Los Angeles Mission College

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1 Los Angeles Mission College Math : Elementar Algebra Common Final Practice Set This practice set is a compilation of 0 questions that are similar in content to those on the common final. Since the content is similar, it is important for ou to work out and understand the concept of each problem given in this practice set. The actual common final eam given at the end of the semester will consist of two parts: Part I: 0 multiple-choice questions. Part II: to free response questions. It is recommended that ou spend approimatel hour and minutes on the multiplechoice section and about minutes on the free response part. Work must be shown in a clear and logical manner for both Part I and Part II. On the multiplechoice part, credit will be given based on the correct answers onl. On the free response part, partial credit will be given based on the clarit and logic of each step. You will be allowed to use a scientific calculator, but not a graphing calculator, computer, or cell phone. Backpacks are not allowed in the eamination room either. Finall, in order to be admitted to the common final eam ou need to arrive minutes before the eam begins and show a picture ID. Bring a couple of sharpened # pencils, a good eraser, and a scientific calculator. Scantrons and scratch paper will be provided.

2 I. Solving First Degree Equations or Inequalities. Solve: ( t + ) = ( t ) t = b) t = t = t = t = 8. Solve: ( n ) ( n ) 0 + = 8 n = 88 b) n = n = 8 n = n =. Solve: n n + = 8 n = b) n = 7 n = n = 8 n = 8. Solve: 7 8 < 8. Write the answer in interval notation., b) (, ), (, ) (, ). Graph the solution to: + 8. Write the answer in interval notation. [, ) b), 7 (,], 7 (,0] [ [ ] ] ] Math Practice Final Eam Page //008

3 . Graph the solution to: ( ) 8( ) < +. Write the answer in interval notation. ( 7, ) b) (,7) (, ) (, ) (, ) ( ) ) ( ( Solve:. Write the answer in interval notation. 0, b),, 0, [, ) II. Polnomials and Eponents 7 8. Multipl: ( ) + + b) +. Multipl: ( + )( 7) b) Math Practice Final Eam Page //008

4 0. Simplif: + 8 b) Divide: ( 7 ) ( ) b) Divide: ( + + ) ( ) + + ( )( ) b) Evaluate: ( ) 0 b). Evaluate: b) Math Practice Final Eam Page //008

5 . Simplif: ( ) ( ) 7 b) Simplif: ( ) (Epress the answer using a positive eponent) b) Simplif: 7 7 b) (Epress the answer using a positive eponent) III. Factoring 8. Factor completel: ab + a + bc + c a ( b + ) + c( b + ) b) ( a + )( b + ( a + ) ( a + b( a + + ( a + ( a + ( b + ). Factor completel: a + a ( ) a ( + ) b) ( )( ( ) ( a ) ( ( )( + ) ( ) a ( ) Math Practice Final Eam Page //008

6 0. Factor completel: 8 + ( 7 ) b) ( 8 ) + ( 7 ) + ( 7 + ) ( + ). Factor completel: ( 7 + 8)( 7 8) b) ( + )( ) ( + )( ) 7 8 Non-factorable ( ). Factor completel: a + ab b ( a b)( a + b) b) ( a + b )( a b) ( a + b)( a b) ( a + b)( a b) ( a b)( a b). Factor completel: + ( + )( + ) b) ( )( ) ( 8 )( + ) ( )( 8 ) ( )( ). Factor completel: 0 + ( )( ) b) ( )( + ) ( + )( ) ( )( + ) ( )( ) Math Practice Final Eam Page //008

7 . Factor completel: ( )( ) + b) ( ) ( + ) ( + )( + )( ) ( )( + )( + )( + ) ( + )( + )( + ) IV. Simplifing Algebraic Fractions. Simplif: b) Simplif: n n + 7n n + n n + n + n n ( )( ) b) n n n ( n + 7n ) ( n ) n + n n + n + ( n + ) + n 8. Simplif: + + ( + )( + ) ( + ) ( ) b) ( )( ) + ( + ). Simplif: ( a 7 )( a + ) a a a a a a + a a a + a ( + ) b) 7 a a 7 a 7 a Math Practice Final Eam Page //008

8 0. Simplif: b). Simplif: + ( + )( + ) b) ( )( + ) + ( + )( ) ( + ) +. Simplif: b) ( )( ) ( ) ( ) 7 ( + ). Simplif: + b) + + ( )( ) ( ) Math Practice Final Eam Page 7 //008

