Download M1470 F 11 All Tests

Math
1470
Test
#1 2.1-2.7
Name __________________
1. For the quadratic function f (x) = " x 2 + 10x + 4 , complete the square and
determine which way the function opens, its vertex, and the equation of its line of
symmetry.
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2. A farmer has 288 feet of fencing and wants to build two identical pens for his
prize-winning pigs. The pens will be arranged as shown. Determine the
dimensions of a pen that will maximize its area.
y
x
3.
1 2 1
x + x+3
64
2
where x is the horizontal distance in feet from the point where the ball is punted.
How far, horizontally, is the ball from the kicker when it is at its highest point?
The ball hit the ground. How far from the kicker did the ball hit the ground?
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The height, h(x), of a punted rugby ball is given by h(x) = "
4. For each of the following functions, pick the letter that describes the general
shape of the function.
a. Because the degree is even and the leading coefficient is negative, the
graph falls to the left and falls to the right.
b. Because the degree is even and the leading coefficient is positive, the
graph rises to the left and rises to the right.
c. Because the degree is odd and the leading coefficient is negative, the
graph rises to the left and falls to the right.
d. Because the degree is odd and the leading coefficient is positive, the graph
falls to the left and rises to the right.
x 4 "17x 2 +16
i. f (x) =
______________
20
ii. g(x) = 3x 5 "12x 3 " 31
______________
4
3
iii. h(x) =" 2x + 4 x "26
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8
! iv. i(x) =" (x 3 + 4 x 2 " 7x +1)
______________
9
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5. Let P(x) = x 3 + 4 x 2 " x " 4 . Write P(x) as the product of factors. Then, list the
zeroes of P(x) .
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6. Let P(x) = x 3 + 4 x 2 + 4 x +16 . Write P(x) as the product of factors. Then, list the
zeroes of P(x) .
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7. Simplify i"(9 + 4i) and write the answer in standard form.
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8. Simplify (4 + i)(2 + 12i) and write the answer in standard form.
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9. Simplify
6 + 3i
and write the answer in standard form.
5 + 4i
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4 x 2 + 33x + 35
. Find the function’s domain and
5x 2 + 39x + 28
identify any horizontal and vertical asymptotes.
10. Consider the function f (x) =
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Domain
: __________
Vertical asymptotes : __________
Horizontal asymptotes: __________
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11. Suppose a species of sea turtle is confined to an island and has a current
population of 71 turtles. If the population, P , modeled by
71(2 + 0.03t)
P(x) =
, t "0 where t is the time in years, how many turtles are
2 + 0.06t
predicted to be on the island in 5 years? Round to the nearest integer. What is the
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limiting size of the population as time increases (t " #) ? Round to the nearest
integer.
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12. Find the solution set to the inequality
x "6
#" 7 .
x + 10
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Xtra - Credit
13. A Norman window has the shape of a rectangle surmounted by a semicircle as in
the figure below. If the perimeter of the window is of the window is 40 ft. express
the area, A, as a function of the width, x, of the window.
y
x
Math
1470
Test
#2 3.1-4.5
Name __________________
14. If $5000 is invested at 9% interest, find the amount after 7 years if the interest is
compounded
a. Quarterly
b. Monthly
c. Continuously
1
15. Write 5ln x " ln y + 6ln z as a single logarithm
2
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16. Answer the following
a. True or False:
ln x
= ln(x " y )
ln y
b. Write the equation in logarithmic form 7"2 =
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1
49
17. Solve for x: 5 x = 41
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18. Solve for x: log 2 (x) + log 2 (x " 3) = 2
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19. Answer the following:
a. Express 330° in radian measure
5"
b. Express
in degree measure
9
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20. Solve for x in the figure below.
B
35
m!BAC = 20.00°
A
x
C
21. Find sec(θ) given that the terminal side of θ lies in Quadrant III and tan(θ) = 6.
22. Identify the following in the equation y = 3cos(
a.
b.
c.
d.
Amplitude
Period
Horizontal shift
Vertical shift
2! (x ! ! )
) +1
5
23. An observer in a lighthouse 250 feet above sea level spots a ship off the shore. If
the angle of depression to the ship is 5°, how far out is the ship.
Math
1470
Test
#3 4.6-5.3
Name __________________
3
24. Given that the tan " = , find the other five trigonometric functions of " .
2
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x
25. Given that the sin " = , find the other five trigonometric functions of " .
3
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26. The height of an outdoor basketball backboard is 12
casts a shadow 17
1
feet long. Find the angle of elevation of the sun.
3
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1
feet, and the backboard
2
27. A jet leaves Reno, Nevada and is headed toward Miami, Florida at a bearing of
100°. The distance between the two cities is approximately 2472 miles. How far
north and west of Miami is Reno? When the jet makes the return flight to Reno
from Miami, what should the bearing?
28. A ship leaves port at noon and has a bearing of S 29° W. the ship sails at 20 knots.
How many nautical miles south and how many nautical miles west will the ship
have traveled by 6:00 PM? At 6:00PM the ship changes course to due west. Find
the ship’s bearing and distance from port of departure at 7:00PM.
