1. No category


COLLEGE
READINESS
STANDARDS
LEVEL
28‐32
PRACTICE
SUMMER
2011
BOA
601
‐
SOLVE
WORD
PROBLEMS
CONTAINING
SEVERAL
RATES,
PROPORTIONS,
OR
PERCENTAGES
BASIC/REVIEW
1. Last
season,
the
Olympic
Women’s
Beach
Volleyball
duo
of
Misty
May
and
Kerri
Walsh
won
55
of
their
games.
The
ratio
of
their
wins
to
losses
was
5
to
1.
This
season,
the
women
played
the
same
number
of
games
as
last
season,
but
had
8
more
wins.
What
is
the
ratio
of
their
wins
to
losses
for
this
season?
2. Stephanie
can
do
2
math
problems
in
10
minutes
and
Dillon
can
do
3
math
problems
in
the
same
amount
of
time.
How
many
total
math
problems
can
Stephanie
and
Dillon
do
in
2
½
hours?
3. Kayla’s
chemistry
teacher
asked
her
to
find
the
number
of
atoms
in
22
grams
of
copper.
Use
the
following
information
to
help
Kayla
out:
63.5
grams
of
copper
=
1
mole
of
copper
1
mole
=
6.02
x
1023
atoms
of
copper
FOCUS
4.
Use
the
following
conversions
to
solve
the
problems:
1
km
=
0.6214
mi
1
gal
=
3.7854
liters
a. Ms.
Bujdei
went
to
Europe
last
summer
and
traveled
345
km
in
6
hours.
What
was
her
average
speed
in
miles/hour?
b. In
America,
a
car's
gasoline
efficiency
is
measured
in
miles/gallon.
In
Europe,
it
is
measured
in
km/L.
If
your
car's
gas
mileage
is
40.0
mi/gal,
how
many
liters
of
gasoline
would
you
need
to
buy
to
complete
a
142
km
trip?
5. Mrs.
Snow
is
shopping
for
a
new
laptop.
The
Apple
Store
has
the
one
she
wants
for
$949.99.
In
addition,
she
needs
to
buy
an
extra
memory
card
for
$49.99
and
the
extended
warranty
AppleCare
will
cost
her
$150.00.
Since
Mrs.
Snow
is
a
teacher,
Apple
will
give
her
15%
off
her
purchase
of
the
laptop
and
memory,
but
not
on
AppleCare.
If
the
sales
tax
is
9.75%
in
Cook
County,
what
will
be
the
total
cost
of
the
laptop?
6. For
every
four
girls
registered
for
summer
school,
there
are
five
boys
registered.
If
the
principal
has
set
summer
staffing
levels
at
one
teacher
for
every
27
students,
and
there
are
252
girls
registered
for
summer
school,
how
many
teachers
does
the
principal
need
to
hire?
7. Ann
and
Bob
have
started
their
own
business
making
hand‐made
greeting
cards.
Ann
can
make
a
card
in
ten
minutes
while
it
takes
Bob
six
minutes
to
make
the
same
card.
They
recently
received
an
order
for
90
custom
cards.
If
they
start
working
on
the
order
together
at
7:30
am
and
take
one
15
minute
break
at
9:00
am,
at
what
time
will
the
finish
the
order?
8. Dr.
Anderson
has
ordered
a
special
medicine
from
Europe.
It
comes
with
strict
instructions
to
use
32
milliliters
per
kilogram
that
the
patient
weighs.
However,
all
of
Dr.
Anderson’s
scales
only
tell
weight
in
pounds.
So,
he
wants
to
know
ho
many
milliliters
per
pound
he
should
use.
There
are
approximately
0.4536
kilograms
in
one
pound.
A
patient
weighing
167
pounds
needs
the
special
medicine.
How
many
mL
of
the
special
medicine
should
Dr.
Anderson
give
the
patient?
PSD
601
–
CALCULATE
OR
USE
A
WEIGHTED
AVERAGE
BASIC/REVIEW
1. In
Ethan’s
English
class,
homework
counts
for
20%
of
the
semester
grade,
quizzes
for
40%,
tests
for
30%,
and
projects
for
10%.
