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Challenge Exam for the Precalculus
Placement Test
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| 1. |
Find the radian measure of an angle whose degree measurement
is 330o. |
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| 2. |
Which of the following numbers is the smallest? |
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| 3. |
In a right triangle ABC, angle C is the right angle, side
AC = 5 |
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and sinB = 0.64. Find the length of side AB to the
nearest tenth. |
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| 4. |
| Evaluate: |
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| 5. |
Simplify sin(180o - q
) in terms of sinq or
cosq . |
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| 6. |
Evaluate sin2(4q
) + cos2(4q
) for all q . |
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| 7. |
In a right triangle ABC, angle C is the right
angle. |
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If side AB = 2 and AC = x, .
find an expression for tan B. |
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| 8. |
Rewrite the trigonometric identity for sin2q
and cos2q in terms of the angle
q |
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| 9. |
Final all solutions of x in the interval 0o
£ q
< 360o
satisfying the equation |
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2sin2q
+ sin2q -1
= 0. |
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| 10. |
For what values of q
in the interval 0 £
q < 2p
is cos4q
= 1. |
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| 11. |
| What is the period of |
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| 12. |
Use the law of cosines given below to find an
expression for angle A in |
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triangle ABC if AB = 8, AC = 4, and BC = 6. |
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Law of cosines: a2 = b2
+ c2 – 2bccosA. |
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| 13. |
| Evaluate: |
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| 14. |
Simplify: (cos2q)
(tanq)
(csc2q) |
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| 15. |
Let f(x) = –x2 + 5. Evaluate
f(1). |
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| 16. |
Find the slope of the line 3x – 5y = 1. |
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| 17. |
Write the equation of the line passing through the point
(3, –4) having |
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| slope |
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| 18. |
A rectangle has vertices (7, 7), (10,7), (7, –2) and (10,
–2). |
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Find the length of the diagonal. |
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| 19. |
| If f(x) = x2, simplify
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| 20. |
Graph | x | and | x +1| and | x–1| |
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| 21. |
If x = e y – 2.
Solve for y in terms of x |
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| 22. |
The graph of the parabola y = –x2 +
16x + 1 is symmetric with respect to |
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what line? |
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| 23. |
| If f(x) = 9x2 +1 and
g(x))= |
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Find f(g(x)) and g( f(x)).
Simplify if possible. |
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| 24. |
| If |
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For which value(s) of x is f(x) = 1? |
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| 25. |
| Find the domain and range of |
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| 26. |
Find the points of intersection of the graphs y =
2x2 and y = 3-5x. |
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| 27. |
| Simplify: |
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| 28. |
| Use log rules to simplify . |
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| 29. |
The polynomial x(x2 –16)(x2
+ 16) has how many real roots? |
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| 30. |
Consider y = lnx. What is the range and domain?
What is the x intercept? |
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Discuss the behavior of the graph as x®
¥ and as x®
0+ |
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Close |
