Math
1030
Practice Exam 2
March 9, 2012
Answer all questions below. Every question is worth the same number of
points. You may use the available space for work, but must write ALL
answers on the answer sheet.
No cell phones, calculators, or notes are allowed during the exam. These
rules will be strictly enforced.
Name: _____________________________________________ Number:
_______________
‘lime or False: For #1-8 decide whether the statement is true or false. Write the entire
word “flue” or the entire word word “False.”
Tcac
F&~Sc
1. a(b+c)=ab+ac
2.
3.
(z+y)?~=z72±yhl
m=~/~y~J
4. ~&±y=~€+~/~
5. (xy)’~
6.
(.
t
=
\,~y)
if’
çy-=7
$~ ~ ± x3
W-a\s-c
+
Tcu~c
3z2
—
41 has S roots.
Alegbra
9. Find x where (7—
±4
=
12
10. If g(x) is an invertible function, and g(2)
=
7, then what is g~’(7)?
11. Find the inverse of f(x)
=
-~/2z ± 4. (You can check your answer by seeing if f’o f (z)
12. What is the implied domain of g(x)
interval.)
5
=
2-~5z ± 1
C
Page 2
—
=
23? (Your answer should be an
x)
13. Find the quotient
4x2
6x3 + 2
2x2—1
—
~-s,c
2.
Z)(
42~
-\
9,
4’,3 —~3%
4-7.
->
~~‘.S)( i-9
14. Find the quotient
Lj
4x3
5x + 6
z—2
—
a
-5
(0
B
15. \‘Vhat is the slope of the straight line in 1R2 that passes through the points (2,4) and
(5,10)?
‘5-a
Page 3
:3—
16. Complete the square: Write 2z2
—
4z + 5 in the form
afr + fl)2 +
25
It
17. How many roots does 2x2
—
6z + 10 have?
7-.
b
-~-)-aC~
3(~-
qQz)(~o) 40
.4>
Lnb
13. Find the roots of —2x2 + 6x + 2
‘94
-a
Page 4
1~a_~g)
~,
where a, fi, 7 E lit
20. (2 points) Completely factor —2z3 + 6z2 2z+ 6. (Hint: 3 is a root) (Your answer should
be a product of a constant and maybe some linear and quadratic polynomials that have
leading coefficients equal to 1, and such that any of the quadratics in the product have
no roots.)
—
-2
C
-ç
-~
C
0
~
0
(%~_l~
~
Page 5
Graphs
21. List all the monic linear factors of p(x) that you know from the graph below.
.1
22. Graph —2~x
23. Graph ~/1~
—
—
1 and label its x-intercept
1 and label the y-intercept.
24. Graph —3(x + 2)2
25. Graph 2x
—
—
I and label its vertex.
3 and label its z- and y- intercepts.
26. Graph the polynomial p(x)
—2(x
—
2)Qv + 3)(z
Page 6
—
4). Label the x- and y-intercepts.
Number:
Name:
12.
1.
-3x
F~dsc
2.
Tcv~.e.
3.
\tct\ce
4.
Tciie~
5.
Tcuj’.
6.
8.
Tcu...e
~se
9.
‘>(t~~F:~
•f.
.
~
10.
+
13.
14.
q~41x4l\ 4
17.
as
a
15.
16.
i-q
~(~-O2~3
no
ice
4-s
~~~i-JjZ~
18.
—
/
19.
20.
2L
1L
Page 7
-~
4’~2~
(x-~) ( Cfl)
~x~\\ (~-~(X-3)~ (x-~)
23.
22.
-2-
25.
24.
-t
I
a)
-3
q
-3
26.
Page 8
(0~-