Ethan’s
current
homework
average
is
an
85.6%,
his
quiz
grade
is
a
94%,
his
test
average
is
an
87.6%
and
he
has
had
no
projects
assigned.
What
is
Ethan’s
current
English
grade?
2. Mr.
Wills
drove
2
hours
to
get
from
Arlington
Heights
to
Rockford.
He
traveled
at
65mph
for
40
minutes,
50mph
for
25
minutes,
45mph
for
10
minutes,
55
mph
for
25
minutes,
and
60mph
for
20
minutes.
What
was
Mr.
Wills’
average
speed
for
the
trip?
FOCUS
3. In
Jack’s
math
class,
the
semester
grade
is
calculated
using
a
weighted
average.
Skill
Assessments
count
for
35%
of
the
grade,
45%
of
the
grade
is
tests,
and
20%
is
the
final.
If
Jack
currently
has
an
average
of
87%
on
his
tests,
and
a
93%
on
his
Skill
Assessments
grade,
what
does
he
need
on
the
final
to
earn
an
A
(90%)
in
the
class?
4. At
a
certain
company,
the
average
number
of
years
of
experience
for
the
company’s
employees
is
9.3
years.
The
average
number
of
years
of
experience
is
9.8
years
for
the
male
employees
and
9.1
years
for
the
female
employees.
If
there
are
52
male
employees
at
the
company,
what
is
the
ratio
of
the
number
of
the
company’s
male
employees
to
the
number
of
the
company’s
female
employees?
5. In
chemistry,
the
atomic
mass
of
an
element
is
the
weighted
average
of
the
mass
of
its
atoms.
What
is
the
atomic
mass
of
Hafnium
if
out
of
every
200
atoms,
10
have
mass
176.00
g/mol,
38
have
mass
177.00
g/mol,
54
have
mass
178.00
g/mol,
28
have
mass
179.00
g/mol,
and
70
have
mass
180.00
g/mol?
PSD
602
‐
INTERPRET
AND
USE
INFORMATION
FROM
FIGURES,
TABLES,
AND
GRAPHS
GRE
601
‐
INTERPRET
AND
USE
INFORMATION
FROM
GRAPHS
IN
THE
COORDINATE
PLANE
BASIC
1.
a. If
a
surveyed
person
is
chosen
randomly,
what
is
the
probability
that
they
attend
soccer
games?
(In
simplest
form)
b. What
is
the
ratio
of
the
total
number
of
people
who
attend
football
games
to
the
number
of
people
who
attend
high
school
sports
games?
(In
simplest
form)
2. The
following
graph
shows
the
speed
of
a
car
in
the
first
few
seconds
after
it
takes
off
from
a
stoplight.
a.
What
is
the
car’s
speed
4
seconds
after
it
takes
off?
b.
If
you
were
to
find
the
acceleration
of
the
car,
what
is
the
mathematical
term
for
what
you
would
be
finding
?
c.
What
is
the
rate
of
acceleration
per
second
of
the
car?
3.
The
table
below
represents
the
number
of
people
at
the
home
football
game
at
various
times
during
the
game.
Use
this
information
to
answer
the
questions
that
follow.
Time
Number
of
People
a)
How
many
more
people
were
in
the
stadium
at
7:15
than
there
were
6:00
22
at
6:30?
6:30
410
7:00
1730
b)
Over
which
interval(s)
of
time
was
the
number
of
people
in
the
7:15
1990
stadium
decreasing?
7:30
2015
8:00
2058
c)
During
which
time
period(s)
must
there
have
been
2,050
people
in
8:30
1546
the
stadium?
Justify
your
answer.
9:00
1835
CONTEXT
4.
Jonathan
leaves
his
house
in
the
morning
for
a
quick
run.
After
10
minutes
of
running,
Jonathan
stops
at
iHOP
to
grab
breakfast
with
his
friends.
40
minutes
later,
Jonathan
takes
20
minutes
to
walk
back
home.
Which
of
the
following
graphs
shows
Jonathan’s
distance
from
his
house
for
the
70
minutes?
