IMSA
MI-4
Prob. Set #9
DUE: Fri.. Nov 15
Fall 13
1) NC Solve the following equations:
a)
x2  x2  4
b)
x  12  2  x  6
2) NC Solve the following equation over the complex numbers:
4 z 3  32  0
3) NC Solve the following system of equations: 
 x 2  xy  8

 y 2  xy  4

4) NC a)
b)
Find the vertex of the parabola with equation y = 2x2 + 6bx – 1 in terms of b.
Determine the equation of the locus of points created by the vertex of the parabola
in part a) as the value of b varies.
5)
A drawer contains eight matching brown socks and twelve matching blue socks. If two socks are
pulled out of the drawer at random (without replacement and no peeking allowed), what is the
probability that they are a matching pair of socks?
6)
Sue rides her bike at a rate of 15 mph to May’s house 5 miles away. Then Sue and May walk to
a park 2 miles away at a rate of 3 mph. What was Sue’s average speed for the entire trip?
7) NC Solve the following equations:
a)
1
3x  5 x 3  3x  4   5 x  2
3
b)
1
1
1
6  9 x  13  6 x  6  4 x  0

5
 4 
8) NC Find the exact value of cos  cos 1    tan 1     .
 13 
 3 


9) NC Evaluate:

1 1 
 j j
3 2 
j 1
2
page 1
Fall 2013
IMSA
10)
MI-4
Prob. Set #9
DUE: Fri.. Nov 15
Fall 13
Solve. (Show some steps with trig. Calculator decimals at the end to the nearest hundredth of a
radian.)
15 sin2x = cos x +13
11)
Solve the following inequality (show method – no graphing allowed):
x 2  2 x  6  3x
12)
Rewrite the expression 5cos( x)  12sin( x) in the form A sin(  x) . State  to the nearest
hundredth of a radian.
13)
If a sequence begins –5, x, y, 40, find all possibilities for x and y so that the sequence is:
a)
arithmetic
b)
page 2
geometric
Fall 2013