Math 112 Fall 2014 Midterm 1 Review Problems Page 1. (E) None of these

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1 Math Fall Midterm Review Problems Page. Solve the equation. The answer is: x x 7 Less than Between and Between and Between and 7 (E) More than 7. Solve for x : x x 8. The solution is a number: less than between and between and between and (E) greater than. Solve the equation. The answer is: p. p. 7p. p. p. p. p. (E) None of these. Solve the equation. x x x The answer is: x x x 8 x (E) There is no solution

2 Math Fall Midterm Review Problems Page. Determine the values of x and y that solve the system of equations below. x y x y What is the value of x? 8 x x x 7 x (E) x 7. Solve for x : x x x x x x x (E) There is no real solution 7. Which one of the following would be the correct mathematical expression for the following statement: The sum of a number and less than twice the number is four times the number. x x x x x x x x x x x x (E) x x x 8. A new car salesperson is paid a monthly salary of $ plus a commission of % of all the sales she makes each month. What monthly sales figure would give her of a monthly income of $,? $ $, $, $, (E) $,

3 Math Fall Midterm Review Problems Page 9. The rental fee for a compact car is $8 per day (Monday through Thursday) and $ per day (Friday through Sunday). This rental fee includes free miles per day. Additional miles cost $. per mile. Write an equation for the total cost of a rental, c x, from Wednesday through Saturday ( complete days) where x represents the number of miles traveled and x is greater than. (You may ignore the tax). c x 8.x c x 8x.x cx 8. x cx 8 x. x. A couple invests $ to build a rose garden. On the average, it costs them $. to grow each rose. If each rose can be sold for $.7, how many roses must they sell to break even?,,, 8, (E) None of these. You invest a total of $ in two accounts. The first pays % annual interest, the other pays 9% annual interest. At the end of one year you collect $8. in interest. How much was invested in the first account? between $ and $ between $ and $ between $ and $ between $ and $ (E) between $ and $. A shop owner wants to mix high quality coffee beans that cost $. per pound with cheaper beans that cost $. per pound to get a -pound blend that should be worth $. per pound. How much of the cheap coffee should be used?.87 pounds. pounds 7. pounds. pounds. A chemist needs ml of a % acid solution, but has only 7% and % solutions available. How many ml of the % solution should be added to get the desired solution? ml ml 7 ml 8 ml (E) 9 ml

4 Math Fall Midterm Review Problems Page. An airplane flies 9 miles with the wind and miles against the wind in the same length of time. If the speed of the wind is a fixed mph, what is the speed of the airplane in still air? mph mph mph mph (E) 9 mph. George and Matt have a painting business. George has less experience and it takes him hours more to paint a medium-sized room than it takes Matt. Working together they can paint a medium-sized room in hours. How long does it take George to paint a mediumsized room by himself? Round your answer to the nearest tenth of an hour if necessary. hours.7 hours. hours. hours (E).8 hours. The typical costs for two different kinds of heating systems for a bedroom housing unit are given in the table below: Type of System Installation Cost Operation Cost/Year Electric $, $, Solar $, $ After how many years of operation will the total costs of solar heating and electric heating be the same? less than years between and years between and years between and years (E) more than years

5 Math Fall Midterm Review Problems Page 7. Solve for x. The largest real solution is: x 8x x x x x (E) x 8. Solve for x. The smallest real solution is: x 9 x 9 x 9 x x x (E) There is no real solution 9. Solve for x. The solution(s) is/are: x x 7 x, only x, only x, only x 8, only (E) x, only

6 Math Fall Midterm Review Problems Page. An item is originally priced at P dollars, but is placed on sale at a discount of % off. If the sales tax is %, what is an expression for the final sales price?..p.p.7.7p..p. (E)..7P. The sum of three consecutive odd integers is. Determine the largest of the three integers. The largest of the three integers is: (E) 8. The height of a leaf above the ground after it falls from a tree is given by the formula s t.8t 7., where time is given in seconds and height is given in feet above the ground. When would the leaf land on the top a person s head if the person was seated on the ground under the tree and their head was.7 feet above the ground? The amount of time is: Between. and. seconds Between. and. seconds Between. and. seconds Between. and. seconds (E) Between. and. seconds. As part of a physics experiment, Ming drops a baseball from the top of a -foot tall building. The distance h, in feet, that the ball travels is given by h t, where t is measured in seconds. For how many seconds will the baseball fall? Round your answer to the nearest tenth of a second.. sec.7 sec. sec. sec (E).9 sec