A.
B.
C.
D.
E.
5. The
table
and
graph
below
shows
data
about
Elk
Grove
High
School
juniors
taking
the
Math
portion
of
the
ACT
from
2006‐2010.
a.
The
federal
No
Child
Left
Behind
law
mandates
that
in
order
to
fulfill
adequate
yearly
progress
(AYP),
a
certain
percentage
of
students
must
meet
or
exceed
standards
in
each
subject
area.
Each
year,
the
percentage
gets
higher.
Indicate
for
each
year
whether
or
not
the
junior
class
made
AYP
in
Math.
YEAR
2002
2003
2004
2005
2006
2007
2008
2009
2010
%
REQUIRED
FOR
AYP
40
40
40
47.5
47.5
55
62.5
70
77.5
%
MEET
OR
EXCEEDS
MADE
AYP?
b.
Based
on
the
information
above,
write
three
conclusions
you
can
make
about
the
requirements
for
AYP
and
EG’s
performance
since
2002.
6. Karen
went
on
a
200
mile
road
trip,
leaving
from
home
at
noon.
The
graph
at
right
shows
Karen’s
distance
from
home
(in
miles)
as
she
traveled
for
6
hours.
Make
up
a
story
that
accounts
for
the
6
distinct
parts
of
her
trip.
In
particular,
be
sure
to
identify
the
speed
at
which
she
traveled
and
what
you
think
her
average
speed
was.
200
180
160
140
120
Distance
100
80
60
40
20
-1
1
-20
2
Time
3
4
5
6
7.
In
the
year
1995,
there
were
1.5
million
kids
playing
video
games.
In
the
year
1997
there
were
3
million
kids
playing
video
games,
and
in
1999
there
were
6
million.
a.
Make
a
table
of
values
for
the
data
above.
Use
the
pattern
to
predict
the
number
of
kids
playing
video
games
in
2001,
2003,
and
2005.
22
20
18
16
14
12
10
8
6
4
2
b.
Make
a
scatterplot
of
your
points.
Label
your
axes!
5
10
15
20
c.
What
type
of
function
does
your
graph
look
like?
c. Write
the
equation
of
the
function.
Let
t=0
represent
the
year
1995,
t=2
represent
1999,
and
so
on.
8.
Answer
the
questions
about
f(x)
graphed
below.
a. What
is
the
approximate
relative
maximum
of
f(x)
on
the
interval
[‐10,10]?
b. How
many
solutions
does
f(x)
have
on
the
interval
[‐
10,10]?
Estimate
the
solutions.
c. Approximate
f(‐6)
and
f(2).
PSD
603
–APPLY
COUNTING
TECHNIQUES
BASIC
1. Ms.
Washington
has
9
dress
shirts,
4
pairs
of
dress
pants,
5
pairs
of
work
shoes,
and
5
necklaces.
How
many
different
outfits
can
she
make?
2. Carmen
bought
a
new
lock
for
her
gym
locker.
It
has
the
numbers
1‐9
on
it
and
she
is
able
to
make
up
her
own
combination
of
4
digits,
which
may
be
repeated.
How
many
different
combinations
can
she
choose
from?
3. Jason
also
bought
a
new
lock.
His
lock
has
the
digits
0‐9
on
it,
but
digits
may
not
be
repeated.
How
many
different
combinations
can
Jason
choose
from?
FOCUS
4. Jasper
and
Scot
are
two
candidates
out
of
14
who
can
be
chosen
for
a
special
project
requiring
two
people.
What
are
the
chances
that
they
are
chosen?
5. The
teachers
at
EGHS
must
change
their
net
login
passwords
once
a
year.
The
password
must
consist
of
6
letters,
2
numbers
(0
–
9),
and
1
special
symbol
(12
to
choose
from).
Jack
thinks
this
will
be
an
easy
password
to
hack.
If
he
types
in
a
random
password
meeting
these
requirements,
what
is
the
probability
that
he
will
get
it
right?
6. The
student
council
is
in
the
process
of
choosing
new
officers.
They
are
voting
in
the
roles
of
President,
Vice
President,
Treasurer,
and
Secretary.