9 . Simplif: ( + )( + ) b) ( ) ( + )( + ) ( + ) ( + ) ( + ). Simplif: ( + )( + )( ) b) ( + )( + )( ) 0 ( + )( + )( ) 0 0 ( + )( + )( ) ( + )( + )( )( ). Simplif: b) Simplif: 7 ( 0) b) Math Practice Final Eam Page 8 //008

10 8. What is the restriction on in the following epression? b) 0 + (Do not solve the equation),. What values of will make ( )( + ) undefined? {, } b),, {, } {, } 0. Evaluate: for = and = 7 b). Evaluate: for = and = 7 b) 7. Evaluate: + for = and = 78 b) 8 78 Math Practice Final Eam Page //008

11 V. Roots and Radicals. Simplif: b) 0 0. Simplif: b). Simplif: 7 b) Simplif: 0 b) Simplif: ( )( + ) 7 7 b) Math Practice Final Eam Page 0 //008

12 8. Simplif: ( + )( ) + b) Simplif: 0 b) Simplif: 8 b) 8. Simplif: + b) + + Math Practice Final Eam Page //008

13 . Simplif: + 0 b) VI. Solving Second Degree Equations, Rational Equations, and Radical Equations. Solve: { } n = n 8 b) {, } {, } {, } { 0, 8 }. Solve: 7 = + {, } b) { } {, } {, } t. Solve: + = t + t { } b) {,} { } { } 0 Math Practice Final Eam Page //008

14 . Solve: + = 0 { ± } b) { ± 0} { ± } { } ± { 7, } 7. Solve: n + = n ± b) ± { } ± 8. Solve and check: n = { } b) { } { } { } ±. Solve and check: 8 = { } b) No Solution { ± } { } ± { } Math Practice Final Eam Page //008

15 VII. Graphing Linear Functions 0. Graph = b) Graph < b) Math Practice Final Eam Page //008

16 . Graph + b). Graph + = 0 b) Math Practice Final Eam Page //008

17 . Graph b). Graph = 0 b) Math Practice Final Eam Page //008

18 . Graph = b) Graph + = b) Math Practice Final Eam Page 7 //008

19 8. Graph: = b) VIII. Slope and Equation of a Line. Find the slope between (, ) and (, 8). b) 70. Find the slope of the line determined b (, ) and (, ) Undefined b) 0 Math Practice Final Eam Page 8 //008

20 7. Write the equation of the line that has a slope of and contains the point (, ). Epress the equation in the form A + B = C, where A, B, and C are integers. + = 0 b) = = = = 0 7. Write the equation of the line that goes through(, ) and (, 0 ). Epress the equation in the form A + B = C, where A, B, and C are integers. = 8 b) = 7 = = = 7. Find the equation of the line that contains the point (, 8) and has a slope of. Epress the equation in the form A + B = C, where A, B, and C are integers. + = 8 b) + = 0 + = 8 = 8 + = 7. Find the equation of the line that contains the points(, ) and (, 7). Epress the equation in the form A + B = C, where A, B, and C are integers. = b) 7 = = = + = Math Practice Final Eam Page //008

21 7. Determine the slope and -intercept of =. m =, - intercept = b) m =, - intercept = m =, - intercept = m =, - intercept = m =, - intercept = 7. Determine the slope and -intercept of + 7 = 0. m =, - intercept = 0 b) m =, - intercept = 0 7 m =, - intercept = m = 0, - intercept = 7 7 m =, - intercept = 0 7 IX. Sstems of Equations 77. Solve for : + = 7 = b) Solve for : + = 7 + = 8 b) Math Practice Final Eam Page 0 //008

22 7. Solve : + = + = (, ) b) Infinitel man solutions. No solution. (, ) (, 7) 80. Solve for : = = No solution. b) 0 Infinitel man solutions. X. Word Problems 8. One more than five times a certain number is equal to less than nine times the number. What is the number? 8. Find two consecutive whole numbers such that the smaller number subtracted from five times the larger number equals The sum of two numbers is 7. If twice the smaller number is more than the larger number, find the numbers. Math Practice Final Eam Page //008

