1) [3pts] 2. Simplify the expression. Give your answer as a reduced fraction. No credit for decimal answers. ( ) 2) [4pts] ( 3 2 ) 1
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1 Math 097 Winter 2018 Final Exam (Form A) Name: Instructor s Name: Score: /100 (+ 3 bonus) 1. Evaluate 2(x h) 3 when x = 2 and h = 5. 1) 2. Simplify the expression. Give your answer as a reduced fraction. No credit for decimal answers. ( 3 2 ) 1 ( ) 2) [4pts] 3. Expand and simplify: (8x 1)(x + 3) 3) 4. Simplify 6t 2 3t 3 9t 9 leaving positive exponents only. 4) 5. Simplify: 8y 2y 2 2y 5) 6. Find all solutions of b in the equation: 3(7b 1) = b 6) b = [4pts]
2 7. Find all solutions of m in the equation. Give your answer as a reduced fraction or integer (not as a decimal). m 6 = ) m = 8. Find all solutions of x in the equation: 2 3 x + 10 = 16 8) x = [4pts] 9. Solve y 2x = 2(x + y) 3 for y in terms of x. Simplify your answer. 9) y = [4pts] 10. Use factoring to find all solutions for x in the equation: x 2 + 4x 21 = 0 10) x = [4pts] 11. Give all solutions m to the equation: 2(m 1)(2m + 5) = 0 11) m = 2
3 12. Factor 10a 3 b 40a 2 b completely. 12) 13. Is (x, y) = (2, 3) a solution for the system of two equations below? y = 3x 9 x + 2y = 2 Remember to show work to earn credit. 13) Circle one: [4pts] YES NO 14. An air filter catches dust particles that are inches in diameter. What is this distance in scientific notation? 14) in 15. Answer questions about the rectangle below. 6x-14 x a. If the perimeter of the rectangle is 98cm, find the two side lengths. 15a) x= 6x-14 = b. What is the length of the diagonal? 15b) [4pts] 3
4 16. Car tires need to be replaced when the treads (grooves) are too shallow. Below is a graph of the miles driven on a set of tires vs. the tire tread depth in millimeters. Use it to answer the questions. a. After how many miles will the tire tread depth be 5mm? 16a) miles b. Find the slope of this line as a fraction. 16b) [4pts] c. Give the slope s units. 16c) d. Write a sentence explaining what the slope and its units mean in this context. e. The following question is an optional bonus and can only help your grade. The odometer in your car stopped working, but you want to compute how many miles you drive on a road trip. Before the trip, your tire tread depth is 5.5mm. Afterwards, it is 5.35mm. How far did you drive on the road trip? Include units. 16e) [Bonus: +3] 4
5 17. Which of the following are equivalent to x 3? There may be more than one answer. [Circle all your answers] [6pts] a. 5x4 5x b. 1 c. 1 x 3 x 3 x9 d. e. x 3 x7 x 4 f. y 0 x x Which of the following are equivalent to x 2 + 4? There may be more than one answer. [Circle all your answers] [4pts] a. (x + 2) 2 b. 8+x2 2 c. Four more than the square of x d. (x + 2)(x 2 ) Tony earns $32,500 a year. His work offers him two options for a raise: An 8% raise, OR a $2,000 raise. a. What is Tony s new salary if he accepts the 8% raise? 19a) [4pts] b. Which raise should Tony take to earn more money? [Circle one] 19b) 8% OR $2,000 [1pt] 20. Enter the correct inequality sign " > " or " < ". a b. (5 3 4 )2 4 ( ) c. 30,
6 21. On a math test, 12 students earn an A. This number is exactly 25% of the number of students in the class. How many students are in the class? 21) 22. For the linear equation 3y 5 = 1 + 2x Give the x-intercept and y-intercept as coordinate pairs. 22) x-intercept: (, ) y-intercept: (, ) 23. a. On the coordinate axes below, plot the line y = 1 x 2. 3 b. On the same coordinate axes, plot the line x = 3. c. Using the graph, find the solution to the system of equations { y = 1 3 x 2 x = 3 23c) (, ) 6
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