Math 1170 – Spring 2015 FINAL Test Review Names________________ For full credit circle answers and show all your work. 1. Simplify the expression: 2 3 3 2 2. Write the number in scientific notation. Land area of a planet: 61,900,000 square miles () () = 3. Factor out the common factor. 4. A soda company had sales of $19,570 million in 2002 and $35,137 (x + 3)2 − 4(x + 3) = million in 2010. Use the Midpoint Formula to estimate the sales in 2006. Assume that the sales followed a linear pattern. 5. Find the center and radius of the circle. (x − 1)2 + (y + 5)2 = 16 6. Identify any intercepts and test for symmetry: y = 4 − |x| Sketch the graph: Sketch the graph: 7. Solve the equation and check your solution. 4x + 8 = 13 − 2x 8. Solve the equation and check your solution: 9. Write the quotient in standard form: 2 3 − 7 10. Solve the equation: 4 3 − =4 3 8 x4 − 81 = 0 11. Solve the quadratic equation by completing the square: 12. A winch is used to tow a boat to a dock. The rope is attached to the boat at a point 15 feet below the level of the winch (see figure). x2 + 6x + 4 = 0 Find the distance from the boat to the dock when there is 70 feet of rope out. (Round to one decimal place.) 13. Write the quotient in standard form: 4 3 + 7 14. Solve the equation: 15. Solve the quadratic equation by completing the square: 16. Solve the quadratic equation by completing the square: x2 + 6x + 8 = 0 x2 - 8x + 10 = 0 17. Solve the equation: 18. Write an equation that has the given solutions: 0, 7, 9 x4 − 16 = 0 |7x + 3| = 11 19. Solve the quadratic equation by completing the square: 20. Solve the inequality. Then graph the solution set and give the answer using set notation. x2 + 6x + 8 = 0 −7 ≤ −2x − 5 < 3 Inequality solution: Graph: Set notation: 21. Find the slope and y-intercept (if possible) of the equation of the line and sketch a graph. 15x − 6y = 72 22. Write equation of the line through the point (6, 1) and perpendicular to the line: 6x − 2y = 9. Sketch: 23. Solve the quadratic equation by completing the square: x2 - 4x - 12 = 0 25. Find the zeros of the function algebraically. 2 − 9 + 14 () = 2 − 4 24. A sub shop purchases a used pizza oven for $3265. After five years, the oven will have to be discarded and replaced. Write a linear equation giving the value V of the equipment during the five years it will be in use. 26. Identify the intervals on which the function () = 3 − 3 2 + 2 is increasing, decreasing, and constant. Increasing: Decreasing: Constant: 27. Solve the quadratic equation by completing the square: 28. Find the domain and range of the function: () = √ − 10 x2 - 4x - 9 = 0 Domain: Range: 29. Find and simplify a polynomial function that has the given zeros: 2, −6 30. You plan to construct an open box from a square piece of material, 11 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure). Write a function V that represents the volume of the box. V(x) = 31. Write the quadratic function in standard form and sketch it’s graph: h(x) = x2 − 4x + 6 32. Write the quadratic function in standard form, then provide it’s vertex, axis of symmetry, and any x-intercepts. f(x) = −(x2 + 2x − 3) Standard form: Graph: Vertex: Axis of symmetry: X-intercepts: 33. The sales y (in billions of dollars ) for Harley-Davidson from 2000 through 2010 are shown in this table: Create a scatterplot of the data. Use regression to find a quadratic model for the data. Sketch the data points and the curve. In what year were the sales for Harley-Davidson the greatest and what are the sales from the quadratic model. Give both answers to two decimal places. Equation: Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Max sales year: Sales 2.91 3.36 4.09 4.62 5.02 5.34 5.80 5.73 5.59 4.78 4.86 Amount: Math 1170 – Spring 2015 FINAL Test Review Names________________ For full credit circle answers and show all your work. 1. Use algebraic long division to divide: x3 − 52x − 96 by (x + 6). Write the polynomial as a product of linear factors. 2. Use synthetic division to divide: x3 − 52x − 96 by (x + 6). Write the polynomial as a product of linear factors. 3. Consider the polynomial: f(x) = 2x3 + x2 − 41x + 20. List all the possible rational zeroes of the polynomial: 4. The total numbers of people 16 years of age and over (in thousands) not in the U.S. civilian labor force from 1998 through 2010 are given by the following ordered pairs. (1998, 67,547) (2005, 76,762) (1999, 68,385) (2006, 77,387) (2000, 69,994) (2007, 78,743) (2001, 71,359) (2008, 79,501) (2002, 72,707) (2009, 81,659) (2003, 74,658) (2010, 83,941) (2004, 75,956) Construct an appropriate model where y represents the total number of people (in thousands) 16+ years old in the US civilian labor force and t = 0 represents 2000. Write the polynomial as a product of linear factors: 5. State the domain then find all vertical and horizontal asymptotes of the graph of the function: 3 () = (−6)3 Domain: Use the model to predict the number of people in the US civilian labor force in the year 2020. Yes, please do label your answer! Vertical Asymptotes: Horizontal Asymptotes: 6. Consider the following: () = 2 +4 7. Consider the polynomial: f(x) = 2x3 + x2 − 41x + 20. Identify all x-intercepts: Write the polynomial as a product of linear factors: Identify all y-intercepts: Find any vertical or slant asymptotes. 8. The game commission introduces 100 deer into newly acquired state game lands. The population N of the 20(5+3) herd is modeled by: = 1+0.04 , ≥ 0 where t is time in years. Find the population after 15 years: Find the deer population after 25 years: What is the limiting size of the deer herd as time increases? 9. State the domain then find all vertical and horizontal asymptotes of the graph of the function: 3 () = (+4)3 10. Consider the following: () = 3 2 −5 2 Identify all x-intercepts: Domain: Identify all y-intercepts: Vertical Asymptotes: Find any vertical or slant asymptotes Horizontal Asymptotes: 11. Consider the polynomial: f(x) = x3 − 4x. Write the polynomial as a product of linear factors: 12. A driver average 50 miles per hour on the round trip between two cities 100 miles apart. The average speeds for going and returning were x and y miles per hour, respectively. 25 Let = −25 represent y in terms of x for the context of this problem. Determine the vertical and horizontal asymptotes and their meaning: Vertical asymptote: Meaning: Horizontal asymptote: Meaning: 13. Find the standard form of the equation of the 14. Find the standard form of the equation of the ellipse with the given characteristics and center at the parabola. Recall standard form of a parabola looks origin. Recall standard form of an ellipse looks like: like: 2 = 4. 2 2 + 2 = 1. 2 15. Consider the following: () = 4 2 −5 8 Identify all x-intercepts: 16. Write the equation of the circle in standard form. Recall standard form for a circle is: ( − ℎ)2 + ( − )2 = 2 9x2 + 9y2 + 36x − 72y + 80 = 0 Identify all y-intercepts: Find all asymptotes. 17. Solve the system by the method of substitution. x − 4y = −13 x + 3y = 1 19. Solve the exponential equations algebraically. Approximate the result to three decimal places. 4ex = 81 ln(x − 4) = ln 8 Identify the center of the circle: Identify the radius of the circle: 18. Solve the exponential equation algebraically: 2 = −6 20. Word on the street is I will need a million dollars to be able to retire. Suppose I have $250,000 in my retirement account and will earn an 8% rate of return. Using the formula: = and what you know about exponential functions to determine the amount of time until I can retire. Give your answer in years and months rounding appropriately.

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