Download Final Exam Review Worksheets

Final Exam Review Worksheets
Math 1151, Precalculus 2
1. Graph f (x) = −2x2 − 4x − 1 using transformations. What is the vertex? What are
the roots?
2. Find all the asymptotes of f (x) =
x2 −5x−2
x−5
and of g(x) =
−x2
.
x2 +5x+6
3. Let f (x) = x4 − 5x3 + 5x2 − 5x + 4. Use the Rational Zeros Theorem and Descartes
rule of signs to help you completely factor f (x) into linear factors.
4. Graph f (x) = 2 sec(2x + π2 ).
5. Find the exact value of cos(cos−1 (1/2) + sin−1 (3/5)).
√
√
6. Solve the trigonometric function 4 sin(2θ + 2π
) + 3 3 = 3 on the interval [−2π, 0).
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7. If cot θ = −2 and sec θ < 0 find sin(2θ), cos(2θ), sin(θ/2) and cos(θ/2).
8. Solve a triangle with sides a = 4, b = 3, c = 6. And find the area.
√
9. Given the rectangular coordinate (x, y) = (− 3, 1), find a set of polar coordinates
(r, θ) for the point.
10. Find the partial fraction decomposition of
x+4
+ 1)
x2 (2x2
11. Solve the system





x + y + z = −3 (1)
2x − 3y + 6z = −21 (2)




−3x + 5y = −14 (3)
12. Solve the system

 x2 − y = 0 (1)

xy = 1 (2)
13. Two pulleys, one with radius 2 inches and the other with radius 8 inches are
connected by a belt. If the 2-inch pulley is caused to rotate at 3 revolutions per minute,
determine the revolutions per minute of the 8-inch pulley.
14. To measure the height of a mountain, a surveyor takes two sightings of the peak
at a distance 900 meters apart on a direct line to the mountain. The first observation
results in an angle of elevation of 47◦ and the second results in an angle of elevation of
35◦ . How high is the mountain?
15. How many rows are in the corner section of a stadium containing 2040 seats if the
first row has 10 seats and each successive row has 4 additional seats?
16. Initially, a pendulum swings through an arc of 2 feet. On each successive swing,
the length of the arc is .88 of the previous length.
(a) What is the length of the arc of the 10th swing?
(b) On which swing is the length of the arc first less than 1 foot?
(c) After 15 swings, what total length will the pendulum have swung?
(d) When it stops, what total length will the pendulum have swung?
17. The circle given has diameter 6 inches. Let
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FOE be 88◦ ,
AOB be 30◦ . Find the area of the shaded region.
Find the perimeter of the shaded region in this figure.
6
DOC be 60◦ and
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