23 8. How man liters of a 0% salt solution must be mied with liters of a 0% salt solution to obtain 0% salt solution? 8. How man liters of pure alcohol must be added to 0 liters of a 0% solution to obtain a 0% solution? 8. A woman invests a total of $000. Part of it is invested at 0% and the remainder at %. Her total earl interest from the two investments is $0. How much did she invest at each rate? 87. Suppose that Lou invested a certain amount of mone at % interest and $0 more than that amount at 0%. His total earl interest was $0. How much did he invest at each rate? 88. Kirk starts jogging at miles per hour. One-half hour later, Nanc starts jogging on the same route at 7 miles per hour. How long will it take Nanc to catch Kirk? Math Practice Final Eam Page //008

24 8. Suppose that Celia rides her biccle 0 miles in hours less time than it takes Tom to ride his biccle 8 miles. If Celia rides miles per hour faster than Tom, find their respective rates. 0. The length of a rectangle is inches less than twice its width. If the area of the rectangle is square inches, find the length of the rectangle.. The sum of the areas of two circles is 80π square centimeters. Find the length of the radius of each circle if one of them is twice as long as the other.. Cind has coins consisting of nickels and dimes. The total value of the coins is $.0. How man coins of each kind does she have?. Three cans of prune juice and cans of tomato juice cost $.8. On the other hand, cans of prune juice and cans of tomato juice cost $.. Find the cost per can of each. Math Practice Final Eam Page //008

25 . Each of three consecutive even whole numbers is squared. The three results are added and the sum is. Find the numbers.. Bett bought 0 stamps for $.. Some of them were $.00 stamps and the rest were -cent stamps. How man of each kind did she bu? XI. Formulas and Functions. What is the restriction on b) + f ( ) =?, 0 7. Solve for b: A = bh A b = b) b = Ah h A b = h h b = A b = h A 8. Solve for L: P = L + W P + W L = b) W P L = P + W L = P W L = W L = Math Practice Final Eam Page //008

26 C + 0. Solve for C: F = F + 0 C = b) F C = F 0 C = F C = F C = Solve for : = = b) = 7 = + 7 = = 0 0. If f ( ) =, find f ( ). 0 b) If f ( ) = ; find f (). b) Math Practice Final Eam Page //008

27 Common Final Practice Set Answer Sheet. ( t =. (b) n =. ( n = 8. ( (, ). ( (,]. ( (, ) 7. (b), 8. (. (b) 0. (. (. (. (b). ( 7. (. (b) ( 8. ( ( a + ( b + ). (b) ( )( 0. ( (7 + ). ( (7 + 8 )(7 8 ). ( ( a + b)( a b). ( ( )(8 ). ( ( )( ). (. ( 7. (b) 8. (. ( ( + )( + )( ) ( n )( n ) n + a 7 a 0. (b). (. (. ( + 7. (b) ( ). ( ( + )( + )( ) 7. b) 7 8. (. ( {, } 0. (. (b). ( 78. (. (. (b). ( 7 7. ( 7 7

28 8. ( +. (. (b) 0 0. (. ( +. (b). ( {0,8}. (. (. ( {}. ( {-± } 7. ( ± 8. ( {}. ( {}. ( 0. (b) ( Math Practice Final Eam Page //008

29 . (. ( 70. ( Undefined 7. ( = 7. ( = 7. (b) + = ( = ( m =, -intercept =. ( - 7. (b) m = 77. (, -intercept = ( 7. ( No solution ( Infinitel man solutions The number is. 8., 8., 7. (b) 8. 0 liters 8. 0 liters 8. $,000 at 0% and $,000 at % $00 at % and $0 at 0% 88. ¼ hr. 8. Tom: 7 mph; Celia: 0 mph 0. Length = in -. Radius of small circle = cm. Radius of large circle = 8 cm. 8. (. 8 nickels and dimes. Prune juice: $0.8 per can. Tomato juice: $0. per can..,,. $.00 stamps and 8 $0. stamps - -. ( ( A b = h 8. ( L = P W Math Practice Final Eam Page //008

30 . (b) 00. ( F 0 C = 7 = 0. ( 0. ( Math Practice Final Eam Page //008

Math 0308 Final Exam Review(answers) Solve the given equations. 1. 3x 14 8x 1

Math 0308 Final Exam Review(answers) Solve the given equations. 1. 3x 14 8x 1 Math 8 Final Eam Review(answers) Solve the given equations.. 8.. 9.. 9 9 8 8.. 8 8 all real numbers 8. 9. all real numbers no solution 8 8 9 9 9 Solve the following inequalities. Graph our solution on