pretest07fk - MAC 2311 Quiz on Pre-Reqs and Key Sept 4 2007...

MAC 2311 Sept 4, 2007
Quiz on Pre-Reqs and Key Prof. S. Hudson
The problems are worth 15 points each, except 1) is worth only 10. The quiz took about
35-40 minutes.
1) What is an equation of a line through (-4,7) and perpendicular to y =
2
3
x + 5?
2) Find cos(75
◦
) using the addition formula for cos( a + b ).
3) Solve for x , given that (ln( x ))
2
= ln( x
4
). There may be 2 or 3 solutions.
4) Solve for x , given that ( x
2
- 5 x + 4) / ( x
2
- 4) ≤ 0. Answer with interval notation, if
possible.
5) Solve for x , given the double inequality x + 3 < 2 x + 8 < 3 x + 10. Answer with interval
notation, if possible.
6) Simplify this formula using the triangle method: cos(tan
- 1
( x )).
7) Derive the formula for the area of a sector. See the picture. Your answer should include
the correct formula and a clear explanation (in words, of course) of why it is true.
Remarks and Answers: If you scored below 50/100, your chances of passing are not
too good. If you plan to try, you need to bring your algebra and/or trig skills up to par
before the first exam. If you scored below 40/100, you must see me about remedial work