Name of Math lover: m favorite student Math 60: ELEMENTARY ALGEBRA Xtra Practice for the Last Eam Question : What s going to be on the final eam? Answer : Material from Chapter 1 to Chapter 9. Date: To better prepare for Chapter 1 Chapter 6: Use our midterm eams to prepare for the material from Chapter 1 Chapter 6. Problems ver similar to the ones on the midterms ma be reccled on the final eam. If a mathematical topic from these chapters did not appear on the midterm, then that tpe of problem will not appear on the final eam. To better prepare for Chapter 7 Chapter 9: Use our homework, lecture notes, and quizzes from these chapters as a stud guide for the final eam. Wait! I almost forgot... 1. You are epected to bring a pencil, an eraser, and a pencil sharpener (if ou need one). A scientific calculator is recommended NO GRAPHING CALCULATORS ALLOWED. Have these instruments read at the beginning of class as ou WILL NOT be allowed to take them out from our purse and/or backpack during the eam.. Sharing of instruments WILL NOT be allowed once the eams have been distributed. (Note: If ou are done with the eam, ou still cannot share an instruments) 3. Cell phones are not allowed on our desks during the eam a cell phone IS NOT a calculator ou know what a calculator is Part I: No Calculators Allowed The eam will be given in parts. Part I: No Calculator. Part II: Ok to use a non-graphing calculator Note: Some equations will be on the non-calculator part. Simplif. Add, subtract, or multipl. 1. ( )(5 5 3 ). ( 3 ) 3. 3. 8 3 7 3 Simplif. 5. ( + 7)( 7) 6. 8 5 8. 50 + 8 00 + 7 3 9. 6a 6 96a + 150a 10. 6z 5 z 6 3 5 11. 3 1 3 5 7. 3 7 + 8 50 6 98 Please note: At an point during the eam, if ou... (1) talk to another student, () use our cell phone, or (3) use a graphing calculator, then... You will be accused of cheating and will receive a ZERO on the eam No Eceptions! The last Xtra Practice guide, M60 pg 1 Fall 016
Part II: Ok to Use a Calculator Don t forget to show enough work in order to receive credit Solve, then graph the solution on a number line. 1. + < 3 + 6. (3 + ) 5 + 7 3. 3(1 3) < 7 ( + 3) You MUST use a ruler or some other straight edge when graphing our lines. You ma not use a sheet of paper as a straight edge.. Graph the solution set: 6 5. Find the slope of a line that passes through the points (, 1) and (, 3). 6. Find the equation of a line that passes through (, 3) with a slope of slope-intercept form. 1. Write the equation in 7. Find the equation of a line that passes through the points (, 7) and (, 1). Write the equation in slope-intercept form. The last Xtra Practice guide, M60 pg Fall 016
8. Solve the sstem b graphing. + = 3 = 6 9. Solve the sstem b elimination. 3 = + 3 = 0 10. Solve the sstem b substitution. 3 = 8 + = 3 Solve the sstem of linear equations. Feel free to use the method of our choice. 11. 3 = 15 + 7 = 1+ 1 1. 13. 3 + = 10 10 = + 10= + 38 3 = 16 Simplif: Add, subtract, or multipl. 1. ( + 1)(3 8) 15. ( 10) ( + 3 ) 16. Subtract ( + 8 7) from (5 3 6 + 7) 17. (3 + )( 1) Divide. 18. ( 3 0 + ) ( ) 19. + 3 + 5 + 3 + 1 3 Factor completel. 0. 3 + 5 1. 3 3 + 15 + 18. 3 3 3. + 3 6. 6 5. 6 6. 36 + 8 + 9 7. 9 8 + 36 Look! These are not equations, sooooooooooooooooo... don t tr to solve them! Just go ahead and factor the polnomials Perform the indicated operations 8. m m 6 m 5m 3 m 3m m + 11m+ 1 30. + 9. 8 + + The last Xtra Practice guide, M60 pg 3 Fall 016
Perform the indicated operations. 3 31. 3 33. + + 1 1 7 15 3 13 10 3. 1 + + 3+ 3 6+ 5 3. + ( + ) Form an equation(s) and solve it to answer the remaining problems. Please write our answer in a complete sentence. Don t forget, whenever ou introduce a variable, ou must clearl define it, beginning with a Let statement, e.g. Let = or a where statement, e.g. where = A big warning for the application problems... Since ou are to form an equation and solve it to answer the word problems, then our answer has to come from the equation ou formed and solved. Use Let or where statements to clearl define what the variable(s) represent. e.g. Let a = adults This is a poor wa to define the variable. The reader does not have enough information to understand what a represents. However, Let a = the number of adult tickets sold Now this is much more like it! B clearl defining the variable, the reader has a clear idea (pardon the redundanc) of what this variable represents. 35. A group of 36 girl scouts went to Disneland. The adult tickets cost $0 and the children s cost $10. If the amusement park collected $0 from the group, then how man of them were adults? How man of them were children? 36. A coin purse contains 18 coins in nickels and dimes. The coins have a total value of $1.15. Find the number of nickels and dimes in the coin purse. 37. The sum of four consecutive even integers is 8. Find the numbers 38. The sum of three consecutive odd integers is 5. Find the numbers 39. The sum of three consecutive integers is. Find the numbers 0. The product of two positive integers is 7. Find the integers if the largest integer is 3 less than four times the smallest integer. 