If
there
are
27
students
in
the
student
council,
how
many
different
combinations
of
officers
are
there?
7. Mr.
Carlson
put
the
names
of
his
46
students
in
a
hat.
Mr.
Carlson
has
19
juniors
and
27
sophomores.
a. If
Mr.
Carlson
draws
two
names
out
of
the
hat,
how
many
different
combinations
of
two
names
can
he
have?
b. Mr.
Carlson
wants
to
draw
the
names
of
one
sophomore
and
one
junior
student.
How
many
of
these
combinations
are
there?
PSD
604
‐
COMPUTE
A
PROBABILITY
WHEN
THE
EVENT
AND/OR
SAMPLE
SPACE
ARE
NOT
GIVEN
OR
OBVIOUS
BASIC
1. Point
Q
is
randomly
chosen
on
JM .
Find
the
probability
that
point
Q
is
on
JL .
!
J
"
K
#
L
2. Find
the
probability
that
a
dart
thrown
at
the
figures
shown
below
lands
in
the
shaded
area.
Express
your
answers
in
simplest
exact
form.
a.
b.
c.
M
3. What
is
the
probability
that
the
spinner
lands
on
2
or
3
points?
FOCUS
4. The
stop
light
at
the
corner
of
Arlington
Heights
Rd.
and
Golf
Rd.
changes
every
4
minutes.
If
you
arrive
at
a
random
time,
what
is
the
probability
that
you
will
wait
more
than
3
minutes?
5. Two
circles
painted
on
a
dartboard
are
tangent
to
each
other.
The
center
of
the
larger
circle
lies
on
the
smaller
circle.
Find
the
probability
that
a
dart
landing
inside
the
larger
circle
lands
inside
the
smaller
circle
as
well.
Give
your
answer
as
a
reduced
common
fraction.
7. The
diameter
of
the
bulls‐eye
is
6
cm.
The
radius
of
the
middle
circle
is
5
cm.
The
radius
of
the
outer
circle
is
8
cm.
What
is
the
probability
that
a
dart
thrown
at
the
board
will
land
anywhere
inside
the
middle
circle
but
not
on
the
bulls‐eye
(meaning
the
unshaded
area)?
8. A
dartboard
is
in
the
shape
of
a
square
with
an
inscribed
cross
as
shown
below.
Each
of
the
8
vertices
of
the
cross
that
are
on
a
side
of
the
square
is
located
at
a
trisection
point
of
the
side
of
the
square.
The
sides
of
the
square
are
9
inches
long.
If
a
dart,
thrown
at
this
dartboard
is
equally
likely
to
hit
at
any
point
of
the
dartboard,
what
is
the
probability
that
the
dart
will
land
inside
the
cross?
Give
an
exact
answer.
9. You
and
a
friend
agree
to
meet
at
The
Olive
Garden
between
6:00
and
7:00
pm.
The
one
who
arrives
first
will
wait
20
minutes
for
the
other
after
which
the
first
person
will
leave.
What
is
the
probability
that
the
two
of
you
will
actually
meet,
assuming
that
your
arrival
times
are
random
within
the
hour?
(Use
the
graph
below
to
help
you.
Note:
the
two
shaded
areas
both
indicate
you
will
meet
and
the
unshaded
areas
indicate
you
will
not
meet).
60
55
50
45
40
35
Y Axis
6. Point
P
lies
on
side
CD
of
rectangle
ABCD,
where
CD
is
opposite
AB.
If
PC
=
(2)(PD),
find
the
probability
that
a
point
inside
quadrilateral
ABCP
is
also
inside
triangle
ABP.
Give
your
answer
as
a
reduced
common
fraction.
30
t
st
25
u
Yo
20
riv
ar
e
fir
es
s
fir
riv
ur
nd
ar
ie
fr
Yo
15
10
5
0
0
5
10
15
20
25
30
X Axis
35
40
45
50
55
60
NCP
601
‐
APPLY
NUMBER
PROPERTIES
INVOLVING
PRIME
FACTORIZATION
BASIC
1. What
is
the
prime
factorization
of
72?
