Math 026 Review Exercises for the Final Exam

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1 Math 06 Review Eercises for the Final Eam The following are review eercises for the Math 06 final eam. These eercises are provided for you to practice or test yourself for readiness for the final eam. There are many more problems appearing here than would be on the final. These eercises represent many of the types of problems you would be epected to solve on the final, but are not meant to represent all possible types of problems that could appear on the final eam. Note for the final eam you must show all your work in order to receive full credit. Scientific calculators are permitted: graphing calculators or calculators with QWERTY keyboards are NOT permitted. Word problems must be done using algebraic methods to receive full credit.. Solve the following equations: ( ) = [ ( )] ( ) = [ (7 )] = 9 d) 8 = 6 e) = 7 f) =. Solve the following inequalities and graph the solution on the real number line. ( ) < ( ) ( ) 7 < d) 6 e) >. Cathy makes two different types of candy: truffles and jellybeans. She charges $9 a bo for the truffles and $6 a bo for the jellybeans. If she decides to make 8 boes of candy one day, what is the minimum number of boes of truffles she should make if she is to gross at least $6? [Only algebraic solutions will receive credit.] - -

2 . Jake can complete a job in hours while Jerry can complete the same job in hours. How long would it take to complete the job if both Jerry and Jake worked together? How long would it take to complete the job if Jake starts the job two hours before Jerry joins him?. How long will it take someone running at mph to catch up to someone walking at mph with an hour and a half head start? 6. Given f ( ) =, g( ) =, and h( ) = f ( ), f ( ), g(), g( ), h(), h(), find f ( ), g( h), h( ) 7. Use the graph of y = f() below to answer the following questions: a ) Find f(-). Find such that f() = 0. What is the domain of this function? d) Which is larger: f(-) or f()? e) What is f() f(-)? - -

3 8. If f ( ) = and g( ) = 6 9, find and simplify f ( ) g( ). 9. If f ( ) = f ( h) f ( ) h g ( h) g( ) h and g( ) =, find and simplify: 0. Find the equation of the following lines: epress your answer in slope-intercept form. The line passing through (-,) and (,9). The equation of the line that passes through the point (-,) and is parallel to the line y =. The equation of the line that passes through the point (-,) and is perpendicular to the line y = d) The equation of the line with -intercept and y-intercept.. When soft drinks sold for $0.80 per can at football games, approimately 600 cans were sold. When the price was raised to $.00 a can, the demand dropped to 000. Assume that the relationship between the price p and the demand y is linear. Write a linear function giving the demand y as a function of p. Use this function to estimate the number of cans sold if the price is raised to $.0.. Solve the following systems: 6 y = y = 7 y = 8 y = 0 9 6y = 6 y = - -

4 . Sketch a graph of the following inequalities: 7y < y 0. Factor the following completely (if possible): y 0y ()7() d) (a 6 e). Perform the following long division: ( ) ( ) 7 6. Solve for by factoring: 6 9 = 0 ( ) = 0 ( )( ) = ( )( ) - -

5 Perform the operations and epress your answer in simplest form Epress the following as a fraction in simplest form: 6 6 n m m n 9. Solve for : 0 = 7 =

6 0. Solve eplicitly for : y = a by y = 7. Perform the operations and simplify the following. Epress your answers with positive eponents only. ( y )( y ) ( a b ) (6a b ). Perform the operations and simplify the following. Epress your answers with positive eponents only. ( a ( y ) 6 y b )(a b 6 ). Evaluate the following: / 7 ( ) /. Perform the operations and simplify the following. Epress your answers with positive eponents only. 6 / (8a b ) (a b / ) ( / / y y 8 y 6 6 y / ) / - 6 -

