Math 120 online. Practice Midterm Exam #2 Prof. Kinoshita. Fall (Actual midterm will have 100 pts)
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1 Note: The format of this practice midterm will be similar to the real midterm. However, the actual midterm will have less questions and be worth 100 points. There will also be more room to work on the real midterm. Math 120 online Name: Practice Midterm Exam #2 Prof. Kinoshita Score: Fall (Actual midterm will have 100 pts) Directions: 1. Read the directions to each problem carefully. 2. A basic or TI-30 Scientific calculator allowed (NO other scientific calculator allowed) 3. NO graphing calculator, cellphones, etc allowed 4. Show all work for credit (No work = No credit). 5. Show your work on THIS EXAM. If you run out of room, use the scratch paper and write See scratch paper on the exam. 6. Students must use the scratch paper provided by the instructor (or proctoring facility). 7. If you use the scratch paper, be sure to number your work. 8. Circle your final answer (and circle only one final answer). 9. NO notes allowed (Using notes on this exam is considered cheating and will result in a score of 0 on this exam). 10. Be sure to simplify all fractions in your final answer. 1. You must write an equation to solve this problem. Be sure to CLEARLY state what the variable is and what it represents (for example, x = amount invested at 12%) and show the equation. DO NOT SOLVE IT. One maid can clean the house three times faster than another. Working together they can clean the entire house in 3 hours. How long would it take the faster maid cleaning alone? Variable: Equation: Page 1 of 23
2 2. You must write an equation to solve this problem. Be sure to CLEARLY state what the variable is and what it represents (for example, x = amount invested at 12%) and show the equation. DO NOT SOLVE IT. A box with no top is to be constructed from a piece of cardboard whose width measures x cm and whose length measures 6 cm more than its width. The box is to be formed by cutting squares that measure 3 cm on each side from the four corners, and then folding up the sides. If the volume of the box will be 48 cm 3, what are the dimensions of the piece of cardboard? Variable: Equation: 3. You must write an equation to solve this problem. Be sure to CLEARLY state what the variable is and what it represents (for example, x = amount invested at 12%) and show the equation. DO NOT SOLVE IT. A triangular garden has an area of 126 square feet. Its height is 9 feet more than its base. Find the measure of the base. Variable: Equation: Page 2 of 23
3 4. You must write an equation to solve this problem. Be sure to CLEARLY state what the variable is and what it represents (for example, x = amount invested at 12%) and show the equation. DO NOT SOLVE IT. A jet plane traveling at a constant speed goes 1200 miles with the wind, then turns around and travels for 1000 miles against the wind. If the speed of the wind is 50 mph and the total flight took 4 hours, find the speed of the plane. Variable: Equation: 5. Factor the polynomial completely x 2 y y 64 Page 3 of 23
4 6. Factor the polynomial completely a 2 (a + b) 2 ab(a + b) 2 72b 2 (a + b) 2 7. Factor the polynomial completely. (x y) Factor the polynomial completely q 4 Page 4 of 23
5 9. Factor the polynomial completely. 3x 3 +6x 2 y 24xy Factor the polynomial completely. 12a 3 8a 2 b + 9ab 2 6b Factor out the greatest common factor. 72x 8 y 7 +45x 3 y 5 +63x 6 y 2 Page 5 of 23
6 12. Factor by grouping. 24r ry 8xr 9xy 13. Perform the indicated operation and express in lowest terms. z z + 24 z z + 30 z 2 + 4z z z + 35 Page 6 of 23
7 14. Perform the indicated operation and express in lowest terms. 16s 2 +8st + t 2 5s 2 14st 3t 2 2s2 7st + 3t 2 t 2 +3st 4s 2 8s2 2st t 2 5s 2 +6st + t Simplify the complex fraction. Write the answer in lowest terms. 36p 2 9q 2 pq 6 q 3 p Page 7 of 23
8 16. Simplify the complex fraction. Write the answer in lowest terms x x Write the rational expression in lowest terms. m 2 36m 36 m 18. Write the rational expression in lowest terms. 2x + 2 6x x + 10 Page 8 of 23
9 19. Assume that the expressions given are denominators of fractions. Find the lowest common denominator. 2y + 4, y 2 4, y 20. Add or subtract as indicated. Write the answer in lowest terms. 6 x x 2 3x x Page 9 of 23
10 21. Solve the equation. 2(y 5) 2 12 = 5(y 5) 22. Solve the equation using factoring. (x + 8)(x + 6) = 1 Page 10 of 23
11 23. Solve the equation and check the proposed solutions. 2 x x = 36 x 2 4x 24. Solve the equation and check the proposed solutions. 1 w w 8 = 41 3w w 88 Page 11 of 23
12 25. Solve the formula for the specified variable. A = 1 h(b + b) for B 2 B = 26. Solve the formula for the specified variable. 1 a + 1 = c for b b b = Page 12 of 23
13 27. Graph the rational function. Give the equations of the vertical and horizontal asymptotes. f(x) = 1 x + 2 Vertical asymptote: Horizontal asymptote: 28. If s varies directly as t 2, and s = 150 when t = 5, find s when t = 3. s = Page 13 of 23
14 29. If x varies inversely as y 2, and x = 4 when y = 6, find x when y = 2. x = 30. If f varies jointly as q 2 and h, and f = 150 when q = 5 and h = 3, find h when f = 224 and q = 4. h = Page 14 of 23
15 31. Graph the function and give its domain and range. Be sure the domain and range are in interval form. 3 f(x) = x + 5 Domain: Range: 32. Graph the function and give its domain and range. Be sure the domain and range are in interval form. f(x) = x 4 Domain: Range: Page 15 of 23
16 4 33. Express the radical in simplified form Express the radical in simplified form Express the radical in simplified form. Assume that all variables represent positive real numbers. 3 27a 8 b 5 Page 16 of 23
17 36. Graph the circle. Be sure to state the center and radius. (x 1) 2 + (y 6) 2 = 9 Center: (, ) Radius = 37. Find the equation of a circle satisfying the given conditions. Center: ( 9,1); radius: Simplify. Assume that all variables represent positive real numbers. 5 3 x 6 y 5 2x xy Page 17 of 23
18 39. Simplify. Assume that all variables represent positive real numbers. 5 8 m 11 p 7 6m 2 5 p mp Multiply, then simplify the product. Assume that all variables represent positive real numbers. (3 5 2) 2 Page 18 of 23
19 41. Multiply, then simplify the product. Assume that all variables represent positive real numbers. 3 ( )(5 3) 42. Rationalize the denominator. Assume that all variables represent positive real numbers. 98x3 y Simplify. Assume that all variables represent positive real numbers y Page 19 of 23
20 44. Rationalize the denominator. Assume that all variables represent positive real numbers Simplify. Assume that all variables represent positive real numbers. x y 3x + 2y 46. Write the number as a product of a real number and i. Simplify the radical expression. 216 Page 20 of 23
21 47. Find the power of i. i Add or subtract as indicated. Write your answer in the form a + bi (8 + 7i) (3 + 9i) + (8 + 5i) 49. Multiply. Write your answer in the form a + bi (2 8i) Multiply. Write your answer in the form a + bi (5 9i)(7 6i) Page 21 of 23
22 51. Solve the equation, and check the proposed solutions. x 2 + 5x = x 52. Solve the equation, and check the proposed solutions. 2x x = 4 Page 22 of 23
23 53. Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. (2x + 3) (4 x) 1 2 = Solve the formula for the indicated variable. L = 2W k for k k = Page 23 of 23
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