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Name: _____________________ Section Number: _____ Final Exam b, Math 120, fall 2002 12/05/2005 Answers 1. A 2. D 3. D 4. C 5. A 6. B 7. B 8. A 9. A 10. D 11. approximately 4.1 10 4 12. x = 2 [x = −1 does not check.] 13. (−2, 7) x 10 14. a) 4a 4 11a b) 2 15. 4 2 3 (2 p 3) 2 16. p( p 1) y 12 17. 25x 2 18. x + .04x = 23,992. Gabriel earned $23,o69.23 before his raise. 19. Equations: x y 8000 and .04 x .045 y 350 . Solution (2000, 6000) Roza should invest $2000 at 4% and $6000 at 4.5%. 20. a) (x – 4)(x + 7) b) (3x + 1)(x + 4) 21. The width of the rectangle is 8 feet; its length is 12 feet. 22. b 15 ; b 1 . Both check. 2 23.The maximum height of the ball is 1600 feet. It lands 80 feet from where it was hit. 24. The speed of the boat in still water is 7.5 mph. the speed of the current is 1.5 mph. 25. The value of the car 5 years after purchase is $11,141.12 3 1 26. y x Its graph is a straight line with y-intercept 14 and x-intercept 13 . Other 4 4 points on the line are (4,3 14 ), (8,6 14 )( 4,2 34 ), etc. 27. y ( x 5) 2 15 1 Part I: Questions 1 to 10 (6 points each) 1. The slope of the line joining the two points (2, 3) and (4, 1) is: [A] 2 [B] 1 2 [C] 3 5 [D] 1 2. If f(x) = 3x – 4, then: [A] f(3) = 4 3 [B] f(3) = 1 3 [C] f(3) = –1 [D] f(3) = 5 3. The solution to the equation 3(x + 1) = –4(x – 5) + 6x is: [A] 23 7 [B] 23 [C] 1 3 [D] 17 4. Evaluate log 4 64 [A] 16 [B] 1.806 [C] 3 [D] 4 5. Multiply and simplify: (1 + 3 2 )(3 + 2 2 ) [A] 15 + 11 2 [B] 4 + 5 2 [C] 3 + 6 2 [D] 15 6. Evaluate 8 [A] 5.33 [B] 4 [C] 16 [D] 3 16 2 3 2 7. Which of these graphs best represents the function y = 4 x ? [A] [B] A B [C] y [D] y x x C y D y x x 8. Which of these points does not lie on the line y 2( x 1) 2 3 ? [A] (0, 5) [B] (1, 3) [C] (2,15) [D] (2, 1) 9. The solution of the inequality [A] 3 x 5 [B] 1 x 5 [C] x 1 [D] 1 x 3 1 2x 5 5 is: 10. The vertex of the parabola described by the function y 2( x 4) 2 1 is the point: [A] (8, 1) [B] (4,1) [C] (16,1) [D] (4, 1) Part II: WRITE YOUR ANSWERS ON THE SPACES PROVIDED. Show your work. 3 11. (8 points) Calculate: (5.065 10 7 )(8.17 10 4 ) Write your answer in scientific notation. Answer: _______________ 12. (8 points) Solve for x. Check your solution(s). 3 x x 1 Solution(s):___________________ Checks: 13. (8 points) Find the solution to this system of equations: 3 x 2 y 20 5 x 6 y 32 answer: ________________ 14. (8 points) Write in simplified form (leave no radicals in the denominator): 4 a) 2a 44a 7 answer: ____________ b) 15 x 2 6 answer: _____________ 15. (8 points) Consider the quadratic equation x 2 8 x 4 = 0. a) Write the quadratic formula: _______________________________________ b) Use the formula to find the solutions to the above equation. Leave solutions in simplest radical form. solutions: ___________ 16. (8 points) For the operation 4 p2 9 2 p2 p 3 ÷ p 2p 3 a) factor all the numerators and denominators: answer: ___________________________ b) divide and simplify: answer: _____________________________ 5 (5 x) 3 x 2 17. (8 points) Simplify leaving no negative exponents: 4 2 y ( 5 y ) 2 answer: _______________________ 18. (8 points) After his 4% raise, Gabriel earned $23,992 a year. How much did he earn before his raise? i. Write an equation to find how much he earned before the raise. equation: ________________________ ii. Figure how much he earned before the raise, rounded to the nearest penny. answer: ________________________________________________________________ 6 19. (10 points) Roza has $8,000 to invest. She invests part at 4% and the rest at 4.5%. If she earns $350 in interest after one year, how much did she invest at each rate? i. Complete the table: 4% 4.5% Total rates $ invested Interest earned ii. Figure how much she invested at each rate. answers: ________________________________________________________________ 20. (10 points) Factor the following expressions completely. Check by using FOIL multiplication a) (4 points) x 2 3 x 28 answer: _________________ b) (6 points) 3x 2 13x 4 answer: _________________ 7 21. (8 points) A rectangle is 4 feet longer than it is wide. Its area is 96 square feet. Find the dimensions of the rectangle. answer: _____________________________________________________________ 22. (8 points) Solve for b if possible 2 3 1 . Check your answer(s). b5 b3 b Answer(s):_______________ Checks: 8 23. (10 points) The flight of a golf ball over a level course can be modeled by the function f ( x) x 2 80 x , where f(x) (in feet) represents its height above the ground and x (in feet) is the horizontal distance it travels. a. Make a sketch of what’s happening. b. How high is the golf ball at its maximum height? c. How far away does it land? 24. (10 points) Adriana’s18-kilometer boat trip downriver took two hours, but the return trip back upstream took three hours. Figure the speed of the boat in still water and the speed of the current of the river. answer: ________________________________________________________________ 9 25. (10 points) A Schwartzmobile depreciates according to the formula: V (t ) V0 (.8) t , where V(t) represents the dollar value after t years, and V 0 represents the original value of the automobile. Figure the value of a Schwartzmobile purchased 5 years ago for $34,000. Answer: ________________________________________________________________ 26. (10 points) Write an equation of the line that has a slope of the point (-3, -2). 3 4 and passes through a) Equation: _________________________________ b) Graph the line on these axes. Label three points. 27. (4 points extra) Convert the quadratic equation y x 2 10 x 10 into the form y a ( x h) 2 k 10