Name Final Exam Review

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1 Name Final Exam Review For numbers 1 and, solve the given equation. If the solution set is, classify the equation as an identity or a contradiction. 1.) 10x 7 38x ) 13t 5 t 5 3t 1. P1 V1 P V 3.) Solve for P : 3. T T 1 4.) For the given graph of a function, determine the following: f (1) : Domain : Range : Any x values for which f ( x) :

2 5.) Graph in slope-intercept form: y x 3 slope y-int 6.) Graph: x 3y 6 slope y-int 7.) Evaluate a function: g 1 when g n 3n n 7. 8.) Find slope: given the points 3, 8 and 9, ) What is the slope and y-intercept: 15 y x slope 7 y-int 1 10.) Write an equation of a line in slope-intercept form that is perpendicular to y x 3 and through the point 8,

3 11.) In 199, Political Action Committees (PACs) contributed $178.6 million to congressional candidates. In 00, the figure rose to $8 million. Let A(t) represent the amount of PAC contributions, in millions, and t the number of years since 199. a) Find a linear function that fits the data. b) Use the function of part (a) to predict how the amount of PAC contributions in a. 11b. 1.) Find the domain of the function: f x x 3x For numbers 13,14 and 15, solve the system of equations 13.) x y 3z 5 x y z 1 4x y 3z 0 14.) x y z 3 x z x y z 3

4 15.) x 3y 4z 6 x y 3z 10 5x 10y 15z 8 16.) Chick-fil-A recently sold small lemonades for $1.9, medium lemonades for $1.49, and large lemonades for $1.85. During a lunch-time rush, Chris sold 40 lemonades for a total of $ The number of small and large drinks, combined, was 10 fewer than the number of medium drinks. How many drinks of each size were sold? ) Solve: x ) Solve: 3x 5 x 6 18.

5 For numbers 19, solve and graph, state the solution in interval notation. 19.) a ) x ) 3y ) 3 x ) Factor: a a 6a 3. 4.) Factor: 4 4m

6 5.) Factor: x 7y 5. 6.) Simplify: f x 3x 1 x 7x 6. 7.) Divide and, if possible, simplify: 3 x 64 x x x x 7. 8.) Add: 7x 3 x x 8. 9.) Solve the equation: 1 x x x 4 x x 8 9.

7 30.) Solve the equation: 4 5 x 3 3x ) Divide using long division AND synthetic division: x 5x 8 x 3 3.) The A train goes 1 mph slower than the E train. The A train travels 30 mi in the same time that the E train travels 90 mi. Find the speed of each train. 33.) Perform the following operation: 14 a ) Convert to radical form: xy 1/ ) Combine: 5a 6b 35.

8 36.) Simplify: 4 36a b ) Simplify: x y z ) Add: ) Multiply: ) Multiply: ) Solve the equation: y ) Solve the equation: 3 x 3 4.

9 43.) Perform the following operation: 5 4i 3 i ) Perform the following operation: 9i 3 5i ) Perform the following operation: 3 6 i 1 4i ) Perform the following operation: ) Perform the following operation: a b c ab c ) Solve: h 4 6h ) Solve: x 9 4x 49.

10 50.) Write a quadratic equation having the solutions: 4 & ) Given the function: f x x 3 5 a.) Graph f (x). b.) State the vertex. c.) State the axis of symmetry. d.) State the maximum or minimum. b. c. d. 5.) The current in a typical Mississippi River shipping route flows at a rate of 4 mph. In order for a barge to travel 4 mi upriver and then return in total of 5 hr, approximately how fast must the barge be able to travel in still water? ) Good s Candies of Indiana makes all their chocolates by hand. It takes Anne 10 min to coat a tray of candies in chocolate. It takes Clay 1 min to coat a tray of candies. How long would it take Anne and Clay, working together, to coat the candies? 53.

11 In the following questions, state the domain for the function and write your solution set in interval form. 54.) f ( x) 5x ) f ( x) 5x ) 3 f( x) 7x ) Given the two functions, x gx ( ) and h( x) 3x, x 4 a) Find the domain of g a. b) Find the domain of h b. c) Find the domain of g h c. 58.) The number of workers n needed to set up for homecoming varies inversely as the amount of time t allowed for setup. If it takes 1 workers to do the job when there are 4 hours allowed, how many workers are needed if there are only 3 hours allowed?

12 59.) An office contains two printers. Machine B is known to take 3 minutes longer than Machine A to produce the company s monthly financial report. Using both machines together, it takes 6 minutes to produce the report. How long would it take each machine individually to produce the report?

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14 Final Exam A Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 1 1) x + 3 + 5 x - 3 = 30 (x + 3)(x - 3) 1) A) x -3, 3; B) x -3, 3; {4} C) No restrictions; {3} D)