaves the airport traveling at 540 mph. Plane B follows hours later at 60 mph. How long will Plane A have been flying when Plane B catches up?. Train A leaves the station traveling at 10 mph. Train B follows hours later at 150 mph. How long will Train A have traveled when Train B catches up? 4. A sailboat leaves port traveling at 0 mph. A jet boat follows 4 hours later traveling at 100 mph. How long does it take the jet boat to catch up? 18. A plane flies from LA to Denver at an average speed of 40 mph. It returns to LA at an average speed of 60 mph. If the entire trip took 5 hours how long did it take to fly to Denver? 5. Joey takes a train from San Diego to Sacramento and travels at 10 mph. She take a car home and travels at an average of 80 miles per hour. If the entire trip took 10 hours, how long did it take him to drive home? 6. Lisa leaves her campsite in her motorboat and travels up river at only 0 mph. Then she returns downstream at 50 mph. If the entire trip took 8 hours, how long did it take her to go up river? 19. Plane A leaves the airport going West at 80 mph. At the same time, Plane B leaves the airport going East at 60 mph. How long until the planes are 1600 miles apart? 7. Train A leaves the station going North at 10 mph. An hour later, Train B leaves the station going South at 100 miles an hour. How long until the trains are 1000 miles apart? 8. A motor boat leaves the city of Luor going up the Nile at 5 miles an hour. Three hours later, a jet boat leaves Luor going down river at 80 miles an hour. How long until the boats are 910 miles apart? 4

MATH 110: FINAL EXAM REVIEW

MATH 110: FINAL EXAM REVIEW MATH 0: FINAL EXAM REVIEW Can you solve linear equations algebraically and check your answer on a graphing calculator? (.) () y y= y + = 7 + 8 ( ) ( ) ( ) ( ) y+ 7 7 y = 9 (d) ( ) ( ) 6 = + + Can you set