Download M190 F2011 Final condensed

Part I: Questions 1 to 6. Choose any 5 questions from this part. Write OMIT to the left of
the question you leave out.
1) Solve the equation x 2  50  31 for x.
2) Find an equation of the line through point (7, 6) that is parallel to the line through the points (3,4) and (7,8).
3) Given f ( x )  5 x  4 and g ( x ) 
f ( x  h)  f ( x  h)
x4
, find f ( g ( x ))  g ( f ( x )) simplify
5
h
4) Use long division to simplify the fraction
2 x3  4 x2  4 x  8
.
x2
1
a  1 as a completely reduced fraction.
5) Rewrite
1
1
a 1
1
6) Find the center and radius of the circle whose equation is 2 x 2  2 y 2  20  2 y  4 x .
Part II: Questions 7 to 12. Choose any 5 questions from this part. Write OMIT to the left of the question
you leave out.

7)
 x y3 


y x 3 

Simplify
( xy 2 ) 3
1
2
so that only positive powers appear in your answer.
x  y  z  6

8) Use Cramer’s rule to solve for x. Do not solve for y or z:  x  y + 2 z  3
 2 x  y  2 z  2

8u13v11  u2v3 32u9v5 so that your answer involves just one square root sign.
 x  y  1
10) Solve the system of equations:  2
.
2
 x  y  5
9) Simplify
11) The product of two numbers is 63 and their difference is 2. At least one of the numbers is negative.
Find the numbers.
12) Solve the equation
x  5  2  x  3 for x and check your answer(s).
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Part III. Questions 13 to 18. Choose any 5 questions from this part. Write OMIT to the left of the
question you leave out.
13) Find the intercepts and the vertex of the parabola with equation y  2 x2  4 x  6 . Sketch the graph and
label the vertex and intercepts with their coordinates.
14) In triangle ABC, angle C measures 80 degrees, angle B measures 45 degrees, and the length of side BC is
6. Find the length of side AC, correct to 3 decimal places.
15)
A is an acute angle with sec( A) 
4
3
Find the exact values of sin (A). and tan(A). You may leave
square roots in your answer.
16) In triangle ABC, angle A measures 30 degrees, side AC measures 10 centimeters, and the length of side
AB is 12 centimeters. Find the length of side BC, correct to three decimal places.
x
 3 
17) Solve for x and y: 
x 
 2
18)
Solve:
y
7
2
y
5
5
4 2
4
for x.
 
2
x 4 x
x
Part IV: Questions 19 to 24. Choose any 5 questions from this part. Write OMIT to the left of the
question you leave out.
19) Rewrite
x4
5
 2
as a completely reduced fraction.
2 x  10 x  25
20) Rewrite
2 x3  8x
as a completely reduced fraction.
4 x2  2 x3
21) Given the function g ( x)  x  x2 , find and simplify the expression g (3  x)  g ( x  3).
22)
Rewrite the product
23) Rewrite
x 2  3x  3
x2  9
3 x
6  6 x  2 x2
as a completely reduced fraction.
2 32 5
as an expression that doesn’t involve a fraction.
5 3
24) I have 30 coins with total value $5.50. If I have only quarters and nickels, how many of each type of coin
do I have?
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