1. The product of two consecutive odd integers is 15. What are the integers?. The product of two positive consecutive even integers is one hundred sit-eight. What are the integers? 3. Two planes leave an airport at the same time. One plane flies north at 500 mph, and the other plane flies south at 650 mph. In how man hours will the be 05 miles apart?. Two trains, which are 600 miles apart, leave their stations at the same time traveling towards each other. Train A s speed is 0 mph slower than train B s speed. If the meet in 5 hours, what is Train A s speed? 5. The area of a rectangle is 16 square inches (16 in ). The length is times the width. What are the dimensions of the rectangle? 6. The length of a rectangle is 3 feet less than twice the width. The area of the rectangle is 0 square feet (0 ft ). What are the dimensions of the rectangle? The last Xtra Practice guide, M60 pg Fall 016
Math 60 answer ke: the last eam If ou believe that there is a mistake in the ke, then please let me know ASAP. But before ou e-mail me, first check the Math 60 page to see if I have updated an technical difficulties with the ke. Warning!!! Don t forget to bring our test-taking supplies, e.g. non-graphing scientific calculator, pencil, eraser, straight-edge, and pencil sharpener (if ou need one). Please DO NOT ASK our instructor for test-taking supplies. Tip: Check to see if these supplies are in our purse/backpack the night before our eam. 1.. Part I: No Calculators Allowed!!! 10 3 16 6 8 8 3. 9 6 7. 0 18 + 0 8. 18 0 + 80 + 8 18 6. 7 5. 5 Question: Did ou take the multiplication shortcut? Conjugates! So product is a difference of squares. 6. 10 5 9. 3 6a 10. 11. 6a 6a + 0 6a z 5 3+ 9 5 30z Part II: Ok to Use a Calculator 1. >. Remember: An open circle is used when the endpoint is not included. Remember: A closed circle is used when the endpoint is included. 3. > 5 Warning!!! Don t forget to reverse the direction of an inequalit smbol when multipling or dividing both sides of the inequalit b a negative number. 5 Remember: An open circle is used when the endpoint is not included. The last Xtra Practice guide, M60 pg 5 Fall 016
. m beautiful writing or Hints: 3; m =, b = 3 The solution contains all the points on the boundar line (i.e. solid line) The other points that are also solutions are located in the half-plane above the boundar line (i.e. shade above) 5. m = 6. 1 = 1 7. = + 5 First find the slope of the line, and then find the equation of the line. 8. (1, 3) graph each line and see where the meet (intersect) 9. (, ) 10. (, 1) 11. (5, 0) 1. (3, ) 13. (, ) 1. 6 13 8 15. 3 8 Did ou subtract the polnomials? (This is not a multiplication problem) 16. 5 3 8 + 1 17. 6 3 + 5 + 18. + 6+ 1 + 19. + + 3 0. (3 1)( + ) 1. 3( + )( + 3). ( + )( ) 3. ( )( + 3). ( + 8)( 8) 5. (8 + )(8 ) Other acceptable answer: ( + 8)( 8) 6. (6 + 7) 7. (7 6) 8. m m + 3 9. 30. 31. ( + )( ) ( )( + ) ( ) ( + )( + ) ; ( ) ( )( ) + 6 ( + 3) Hint #1: LCD = ( - 3) 3 ( 3) Hint #: ( 3) The last Xtra Practice guide, M60 pg 6 Fall 016
3. 5 ( + )( 3) Hint #1: LCD = ( + )( + 1)( 3) 3 + ( + ) Hint #: ( + )( + 1)( 3) 5 + 5 = ( + )( + 1)( 3) 5( + 1) = ( + )( + 1)( 3) 35. 6 adults, 30 children There were 6 adults and 30 children in the group. Let a = the number of adult tickets purchased and c = the number of child tickets purchased Sstem: a + c = 36 0a + 10c = 0 Alternative Let a = the number of adult tickets purchased Equation: 0a + 10(36 a) = 0 37., 6, 8, 10 + ( + ) + ( + ) = 8 The numbers are, 6, 8, and 10. 38. 13, 15, 17 + ( + ) + ( + ) = 5 The numbers are 13, 15, 17 33. 3. 3 3 ( 3)( + 5) 1 ( 1) (3 )( + 5) + + 10 9 10 ( + ) ( ) Hint #1: LCD = ( + ) ( ) (6+ 5)( + ) + ( ) Hint #: ( + ) ( ) 36. 13 nickels, 5 dimes There are 13 nickels and 5 dimes in the coin purse. Let N = the number nickels and D = the number of dimes Sstem: N + D = 18 5N + 10D = 115 Alternative Let n = the number of nickels Equation: 5n + 10(18 n) = 115 39. 13, 1, 15 + ( + 1) + ( + ) = The numbers are 13, 1, 15 0. 3 and 9 Let = a positive integer Epressions for the two integers: 3 product = 7, so... ( 3) = 7 = 3, 9 Note: Ignore the = 9 because it is not a positive integer. Sample sentence: The integers are 3 and 9. The last Xtra Practice guide, M60 pg 7 Fall 016
1. 3 and 5, or 5 and 3 Let = an odd integer Epressions for the consecutive odd integers: + product = 15, so... ( + ) = 15 = 5, 3 Sample sentence: The integers are 3 and 5, or 5 and 3.. 1 and 1 Let = a positive even integer Epressions for the consecutive even integers: + product = 168, so... ( + ) = 168 = 1, 1 Note: Ignore the = 1 because it is not a positive even integer. Sample sentence: The integers are 1 and 1. 3. 3.5 hours In 3.5 hours, the planes will be 05 miles apart. Tip: Create a table Let = the time it will take for the planes to be 05 miles apart (hours) Equation: 500 + 650 = 05. 50 mph Train A s speed is 50 mph. Tip: Create a table Let B = train B s speed (mph) Equation: 5(B 0) + 5B = 600 5. width = inches, length = 8 inches The dimensions of the rectangle are inches b 8 inches. 6. width = feet, length = 5 feet The dimensions of the rectangle are feet b 5 feet. P.S. Good luck to all!!! The last Xtra Practice guide, M60 pg 8 Fall 016