Pre-Calculus Midterm Exam Score: ______ / ______ Name: ____________________________ Student Number: ___________________ Short Answer: Type your answer below each question. Show your work. 1 Verify the identity. Show your work. cot θ ∙ sec θ = csc θ cot= cos/ sin sec= 1/cos cos/sin*1/cos 1/sin x 2 A gas company has the following rate schedule for natural gas usage in single-family residences:                 Monthly service charge                  $8.80                 Per therm service charge                                 1st 25 therms                      $0.6686/therm                                 Over 25 therms                  $0.85870/therm What is the charge for using 25 therms in one month? Show your work. 8.8+25*0.6686 16.715+8.8 25.52 What is the charge for using 45 therms in one month? Show your work. 8.8+25*0.6686+20*0.85870 25.52+17.174 42.694 Construct a function that gives the monthly charge C for x therms of gas. C(x)=8.8+0.6686x If 0<=x<=25 25.515+0.85870(x-25) If x>25 25.515= 8.8 + 25*0.6686 3 The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is W(t) = where v represents the wind speed (in meters per second) and t represents the air temperature . Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second. (Round the answer to one decimal place.) Show your work. 6.0c 4 Complete the following: (a)           Use the Leading Coefficient Test to determine the graph's end behavior. The leading coefficient is positive x->infinity (b)           Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. 0 with multiplicity 2 and -2 with multiplicity 1 this it touches at 0 and goes through at 2 (c)           Find the y-intercept. Y intercept= the values you get when x=0, therefore the y-intercept is 0 f(x) = x2(x + 2) 5 For the data set shown by the table,  a. Create a scatter plot for the data. (You do not need to submit the scatter plot)  b. Use the scatter plot to determine whether an exponential function or a logarithmic function is the best choice for modeling the data. Logarithmic function Number of Homes Built in a Town by Year 6 Verify the identity. Show your work. (1 + tan2u)(1 - sin2u) = 1 Sec^2u*cos^2u=1/cos^2u*cos^2u 7 Verify the identity. Show your work. cot2x + csc2x = 2csc2x – 1 Csc x is cosecx Cot^2x+1=cosec^2x Lhs=cot^2x+cosec^2x+cosec^2x Cot^2x+cosec^x=1+2cosec^2x 8 Verify the identity. Show your work. 1 + sec2xsin2x = sec2x Sec^2x=1/cos^2x Sec^2xsin^x=sin^2x/cos^2x=tan^2x 1+tan^2x=sex^2x 9 Verify the identity. Show your work. cos(α - β) - cos(α + β) = 2 sin α sin β cos(a-b)=cos(a)*cos(b)+sin(a)*sin(b) cos(a+b)=cos(.

1. Pre-Calculus Midterm Exam
Score: ______ / ______
Name: ____________________________
Student Number: ___________________
Short Answer: Type your answer below each question. Show
your work.
1
Verify the identity. Show your work.
cot θ ∙ sec θ = csc θ
cot= cos/ sin
sec= 1/cos
cos/sin*1/cos
1/sin x
2
A gas company has the following rate schedule for natural gas
usage in single-family residences:

2. Monthly service charge $8.80
Per therm service charge
1st 25 therms $0.6686/therm
Over 25 therms
$0.85870/therm
What is the charge for using 25 therms in one month? Show
your work.
8.8+25*0.6686
16.715+8.8
25.52
What is the charge for using 45 therms in one month? Show
your work.
8.8+25*0.6686+20*0.85870
25.52+17.174
42.694
Construct a function that gives the monthly charge C for x
therms of gas.
C(x)=8.8+0.6686x
If 0<=x<=25
25.515+0.85870(x-25)
If x>25
25.515= 8.8 + 25*0.6686

3. 3
The wind chill factor represents the equivalent air temperature
at a standard wind speed that would produce the same heat loss
as the given temperature and wind speed. One formula for
computing the equivalent temperature is
W(t) =
where v represents the wind speed (in meters per second) and t
represents the air temperature . Compute the wind chill for an
air temperature of 15°C and a wind speed of 12 meters per
second. (Round the answer to one decimal place.) Show your
work.
6.0c
4
Complete the following:
(a) Use the Leading Coefficient Test to determine the
graph's end behavior.
The leading coefficient is positive x->infinity
(b) Find the x-intercepts. State whether the graph crosses
the x-axis or touches the x-axis and turns around at each

4. intercept.
0 with multiplicity 2 and -2 with multiplicity 1 this it touches at
0 and goes through at 2
(c) Find the y-intercept. Y intercept= the values you get
when x=0, therefore the y-intercept is 0
f(x) = x2(x + 2)
5
For the data set shown by the table,
a. Create a scatter plot for the data. (You do not need to submit
the scatter plot)
b. Use the scatter plot to determine whether an exponential
function or a logarithmic function is the best choice for
modeling the data.
Logarithmic function
Number of Homes Built in a Town by Year
6
Verify the identity. Show your work.
(1 + tan2u)(1 - sin2u) = 1
Sec^2u*cos^2u=1/cos^2u*cos^2u

5. 7
Verify the identity. Show your work.
cot2x + csc2x = 2csc2x – 1
Csc x is cosecx
Cot^2x+1=cosec^2x
Lhs=cot^2x+cosec^2x+cosec^2x
Cot^2x+cosec^x=1+2cosec^2x

6. 8
Verify the identity. Show your work.
1 + sec2xsin2x = sec2x
Sec^2x=1/cos^2x
Sec^2xsin^x=sin^2x/cos^2x=tan^2x
1+tan^2x=sex^2x
9
Verify the identity. Show your work.