7 . Convert the following into scientific notation and then perform the computations. Show all work to get full credit. Epress your answer using scientific notation. (,00,000)(0.000) The speed of light is approimately.86 0 miles per second. If the planet Pluto 9 is.67 0 miles from the sun, how long does it take light from the sun to reach Pluto? Epress your answer using scientific notation. 7. Write the following in simplest radical form: Write the following in simplest radical form: y Solve the following for. = = / ( ) = d) = - 7 -

8 0. Perform the operations and epress the following in a bi form. ( i )( i) i i. Show that i is a solution to =.. Solve the following equations: epress your answer in simplest form. = ( )( ) = = d) = 8. Sketch a graph the following functions: Identify the -intercept(s), y-intercept, ais of symmetry, and verte. f ( ) = 6 8 g ( ) = 0 6. Find the length of a diagonal of a square with side 6.. Ale throws a ball straight up into the air. The equation s = s(t) = 6t 80t gives the distance s (in feet) the ball is above the ground t seconds after he throws it. How high is the ball two seconds after he throws it? What is the maimum height of the ball from the ground? At what time does the ball hit the ground? - 8 -

9 6. A company determines that the profit, P(), earned on the sale of items is given by the formula P ( ) = 0 Determine the number of items sold if the company loses $,00. How many items must be sold for the maimum profit? What is the maimum profit? 7. Solve the following inequalities and sketch your solution set on the number line below. Show your analysis < 0 d) < 6 8. Find the domain of the following functions. f ( ) = g( ) = h( ) = 6 9. Given the point (,7) and the point (-, ): Find the distance between the two points. Find the midpoint between the two points. 0. Find the center and the radius of the following: 6 y 0y =. Find the equation of the circle satisfying the following conditions: The circle has center (-,) and radius 6. The circle has center (,7) and is tangent to the -ais. The circle has diameter with endpoints (-,) and (, -)

10 ANSWERS: MATH 06 FINAL EXAM REVIEW EXERCISES. f) 8 = No Solution =, d) No Solution e) = 6, =,. At least 6 boes of truffles.. hrs. from the time Jerry starts) hrs. 8 hours from the time Jake starts (or 8 hrs. 6. f ( ) = 6, f ( ) = 6, g ( ) is undefined, g(- ) = /, h( ) =, h( ) is not a real number ( is not in the domain of h(). h f ( ) =, g( h) =, h( ) = h 7. =, 7 8 d) f () e) h 0. y = y = ( h )( ) y = d) y =. y = 00 p =, y = (,) inconsistent - 0 -

. Not factorable y ( y)( y) ( 7)( ) d) ( a b 8)( a b 8) e) ( ) ( ). 7 R 9 R 8 6. =, =, = 9, 7. 8. 0 ( )( )( ) mn ( n m) 9. 0 = = 0. 6 by y = a 7y = y. 8 y 8 b 6 a b 8 y. 8 9 a. 8. y / ab y /.

11 . Not factorable y ( y)( y) ( 7)( ) d) ( a b 8)( a b 8) e) ( ) ( ). 7 R 9 R 8 6. =, =, = 9, ( )( )( ) mn ( n m) 9. 0 = = 0. 6 by y = a 7y = y. 8 y 8 b 6 a b 8 y. 8 9 a. 8. y / ab y /. 6 (. 0 )( 0 0 ) = seconds or.8 hours y y = 7 ( is etraneous) =, 7 9 = 0 d) = i i 0 0. ( i ) ( i) = i i 8 i = i 8 i =. = ± 6 ± 7 = ± i = d) = ± i - -

12 . 6 inches. 0 feet feet sec items 0 items $00 7. or 7 < < or > d) < 6 or > 8. < 6 9. (, ) 0. C = (, ) : Radius =. ( ) ( y ) = 6 ( ) ( y 7) = 9 ( ) ( y ) = - -

Math 025 Review Exercises for the Final Exam

Math 025 Review Exercises for the Final Exam Math 05 Review Eercises for the Final Eam The following are review eercises for the Math 05 final eam. These eercises are provided for ou to practice or test ourself for readiness for the final eam. There