So Ld—i
MATH 10 50-90
PRACTICE EXAM 1
(Sections 1.1-1.9, 2.1-2.5)
The purpose of the practice exam is to give you an idea of the following:
• length of exam
• chfficulty level ofproblems
• your instructorc problem writing style
Your actual exam will have dfferen t problems. You should review your homework,
quizzes, lecture notes etc., notjust perfect taking the practice exam. However,you can
use the practice exam to gauge how wellyou know the material. To do this, take it under
the same conditions as a normal exam (no notes, no calculator, time yourseif). Then score
your problems against the solution key.
The following instructions are on the exam:
o
Use a PENCIL, erase or cross out errors.
o
SHOW ALL WORK. No points will be given for answers without justification.
o
our answer so it is easy to locate.
o
NO CALCULATORS, NOTES, PHONES, ETC.
o
Answers should be simplified (reduced).
o
The value of each question is shown.
o
Finish in 80 minutes (one hours+ 20 minute grace period). You are responsiblefor keeping track of
the time. The proctor does not say “time is up”. For each minute you take beyond 80 mi yourscore
will be reduced by 0.5%.
Page 1
/28
Page 2
/20
Page 3
Page 4
Page 5
Total
/18
/19
/15
Parent Functions
Parabola:
polynomial
Square root
+k
2
y=a(x—h)
Absolute value
y=alx—hI+k
Cubic
ya(x—I
Rational
ax+b
‘cx±d
/100
MATH 105 0-90, PRACTICE EXAM 1
Page 1 of5
SHOW ALL WORK!
1. (l2pts) Points and lines. Given the points
2. (l6pts) Functions
f(x) = x 7 and g(x)
—
A (-4,-2)
B (-7,4)
=
2— x
.
3
C (-1,9)
Find the following. Simplify if possible.
Find the following. Simplify if possible.
°
a.
a. the midpoint of the segment with
endpoints A and B:
c (2—x
g)(x)
3)
2--7-
4-2
‘.
2-
(cc
b. (g°f)(5)
(s-fl
b. the distance from A to C:
q—
.
()
(—2)
i0 I
: -(-
-
1 u)
4-
2
c.
g’(x)
/
c. the slope of the line containing B and C:
—1 (-)
(-‘a
t-
-2-—i
2—
j)
j
(g’\
7)
d. The equation of the line passing through
BrmIDnrn1 WErnJ1t1II
2—x
X
-
(in slope-intercept form, y=mx+b):
A
C
e.
•k
-I{
‘SE
--EZi±
L
ç
-b
I-h
-
What is the domain of the function in d?
MATH 1050-90, PRACTICE EXAM 1
Graph A
—
—
I
I
—
L
I
I
I
—
I
I
I
I
I
I
—
—
—
—
Page 2 of S
SHOW ALL WORK!
Graph B
—
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
___I___I___.__I___I_6_
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
——I—--—
I
I
I
-
I
I
I
I
I
I
I
I
I)
If
/:
(—4
—
I
j.jj
I
I
I
I
-
-
±
-
—2
——
I
I
I
I
I
LJ.J
I
I
I
I
-
1
_____I___
I
U
-L
3. (pts) Analyzing GRAPH A.
a. h(3)=
b. For which value(s) of x is h(x)
c.
=
o)
Domain(writeasinteiaV
t3
2?
U(
(‘
d. Range (write as inteniaQ
t. 2, 2
i.c) u
)7
L
4. (Zpts) Analyzing GRAPH B.
a. For which x does f(x)
=
g(x)?
1
-
•—)
kJ)
b.
f(x)
_
c.g(x)
S
2
nr
x
(Hint parentfuncons are shown on the cover page)
parentfunctions are shown on the coverpage)
1
MATH 105 0-90, PRACTICE EXAM 1
Page 3 of 5
SHOW ALL WORK!
5. (6 pts) Simplify the expression.
2 +J—ioo
(7i+3)
Write the answer in the form a+bi
-,
-%fi;5--
Z()(3)
.3
--f2i”
‘—tO
-
•i—
I:,
—
6. (14
points)
Quadratic functions. Given this quadratic function
a. Complete the square to rewrite it in the form
f(xJ = a(x-h)
+k.
2
f(x)
2+
—4x
-X—c
L
31
5
4
3i
)
—
c. Graph f(xJ showing Be accurate.
ZLt,’
(&crz
24x
‘)
L
3
33j
0
—5
—
fz
--
—2
—Ii
tI
£tf -1
o
i
zt iz:
/2
3
b. Use the quadratic formula to find the-r-o-o.ts of f(x).
Simplify
—
><
4x’
-
-
2L
s--I’
5
MATH 1050-90, PRACTICE EXAM 1
Page 4 ofS
SHOW ALL WORK!
7. ts) Functions, inverses and graphs
Given the function f(x)
=
2
—
3x
3
-
a. Findf’(x)
)<
2-3
—
-5
—4
—3
-2
/
-I
F
-3L
-.
—1
2
-3
3
H---+---H
r
b. Graph f(x) and f’(x) on the same graph.
c.
-
How are the graphs of f(x) and f
(x) related?
1
f (ec
-.
-
(
..
e. s
C
c
-
—5
(z,o
8. (its) Polynomials. Draw a (polynomial) function that looks like it meets these
J
requirements: ,ç-?‘
\J”—
.‘Degree4
I
4
• Has negative leading coefficient
Has zeros t x=-2, x=O ndaDOUBLE zero
\
1
---2
atx=3
7\
—
—-
-‘
/
----
-I-7
4
—
—
——
I
—
MATH 105 0-90, PRACTICE EXAM 1
9. (9 pts) Polynomials: Given: p(x)
a. Calculate: p(x)÷(x-5)
Page 5 of5
SHOW ALL WORK!
3
4x
—
2
12x
x + 15
—
e. Factorp(x).
(Use synthetic
division or long division)
)
L(
L
-2
Lj
Lj.
Hint: either x-1 or x+1 is a factor of
the polynomial. Decide which one.
Factor it out and then factor the
remaining polynomial more.
jL5
3ci2
+
b. p(5)
=
j
f1e
3f
p(c
_(2(c-3
()
sIc
c. What is the relationship between a.
andb.? (Hint, think ofa theorem.)
T
_Li
-iZI
‘-f —s-
‘I
•-1
C
-c1
Lt
if
I
1S
-12--I
-s
d. What is the y-intercept of p(x)?
r--c
-k
t1
L_(jc)
Qbc)(x+)
L(
c_
i-ic
(Z3)(x-
c
I