7. cos(α - β) - cos(α + β) = 2 sin α sin β
cos(a-b)=cos(a)*cos(b)+sin(a)*sin(b)
cos(a+b)=cos(a)*cos(b)-sin(a)*sin(b)
cos(a-b)-cos(a+b)=(cos(a)*cos(b)+sin(a)*sin(b))-
(cos(a)*cos(b)-sin(a)*sin(b))
cos(a-b)-cos(a+b)=2*sin(a)*sin(b)
10
The following data represents the normal monthly precipitation
for a certain city.
Draw a scatter diagram of the data for one period. (You do not
need to submit the scatter diagram). Find the sinusoidal
function of the form that fits the data. Show your work.
A=(max-min)/2
A=2.14
B=(max+min)/2
B=6.05
W=2pi/Twhere t is the period
W=2pi/t
W=2pi/12
W=pi/6
Y=2.14*sin((pi/6)x-phi)+6.05
6.21=2.14*sin((pi/6)(4)-phi)+6.05
6.21=2.14*sin(2pi/3-phi)+6.05

8. 6.21-6.05=2.14*sin(2pi/3-phi)
0.16=2.14*sin(2pi/3-phi)
0.16/2.14=sin(2pi/3-phi)
Sin(2pi/3-phi)=0.07476635
2pi/3-phi=arcsin(0.07476635)
2pi/3-phi=4.28779745
-phi=4.28779745-2pi/3
Phi=-2.19340235
.
11.
The graph below shows the percentage of students enrolled in
the College of Engineering at State University. Use the graph to
answer the question.
Does the graph represent a function? Explain
No,

9. A vertical line intersects the relation more than once
12.
Find the vertical asymptotes, if any, of the graph of the rational
function. Show your work.
f(x) =
vertical asymptotes:
f(x)=(x-4)/(x(x-4))
f(x)=x
x=0 or x=4
13.
The formula A = 118e0.024t models the population of a
particular city, in thousands, t years after 1998. When will the
population of the city reach 140 thousand? Show your work.
A=140=118e^0.024t
0.024t=ln(1.185441)
T=ln(1.185441)/0.024
T=0.170957798/0.024=7.12 years
The populations would reach 140,000 sometime in 2005

10. 14.
Find the specified vector or scalar. Show your work.
u = -4i + 1j and v = 4i + 1j; Find .
U+v where u=-4i+j,v=4i+j
2j

11. 15.
Find the exact value of the trigonometric function. Do not use a
calculator.
180=pl radians
90=pl/2 radians
45=pl/4 radians
(-5*45)
45=1
16.
Find the x-intercepts (if any) for the graph of the quadratic
function.
6x2 + 12x + 5 = 0

12. Give your answers in exact form. Show your work.
-12-squareroot24/12=-1.40824
-12+squareroot24/12= -0.59175
17.
Use the compound interest formulas A = Pert and A = P to
solve.
Suppose that you have $11,000 to invest. Which investment
yields the greater return over 10 years: 6.25% compounded
continuously or 6.3% compounded semiannually? Show your
work.
Investment= 11000
R=6.25=0.0625
T=10
For the interest
Investment= 11000

13. R=6.3=o.o63
T=10
N= periods, semiannual means twice a year so periods only 2
1000 invested at 6.3%compinded semiannually over 10 years
yields the greater return
18.
Find functions f and g so that h(x) = (f ∘ g)(x).
h(x) = (6x - 14)8

14. H(x)=(6x-14)^8
F(x)=x^8,g(x)=6x-14
19.
Begin by graphing the standard absolute value function f(x) = |
x |. Then use transformations of this graph to describe the graph
the given function.
h(x) = 2 | x | + 2
F(2)=l2l=2
2lxl+2
20.
Find the reference angle for the given angle. Show your work.
-404°

15. Reference angle is 44* and In the 4th quadrant
Score: ______ / ______
1
A change to society due to change in values, behaviors, etc. In
order for social change to occur, there must be people such as
Myles Horton whom act as this driving force of change.
A behavior that leads towards organized action and change.
These interactions involves others in society (large groups or
other individuals).
In Chapters 1-4 of The Long Haul, you will see that Myles
Horton participated in several social actions in which he
promoted social change. You will focus upon one of these social

16. actions this week in order to write a short summary of how he
used the four key components of: Story, Shared Story, Risk-
taking, and collective action to promote social change.
An account of Myles Horton’s past experiences and events that
evolve into something more.How has Myles Horton’s story
transcended to others? What does his story teach others?
An act of doing something which involves risk in order to
achieve a goal or objective.Action that is taken by a group of
people whom have a common goal and objective. Through the
combining of each individuals strengths and knowledge, this
group of people work to achieve a common goal that is shared
by all.