Math 154A Elementary Algebra Fall 2014 Final Exam Study Guide


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1 Math A Elementar Algebra Fall 0 Final Eam Stud Guide The eam is on Tuesda, December 6 th from 6:00pm 8:0pm. You are allowed a scientific calculator and a " b 6" inde card for notes. On our inde card be sure to write an formulas ou ma need. I will not provide ou with an formulas on the eam. The Final Eam is comprehensive; however, not all of the problems that appeared in the previous eams will appear in the final. Use this stud guide to know which math concepts ou need to review. For the Final Eam, ou will need to be able to:. Classif numbers as rational, irrational, real, etc. Compare absolute values. Simplif epressions with fractions, or b using the order of operations. Evaluate epressions...9. Solve linear equations, including equations with fractions. The solution to these equations can be a unique solution, no solution, or all real numbers. Remember that the correct final answer for these tpes of problems is either = #, all real numbers or no solution.... Solve linear inequalities and graph the solution. The solution to these inequalities can be a unique interval, no solution, or all real numbers..8. Solve an application problem. These include but are not limited to problems involving mone and percents... Solve an application problem involving geometr measurement of the sides of a triangle and the perimeter of a rectangle.. 6. Solve an application problem involving motion, mone, and mitures interest problems, distance, rate, and time problems.. 7. Determine if a solution is a point on the line.. 8. Find the intercept and the intercept of a line given an equation of a line. Write the intercepts as points.. 9. Graph the equation of an line; this includes slanted lines, horizontal lines and vertical lines. Know how to graph b using intercepts. (You don't use intercepts to graph the vertical lines, horizontal lines, or lines that go through the origin.). 0. Find the slope of the line given two points... Given a point and slope, graph the line... Given a graph, find the slope of the line or state that the slope is undefined... Given a graph, determine the equation of the line. The answer must be in slope intercept form... Given an equation, determine the slope and intercept of the line represented b that equation. Then use that information to graph the equation... Write the equation of a line if ou are given a point on the line and the slope of the line OR if ou are given two points on the line. The final answer should be in slopeintercept form.. 6. Solve linear inequalities and graph the solution region.. 7. Solve a sstem of linear equations graphicall. This includes sstems that have one unique solution, no solution, or an infinite number of solutions.. 8. Solve a sstem of linear equations b substitution or addition. You must use the method specified to solve the sstem. The sstem might have one unique solution, no solution or an infinite number of solutions..&. 9. Solve an application problem involving interest, mitures, or distance. You saw these tpes of problems twice. Once ou had to solve using variable (linear equations) and again using variables (sstems of equations). You can solve these problems either wa. However, some problems, like the current problems, are easier solved b the elimination method.. &. 0. Solve a sstem of linear inequalities and shade the solution region..
2 Math A Name Final Eam Review. Consider the following set of numbers.,, 0, 0.,,, a) List the rational numbers. b) List the irrational numbers. c) List the integers. d) List the real numbers.. Insert > or < or = between each pair of integers to make a true statement. a.) 7 9 b.) Graph and label 7, 0, 9, and Add:. Add: Subtract: 7. Divide: Subtract: 9. Divide: 9 6 8
3 0. Simplif: ( ) 6. Evaluate the given epression for = , and =  ( ) Directions: Solve each equation.. ( r ) ( r ). z z 7 7. ( k 6) (k ). ( p 8) ( p ) p 9 6. Solve for d: p d 7. Given the area formula for a trapezoid, find h, when A, b, and b 9 A h( b b ) 8. Given the area formula for finding the perimeter of a rectangle, solve forw. P L W 9. Solve for. m( ) 0. Solve for. ( 6 )
4 . Solve the following inequalit and graph it on the number line.. Solve the following inequalit and graph it on the number line. ( m ) ( m) 0. A Sore Loser lost threefourths as much mone on Saturda as he did on Frida. Throughout both das he lost a total of $60. How much mone did he lose on Frida?. How man liters of % alcohol should ou mi with 0 liters of 60% alcohol to obtain a blend of % alcohol?. The length of a rectangle is cm more than three times its width. What is the length and width, if the perimeter is 7 cm? 6. You and a friend go for a bike ride in the same direction along the same path. You travel at 6 miles per hour while our friend travels at a slower pace. After hours ou are. miles apart. Find the speed of ou and our friend. Rate Time Distance You Your friend
5 7. Sa ou travel miles per hour for 0. hours for the first part of our outing. Then, ou travel for 0. hours for a total a distance traveled of. miles, find our average speed of the second part of our outing. Rate Time Distance First part Second part 8. Sa ou and our friend are 0 miles apart and want to meet up with each other. Both of ou left at the same time, but our friend drives mph slower than ou. You both finall meet up after hours. How fast were ou each going? Rate Time Distance You Your friend 9. A Car Rental Compan A charges $80 per week plus $0. per mile to rent a car. Car Rental Compan B charges $0 per week plus $0.9 per mile to rent a car. a) How man miles would ou have to travel per week for both companies to charge the same? b) If ou plan to drive 00 miles, which compan is cheaper? 0. Find the cost of a shirt, if the total with a 9% ta was $9..