29. Factor and simplify:
sec 4 x " tan 4 x
sec 2 x + tan 2 x
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30. Add and simplify:
cos" sin "
+
sin " cos "
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31. Verify the identity: sec 2 x tan 2 x + sec 2 x = sec 4 x
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32. Find all the solutions to the equation in the interval [0,2π).
tan 2 x + tan x = 0
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33. Find all the solutions to the equation in the interval [0,2π).
4 cos2 x " 3 = 0
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Math
1470
Test #4
5.4-6.3
Name __________________
34. Find the exact value of the given expression using a sum or difference formula.
19"
tan
12
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35. Write the given expression as the cosine of an angle.
cos60 cos55"sin60 sin55
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36. Write the given expression as the sine of an angle.
sin25 cos55 " sin55cos25
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37. Use the figure below to determine the exact value of the given function.
find tan 2!
2
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3
38. Find the exact solutions of the given equation on the interval [0,2" ) .
sin2x = cos x
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39. Use the figure below to find the exact value of the given trigonometric expression.
find sin
15
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2
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36
40. Use the half-angle formulas to determine the exact value of the given
trigonometric expression.
3"
tan
8
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41. Use the product-to-sum formula to write the given product as a sum or difference.
"
"
8 sin cos
10
10
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42. Use the sum-to-product formulas to write the given expression as a product.
cos9" # cos 7"
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43. Given C = 123°, a = 12.9, and c = 8.3, use the Law of Sines to solve the triangle (if
possible) for the value(s) of b. If two solutions exist, find both. Round answer to two
decimal places.
44. After a severe storm, three sisters, April, May, and June, stood on their front porch and
noticed that the tree in their front yard was leaning 3° vertical toward the house. From the
porch, which is 101 feet away from the base of the tree, they noticed that the angle of
elevation to the top of the tree was 32° . Approximate the height of the tree. Round
answer to two decimal places.
45. A vertical pole 39 feet tall stands on a hillside that makes an angle of 18° with the
horizontal. Determine the approximate length of cable that would be needed to reach
from the top of the pole to a point 73 feet downhill from the base of the pole. Round
answer to two decimal places.
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46. Find the magnitude and direction angle of vector v = 4i " 6 j . Round direction angle to
nearest hundredth.
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47. Find the component form of vector v if v = 4 and the angle it makes with the x-axis is
60°.
48. Three forces with magnitudes of 66 pounds, 78 pounds, and 132 pounds act on an object
at angles of 130°, 220°, and 290°, respectively, with the positive x-axis. Find the
magnitude and direction of the resultant force. Round answers to two decimal places.
49. A force of F pounds is required to pull an object weighing W pounds up a ramp inclined
at θ degrees from the horizontal. Find F if W = 5000 pounds and θ = 26°.
Math
1470
Test #5
6.5-8.5
Name __________________
50. Find the exact value of the given expression (" 3 " i) 9
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Find the exact value of the given expression (" 3 " i)
1
7
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51. A health insurance company advertises on television, on radio, and in the local
newspaper. The marketing department has an advertising budget of $42,000 per
month. A television ad costs $1000, a radio ad costs $200, and a newspaper ad costs
$500. The department wants to run 60 ads per month, and have as many television
ads as radio and newspaper ads combined. How any of each type of ad can the
department run each month? Write the system of equations, show all your work and
solve using Gaussian elimination.
52. A bank teller is counting the total amount of money in a cash drawer at the end of a
shift. There is a total of $2600 in denominations of $1, $5, $10, and $20 bills. The
total number of paper bills is 235. The number of $20 bills is twice the number of $1
bills, and the number of $5 bills is 10 more than the number of $1 bills. Write a
system of linear equations to represent the situation. Then write the equations in
reduced row echelon form to find the number of bills of each denomination.
53. Evaluate the following expression:
#0 "3& #"6 3&
#4 "4&
"3(%
(+ %
() " 2%
(
$7 2 ' $ 8 1'
$7 "9'
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54. You invest in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average
yields are 6.5% on the AAA bonds, 7% on A bonds, and 9% on B bonds. You invest
twice as much in B bonds as in A bonds. Let x,y, and z represent the amounts
invested in AAA, A, and B bonds, respectively. The total investment was $500000
and the annual return is $38000. Write a system of linear equations to represent the
investment, use the inverse of a matrix to solve for the amount invested in each type
of bond.
55. Consider the following systems of equations. Find all possible solutions for each
system.
x " 3y + z = 1
2x " y " 2z = 2
x + 2y " 3z = "1
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x + y " 3z = "1
0x + y " z = 0
"x + 2y + 0z = 1
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x " 2y + 3z = 9
"x + 3y + 0z = "4
2x " 5y + 5z = 17
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56. Use Cramer’s rule to solve (if possible) the system of equations.
6x " 5y = 17
"13x + 3y = "76
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57. Use determinants to find the area of the triangle with the following vertices.
(6,10) ("4,"5) (6,"1)
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58. Use a determinant to determine if the following points are collinear.
(3,"5) (6,1) (4,2)
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59. Use a determinant to find an equation of the line passing through the given points.
(10,7) ("2,"7)
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