Review

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
(𝑦) (𝑦) =
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 − 7𝑖
10. Solve the equation:
4𝑥 3𝑥
−
=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 + 7𝑖
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.
𝑥 2 − 9𝑥 + 14
𝑓(𝑥) =
2𝑥 − 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 𝑓(𝑥) = 𝑥 3 −
3𝑥 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:
𝑓(𝑥) = √𝑥 − 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
𝑓(𝑥) = (𝑥−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: 𝑔(𝑥) =
𝑥 2 +4
𝑥
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+3𝑡)
herd is modeled by: 𝑁 = 1+0.04𝑡 , 𝑡 ≥ 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
𝑓(𝑥) = (𝑥+4)3
10. Consider the following: 𝑔(𝑥) =
3𝑥 2 −5
2𝑥
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.
25𝑥
Let 𝑦 = 𝑥−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: 𝑦 2 = 4𝑝𝑥.
𝑥2
𝑦2
+ 𝑏2 = 1.
𝑎2
15. Consider the following: 𝑔(𝑥) =
4𝑥 2 −5
8𝑥
Identify all x-intercepts:
16. Write the equation of the circle in standard form.
Recall standard form for a circle is: (𝑥 − ℎ)2 +
(𝑦 − 𝑘)2 = 𝑟 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
𝑒 𝑥 = 𝑒 𝑥 −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: 𝐴 = 𝑃𝑒 𝑟𝑡 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.