7 Math Fall Midterm Review Problems Page 7. Determine the dimensions (i.e. the length and width) of a rectangle whose diagonal is meters and whose perimeter is meters. One of the dimensions is: 8 meters meters meters meters (E) meters. The height of a right triangle is cm more than its base. The area of the triangle is sq cm. Find the length of the hypotenuse. 9 cm 9 cm 9 cm 7 cm (E) cm. The manager of a candy shop sells chocolate covered peanuts for $7 per pound, and chocolate covered cashews for $ per pound. The manager wishes to mix pounds of the cashews to get a cashew-peanut mixture that will sell for $ per pound. How many pounds of peanuts should be used? 8 pounds pounds pounds pounds (E) pounds 7. An experienced bank auditor can check a bank s deposits in half the amount of time that it takes a new auditor. Working together, it takes the auditors hours to do the job. How long would it take the new auditor working alone? hours 7 hours 8 hours hours (E) hours

8 Math Fall Midterm Review Problems Page 8 8. A train that is traveling mph leaves a train station and goes west. Another train leaves the same train station one hour later on a parallel track traveling west at mph. How long will it take the fast train to catch up with the slow train? hours hours hours. hours (E) None of these 9. Janet is training for a triathlon. Yesterday she jogged for miles and then cycled another. miles. Her speed while cycling was miles per hour faster than he jogging speed. If the total time for jogging and cycling was. hours, at what rate did she cycle? Round your answer to the nearest one mph. mph mph mph 7 mph (E) 8 mph. Write the equation of the line (in the form Ax By C ) that passes through the point, and has a slope of. x y x y x y x y (E) x y. Write the equation of the line passing through the points, and,. y x y x 9 y x y x 9 (E) y x. Write the equation of the line through the point, and having undefined slope. x y x y (E) x. Write the equation of the line through the point, and having a slope of. x y x x (E) y

9 Math Fall Midterm Review Problems Page 9. Determine the equation of the line perpendicular to x y that passes through the point,. The sum of the slope and the y-intercept is: (E). Determine an equation of the line containing the point, containing the points, and,. y x y x y x y x (E) y x and perpendicular to the line. Given the line x, determine the equation of the line parallel to this line that passes through the point, 7. y x 7 y x y x (E) y x 7. Given the line x, determine the equation of the line perpendicular to this line that passes through the point,. y x y x y x (E) y x

10 Math Fall Midterm Review Problems Page 8. Determine an equation for the line passing through the point 7, the line x 9. and perpendicular to x 7 y 7 y x y (E) y x 8 9. Determine an equation for the line passing through the point 7, x 9. and parallel to the line x 7 y 7 y x x (E) y x 8. Which of these lines has a slope of zero? x y x y Ax By C, where A is positive, B is negative, and C is a real number. Solve the inequality. The solution is: x x,,,,,, (E) None of these. Which one of these equations represents y as a function of x? x y xy x y x y (E) y x 7

11 Math Fall Midterm Review Problems Page. Which one of the following graphs DOES NOT represent a function?

12 Math Fall Midterm Review Problems Page. Which one of the tables below represents y as a function of x? x y x y x y x y (E) x y. Given f r r r, evaluate t f. t t 7 t t t 7 t t (E) t. Which one of the following points lies on the graph of the equation y x?,,,,

13 Math Fall Midterm Review Problems Page 7. For f x x 9x, find and simplify f ( x h) f ( x). h xh h 8x 9h 8 h h h 8x 8 h x h 9 x h (E) x 9 8. Determine the domain of x x x,, x,, x, (E) x, x g. x x 9. Determine the zero(s) of x x only x,, and x and only x only (E) x and only x r. x x only

