MATH 098 STUDY GUIDE FOR FINAL EXAM

Please note that this study guide does not necessarily represent all of the information you need to know for the final. In addition, it is strongly recommended that you also review the past test reviews, tests, and quizzes.

  1. Factor 8x3+27 completely.
  1. Factor xy2-7y2-4x+28 completely.
  1. Factor 6t2-t-5 completely.
  1. Solve. 3x2x-33x+4=0
  1. Simplify.

a)  x2-5x+62x+4∙x+22x-6

b)  x2-9x2-3x÷xy+5x+3y+152x+10

  1. Mrs. Smith balances the company books in 8 hours. It takes her assistant 12 hours to do the same job. How many hours would it take for them to complete the job together?
  1. The amount P of pollution varies directly with the population N of people. Kansas City has a population of 460,000 and produces about 270,000 tons of pollutants. Find how many tons of pollution we should expect St Louis to produce if we know that its population is 319,000. Round to the nearest whole ton.
  1. Find the domain of the function fx=3x-52x+6.
  1. Simplify.

x-1x2-2x+1-x+1x-1

  1. Simplify.

7x+3x25+1x

  1. Solve.

a)  5y+1=4y+2

b)  xx-3=3x-3-32

  1. Solve for G given that N=R+VG

13.  A cyclist rode the first 20-mile portion of his workout at a constant speed. For the 16-mile portion of his workout, he reduced his speed by 2 miles per hour. Each portion of the workout took the same time. Find the cyclist’s speed during the first portion and find his speed during the cooldown portion.

  1. Simplify and express your answer with all positive exponents.

x2y-7x7y-5z-3

  1. Determine the domain and range of the following graph.
  1. The table below shows the distance traveled on a trip with departure time of noon.

Time / Dt Distance traveled (miles)
Noon / 0
1:00 / 35
2:00 / 70
3:00 / 105
4:00 / 140

a)  Write a linear functionD(t), which fits this data and expresses the distance traveled as a function of time.

b)  What is the slope?

c)  What does the slope represent? (hint: consider the units of the slope)

  1. Graph fx=x+3-5
  1. Graph gx=x-1
  1. Graph hx=13x + 2
  1. Read the excerpt and identify the dependent variable and the independent variable under consideration.

A study analyzed the effect of a medication on cholesterol levels. The higher doses of the medication were associated with lower cholesterol levels.

Dependent Variable:

Independent Variable:

  1. Solve

a)  32x+4-8=1 b) 2x-5≤-7

c) x3+2>5 d) 2x-5≤7

  1. Simplify

a)  48+108. b) 38-518

c) 505-2 d) 323+8

  1. Given the function fx=x3+2x2, find f-2.
  1. Solve 3x-5 = 8.
  1. Simplify 134+3
  1. Solve 3x-17=9+2x.
  1. Divide 3i4+5i. Express your answer in the form a+bi.
  1. Multiply 4+2i11-3i. Express your answer in the form a+bi.
  1. A stone is thrown upward from a bridge. The stone’s height in feet, s(t), above the water t seconds after it is thrown is st=-16t2+32t+256.

a)  Find the maximum height of the stone.

b)  Find the time it takes the stone to hit the water.

  1. Use the discriminant to determine the number and types of solutions.

9x2+8x=3

  1. Determine an equation equivalent to 2x2-8x+3=0 obtained by completing the square.
  1. Solve the equation 2x2+8x+12=0 using any technique you want.
  1. Solve the equation 9x2=36x-40 using any technique you want.
  1. Solve the equation 2x2+3=7 using any technique you want.
  1. Find the distance between (-3, -5) and (5, -2).
  1. Determine the quadratic function with vertex (1, -4) and x intercepts at (-1, 0) and (3,0).
  1. Based on the data in each table, choose the best type of function for describing how the variables are related. (linear, constant, quadratic, or exponential)

a) 

Cell Phone Use (Minutes) / Monthly Cell phone Cost ($)
247 / 31.50
364 / 31.50
418 / 31.50
509 / 31.50
661 / 31.50

b) 

Month / Number of Rabbits
February / 4
March / 18
April / 81
May / 365
June / 1640

c) 

Hours Worked (Week) / Total Wages ($ per Week)
10 / 90
15 / 135
20 / 180
25 / 225
30 / 270

d) 

Time after Rock Thrown (seconds) / Height of Rock Thrown Upward (feet)
0 / 5
0.5 / 17
1.5 / 21
2.0 / 17
2.5 / 5
  1. The number of employees for at a certain company has been decreasing each year by 5%. If the company currently has 640 employees and this rate continues, find the number of employees in 7 years. Use either the formula y=c1-rx or y=c1+rx.
  1. Suppose that Q is jointly proportional to R and the square of S. If Q = 24 when R = 3 and S = 4, find Q when R = 2 and S = 3.

40.  Graph fx=12x+7

  1. Graph fx=x2+2x+5
  1. Graph fx=3x-1

Rev Fall 2015 Page 2 of 8