Math96FinalExamSpring22

MATH 96 Name: Spring 2022 Final Exam 5/8/22 Time Limit: 2 hours This exam contains 8 pages (including this cover page) and 13 problems. Check to see if any pages are missing. Enter your name and your section above. You may not use textbooks, course notes, cell phone, or calculator during this exam. You are required to show your work on each problem on this exam, and the following rules apply: • Organize your work in a reasonable, neat, and coherent way. Work that is jumbled, disor- ganized, or lacks clear reasoning will receive little credit. • Partial credit may be given. Any answer must be supported by calculations, explanation, and/or algebraic work to receive full credit. Unsupported answers will not receive full credit, but well-argue, incorrect solutions may earn partial credit. • If you require more space, use the back of a page. Clearly indicate when you do this below the problem. Do not write in the table to the right. Page Points Score 2 26 3 22 4 24 5 20 6 20 7 14 8 24 Total: 150

MATH 96 Final Exam - Page 2 of 8 5/8/22 1. (13 points) Simplify each expression as much as possible. (a) (4 points) 3 · ( - 4) - 5 · (9 - 11) - 9 - 3 - 2 (b) (4 points) - 3 a 2 b 3 9 a 4 b - 2 (c) (5 points) √ 2 3 a 14 b 8 c 31 d 22 2. (13 points) Perform the indicated operations. Simplify the expression as much as possible. (a) (4 points) 7 √ 40 - √ 8 + 4 √ 50 (b) (4 points) k k 2 - 9 - 4 k - 3 (c) (5 points) 2 4 √ 3 x · 4 4 √ 27 x 6

MATH 96 Final Exam - Page 4 of 8 5/8/22 4. (6 points) Given the quadratic function f ( x ) = x 2 + 10 x + 8 , answer the following. (a) (4 points) Find a formula for f ( x ) in the form f ( x ) = a ( x - h ) 2 + k by using “completing the square” method. (b) (1 point) Find its vertex ( x, y ). (c) (1 point) Find its axis of symmetry. 5. (18 points) Solve each equation. (a) (6 points) 5 t 2 - t - 2 3 = 5 (b) (6 points) - 3 | x - 5 | = 7 (c) (6 points) 2 t t + 2 - 2 = t - 8 t + 2

MATH 96 Final Exam - Page 5 of 8 5/8/22 6. (6 points) Graph the circle ( x + 3) 2 + ( y - 1) 2 = 16. Write the coordinates of its center, and write its radius. x y - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 1 2 3 4 5 6 7 8 - 6 - 5 - 4 - 3 - 2 - 1 1 2 3 4 5 6 7. (14 points) Solve each inequality and graph its solution set on a number line. Express your answer in interval notation. (a) (4 points) - 2 < - x - 12 (b) (4 points) - 1 < - 2 x + 4 ≤ 5 x x (c) (6 points) w - 2 3 ≤ 4 w

MATH 96 Final Exam - Page 7 of 8 5/8/22 10. (6 points) Find a polynomial expression that represents the area of the figure below. Fully expand your polynomial answer. 2 x + 1 3 x - 4 11. (8 points) Divide (3 y 3 - 7 y 2 - 4 y + 3) ÷ ( y - 3) .

MATH 96 Final Exam - Page 8 of 8 5/8/22 Clearly identify your variables. Solve each problem below by setting up equations algebraically. Then use the equation to solve the problem. You do not need to simplify any numeric fraction. 12. (12 points) Suppose that whole milk with 4% fat is mixed with 1% low fat milk to make a 2% reduced fat milk. How much of the whole milk should be mixed with the low fat milk to make 80 gallons of 2% reduced fat milk? 13. (12 points) A boat travels 80 miles downstream with the current in 4 hours, and 80 miles upstream against the current in 5 hours. Find the speed of the current and the speed of the boat in still water.