14 Math Fall Midterm Review Problems Page. Determine the domain of hx 7x., 7, 7,, 7 (E), 7. Determine the domain of f x denominator separately first.),,,, (E) None of these x. (Hint: Determine the domain of the numerator and x. Which one of the following has a domain of all real numbers except x? y x y x y x x y (E) x 8 x y x

15 Math Fall Midterm Review Problems Page. The graph of gx g. y is shown below. Use the graph to determine the domain and range of g x Domain: (, ) Range: [, ) Domain: [., ) Range: [, ) Domain: [, ) Range: [., ) Domain: [., ) Range: [., ) (E) Domain: [, ) Range: (, ) - -. The graph of y f x is shown below. Use the graph to determine the value of f f x (E)

16 Math Fall Midterm Review Problems Page. Identify the open interval(s) where the graph of Tx y is decreasing., and, only, only, only, and, (E), only only. Identify the open interval(s) where the graph of Tx y is positive., only, and, only, only, and, (E), and, only only

17 Math Fall Midterm Review Problems Page 7 7. Given that Lx y is an odd function, complete the table of values: x L x The missing values, from left to right, are:,,,,,,,, (E) None of these 8. Given that Lx y is an even function, complete the table of values: x L x The missing values, from left to right, are:,,,,,,,, (E) None of these

18 Math Fall Midterm Review Problems Page 8 9. Determine which one of the following graphs represents an even function

19 Math Fall Midterm Review Problems Page 9. Determine which one of the following graphs represents an odd function

20 Math Fall Midterm Review Problems Page. Determine which one of the following represents an odd function. g x x. f x x R m m m ht t t (E) F x x. Evaluate g given that: g x x x for x x for x and (E) None of these. Determine the domain and range of x Domain:, x for x f. x for x, Domain:, Range:, Range:, Domain:, Range:, Domain:,, Range:,,. Determine the range of the function given by g x x x x x (,] (,] (,) (,) (E) (, )

21 Math Fall Midterm Review Problems Page. Which one of the following is the graph of the function x x if x f? if x

22 Math Fall Midterm Review Problems Page. Determine the rule that defines the piecewise-defined function graphed below x x if x f x f x if x x x if if x x x x if x f x f x if x x x if if x x 7. If, is a point on the graph of y rx y? the graph of rx, which one of the following points MUST be on,,,, (E),

23 Math Fall Midterm Review Problems Page 8. Which one of the following transforms the graph of f x and a horizontal stretch? y f x y f y f x x (E) y f x y f x y with a vertical compression 9. Suppose gx ( 7, 7] (, ] (, ] (, ] (E) (, 8] y has a domain of, ] (. What is the domain of gx y? 7. Suppose the graph of y x is transformed into following describes the transformations performed? Horizontal compression, reflect over the x-axis, shift right Vertical compression, reflect over the x-axis, shift left Vertical compression, reflect over the y-axis, shift left Vertical compression, reflect over the x-axis, shift right (E) Horizontal expansion, reflect over the y-axis, shift left y x. Which one of the 7

24 Math Fall Midterm Review Problems Page 7. Consider the table of values for the function hx y given below. x h x 8 Which one of the following tables of values represents hx y? (E) x 8 x h x 8 x h 8 x 8 x h x x h x. x h

25 Math Fall Midterm Review Problems Page 7. Consider the graph of f x y given below, Which one of the following represents the graph of - x y f?

26 Math Fall Midterm Review Problems Page 7. The graph of y x can be obtained from the graph of y x by Shifting up units and reflecting over the x-axis. Shifting right units and reflecting over the x-axis. Shifting left units and reflecting over the y-axis. Shifting right units and reflecting over the y-axis. (E) Shifting left units and reflecting over the x-axis.

27 Math Fall Midterm Review Problems Page 7 Fall Midterm Study Guide Answers Question Answer Question Answer D 8 D D 9 A C C E B C E A B 7 B D 8 D E 9 A D B 7 C A 8 E C 9 A D A B C B D D C 7 C B 8 C A 9 E E E 7 B A 8 C B 9 A B C D D A C D A 7 E D 8 C C 9 B B A 7 D E 8 E A 9 B E 7 B E 7 E A 7 A D 7 E 7 C