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Transcript
Math 107 Final Exam, Fall 2000 Name__________________________________ Legibly show all of your work below each exercise. BO your final answers. 1. Complete the following short answer problems forX2 points each: a) Simplify: x 7 + 2 x h) Write x 2 using only positive exponents. b) Simplify: 4 6 2 3 i) Write 65400000 in scientific notation. c) Reduce to lowest terms. 261 . 900 j) Give the slope and the y-intercept for the 1 graph of the equation y x 6 . 2 slope ______ y-intercept ______ 1 1 1 , d) Find the LCD for , . 6 20 15 e) Simplify: 4 2 x 6 3x 5 f) Find the x-intercept for 2x y = 8. g) Evaluate 4 5x for x 2 . k) Subtract: 1 l) Simplify: 5 21 x5 x3 m) Simplify: x 3 n) Simplify: 5 x5 x 3 [30] 2. Perform the indicated operations. Write final answers in simplified form. 3 4 Add: 28 21 (9 points) 3 4 Multiply: 28 21 Divide: 3 4 28 21 3. Give: (6 pts.) 2 _____ 3 2 The absolute value of _____ 3 2 The reciprocal of _____ 3 The opposite of 4. Find the area and perimeter of this rectangle. Remember to include the units. (4 points) area = ______________________________ 5 cm 13 cm perimeter = __________________________ 13 cm 5. Solve the formula for the variable y: 2 x 3 y 6 (4 pts.) 6. Translate from words to symbols: The sum of twice x and three is eleven. (3 pts.) [26] 7. Simplify the following as much as possible, write all answers with positive exponents only and without decimals: (9 pts.) a) b) 3x y 2 xy 3 2 2 x 15 x 2 x 3 3x7 y7 c) 2 y 2 3 1 8 8. Find the slope of the line connecting 2, 6 and 1, 4 9. Given the point (2,4), and slope 1 , find and graph the equation of the line. 2 (4 pts.) (10 pts.) equation of the line: __________________________ [23] 10. The length of a rectangle is one inch less than three times its width. If the perimeter of the rectangle is twenty-two inches, find the dimensions of the rectangle. (10 pts.) Let x = ________________________________________ Let ___________________________________________ Equation(s): Solve. Write your answer in a sentence. 11. Solve each system: 4x + 3y = 15 2x 5y = 1 (12 pts.) 2x 3y 6 x 1.5 y 3 12. Solve and graph the following inequality: (6 pts.) 3 4x > 15 [28] 13. Solve and graph the following inequality: (6 pts.) 3x + 6y < 12 14. Ethan has $8000 to invest. He invests part of the money at 6% and the rest at 8%. If his interest for one year is $600, how much did he invest at each rate? Use the table if you’d like. (10 pts.) 6% 8% Total Amount invested Interest earned 15. Divide. (7 pts.) x 3 2 x 2 3x 5 [23] 16. Find the solution for each equation. (8 pts.) a. 2 x 6 x 12 _________________ solution b. 2 x 6 12 _________________ solution 17. Find the solution for each equation. (12 pts.) a. 2x 3 3x 4 _________________ solution b. 0.2 x 2 0.7 x _________________ solution [20]