6 . Determine whether the ordered pair, is a solution to the equation.. Find the slope of each line. a. b.. Find the  and intercepts of. intercept = (, ) intercept = (, ). Write an equation of the line with slope, m, and has intercept (0, 7) in slopeintercept form.. Write an equation of the line with slope, m 6, and goes through the point (, ) in slopeintercept form. 6. Write an equation of the line that goes through the points (, ) and (0, 9) in slopeintercept form. 7. Find the equation of the line in slopeintercept form.
7 8. Graph and label points: 9 9. Find the inequalit that describes the shaded region. 0. Graph and shade the solution.. Solve the following linear sstem b graphing: 0
8 . Solve the following linear sstem b graphing:. Solve the following linear sstem b substitution: 8 9. Solve the following linear sstem b elimination: With the current, ou can row 6 miles in hours. Against the same current, ou can onl row miles in hours. Find our rowing rate in still water and the rate of the current. With the current Rate Distance Time Rate=Distance/Time Against the current 6. A coin purse contains a miture of 9 coins in quarters and dimes. The coins have a total value of $7.0. Determine the number of quarters and number of dimes in the coin purse.
9 7. You invested $700 in two accounts paing 8% and 7% annual interest. At the end of the ear, the accounts earn the same interest. How much was invested at each rate? 8. The other da I went to Staples to bu some office supplies. I bought pens and binders, which together cost me $9.7. M friend bought of the same pens and of the same binders, and it cost her $9.00. What is the cost for a single binder and the cost for a single pen? 9. Solve the sstem of linear inequalities and shade the solution Solve the sstem of linear inequalities and shade the solution.
10 . a) Rationals:,,0,0., b) Irrationals:, c) Integers:,0, d) Reals: all of them are real. a.) 7 9 b.) 0.7= or r. z. k. p 0 6. d ( p ) p or d 7. h 8 8. W P P L L or W 9. m or m m m m. He lost $0 on Fri and $0 on Sat.. You should mi liters of % alcohol to get a liter blend of % alcohol.. The width is 8cm and the length is 8cm 6. Your friend travels at. mph. 7. You travel 8 mph the second part. 8. You travel at 6mph and our friend travels at 0 mph. 9. a. You have to travel,000 miles for both companies to charge the same. b. Compan B, which charges $ is cheaper than Compan A, which charges $. 0. The cost of the shirt was $7 before ta.. No, (, ) is not a solution.. a. m 0 b. m undefined. intercept (, 0) intercept (0, ) (, ). Parallel lines, no solution.. (7, ). (9, ). Your rowing rate in still water is 6 mph and the rate of the current is mph. 6. The coin purse has quarters and dimes. 7. There is $,60 invested at 8% and $,80 invested at 7%. 8. The pens cost $.0 each and the binders cost $. each Regions do not overlap, so no solution.
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