pre calculus
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pre-calculus2bmidterm2bexam.pdf
Pre-‐Calculus Midterm Exam
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Score: ______ / ______
Name: ____________________________
Student Number: ___________________
Short Answer: Type your answer below each question. Show your work. 1 Verify the identity.
cot θ ·∙ sec θ = csc θ
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? What is the charge for using 45 therms in one month? Construct a function that gives the monthly charge C for x therms of gas.
Pre-‐Calculus Midterm Exam
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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) =
𝑡 33 −
!".!"!!" !!! !!!! !!"#
33 − 1.5958 33 − 𝑡
if 0 ≤ v < 1.79 if 1.79 ≤ v < 20
if v ≥ 20
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.)
4 Complete the following:
(a) Use the Leading Coefficient Test to determine the graph's end behavior. (b) Find the x-‐intercepts. State whether the graph crosses the x-‐axis or touches the x-‐axis and turns around at each intercept. (c) Find the y-‐intercept. f(x) = x2(x + 2) (a). (b). (c).
Pre-‐Calculus Midterm Exam
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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.
Number of Homes Built in a Town by Year
6 Verify the identity.
(1 + tan2u)(1 -‐ sin2u) = 1
7 Verify the identity.
cot2x + csc2x = 2csc2x -‐ 1
8 Verify the identity.
1 + sec2xsin2x = sec2x
Pre-‐Calculus Midterm Exam
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9 Verify the identity.
cos(α -‐ β) -‐ cos(α + β) = 2 sin α sin β
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.
Pre-‐Calculus Midterm Exam
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Multiple Choice: Type your answer choice in the blank next to each question. _____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?
A. Yes B. No
_____12. Find the vertical asymptotes, if any, of the graph of the rational function.
f(x) = !!!
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A. x = 0 and x = 4 B. x = 0 C. x = 4 D. no vertical asymptote
Pre-‐Calculus Midterm Exam
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_____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?
A. 2008 B. 2005 C. 2006 D. 2007
_____14. Find the specified vector or scalar.
u = -‐4i + 1j and v = 4i + 1j; Find 𝑢 + 𝑣 .
A. 34 B. 8 C. 2 D. 5
_____15. Find the exact value of the trigonometric function. Do not use a calculator.
cot − 5𝜋 4
A. -‐1 B. − 2 C. 1 D. − !
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Pre-‐Calculus Midterm Exam
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_____16. Find the x-‐intercepts (if any) for the graph of the quadratic function. 6x2 + 12x + 5 = 0 Give your answers in exact form.
A.
B.
C.
D.
_____17. Use the compound interest formulas A = Pert and A = P 1 + !
!
!" 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?
A. $11,000 invested at 6.25% compounded continuously over 10 years yields the greater return.
B. Both investment plans yield the same return. C. $11,000 invested at 6.3% compounded 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
A. f(x) = 6x -‐ 14, g(x) = x8 B. f(x) = 6x8 -‐ 14, g(x) = -‐14 C. f(x) = x8, g(x) = 6x -‐ 14 D. f(x) = (6x)8, g(x) = -‐14
Pre-‐Calculus Midterm Exam
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_____19. Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to graph the given function. h(x) = 2 | x | + 2
A.
B.
C.
D.
Pre-‐Calculus Midterm Exam
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_____20. Find the reference angle for the given angle. -‐404°
A. 44° B. 46° C. 134° D. 136°