2. Which
of
the
following
numbers
has
the
smallest
prime
factor?
a)
55
b)
57
c)
58
d)
59
e)
61
FOCUS
3. If
the
sum
of
two
positive
prime
numbers
is
prime,
then
one
of
those
two
numbers
must
be
what
number?
4. For
2⋅3 ⋅ ab ⋅ 3⋅5 to
be
a
rational
number,
with
a
and
b
representing
positive
prime
numbers,
the
sum
of
a+b
must
be
what?
5. What
is
the
smallest
positive
integer
k
such
that
the
product
1575k
is
a
perfect
square?
NCP
602
‐
APPLY
NUMBER
PROPERTIES
INVOLVING
EVEN/ODD
NUMBERS
AND
FACTORS/MULTIPLES
BASIC
1. If
a
is
odd
and
the
product
of
a
and
b
is
even,
what
must
be
true
about
b?
2. The
larger
of
two
consecutive
odd
integers
is
three
times
the
smaller.
What
is
their
sum?
3. If
a is
a
multiple
of
3,
b is
a
multiple
of
2,
what
must
be
factors
of
the
product
ab .
4. If
a is
a
multiple
of
b and
both
are
positive
integers,
what
is
the
greatest
common
factor
of
72a and
120b .
5. Let
m and
n be
positive
integers.
If
m + n is
odd
and
mn is
even,
which
of
the
following
can
be
true?
I.
m is
odd
and
n is
even
II.
m is
even
and
n is
odd
III.
m is
odd
and
n is
odd
6. Given
that
12
is
a
factor
of
30x,
where
x
is
a
positive
integer,
what
must
be
a
factor
of
x?
FOCUS
7. Given
that
a
is
an
even
integer
and
that
b
is
a
positive
odd
integer,
is
ab
even
or
odd?
Justify
your
answer.
8. Given
the
two
expressions
3p+4q
and
6(2q+3p),
which
of
the
two
must
be
even
for
all
integers
p
and
q?
Explain
your
reasoning.
9. For
all
integers
k,
is
the
expression
2k+3
even
or
odd?
Explain
your
reasoning.
10. Given
that
k
is
an
integer,
determine
if
the
product
of
2k
and
2k+1
must
be
even,
must
be
odd,
or
is
unable
to
be
determined.
Explain
your
reasoning.
11. If
(15ab)(ab)=540,
then
what
is
the
value
of
a+b
?
12. If
x
=
233a42
and
x
is
a
multiple
of
18,
what
is
the
smallest
possible
integer
value
for
a?
NCP
603
‐
APPLY
NUMBER
PROPERTIES
INVOLVING
POSITIVE/NEGATIVE
NUMBERS
BASIC
1. What
is
the
least
possible
value
of
xy
if
‐6
≤
x
≤
‐4
and
‐4
≤
y
≤
3?
2. What
is
the
greatest
possible
value
of
x
–
y
if
‐2
≤
x
≤
3
and
‐4
≤
y
≤
4?
3. If
x
and
y
are
reciprocals
and
x
>
1,
then
what
must
be
true
about
y?
4. If
x
is
an
integer
less
than
0,
what
is
the
least
possible
value
of
x 2 − 6x + 5 ?
5. If
a
and
b
are
real
numbers
and
a
<
0
and
b
<
a.,
would
the
sum
of
a
+
b
be
positive
or
negative?
FOCUS
6. If
a
and
b
are
real
numbers
and
a
>
0
and
b
<
a,
would
the
product
of
a•b
be
always
positive,
sometimes
positive,
or
never
positive?
7. If
4a=5b=3c,
and
a>0,
arrange
a,b,
and
c
in
order
from
largest
to
smallest.
a+b
8. Let
*
be
an
operation
defined
on
the
real
numbers
by
a*b =
.
Which
of
the
following
is
(are)
true
2
for
all
real
numbers
a,
b,
and
c?
i. a
*
b
=
b
*
a
ii. (a
*
b)
*
c
=
a
*
(b
*
c)
iii. 0
*
c
=
0
NCP
604
–
APPLY
RULES
OF
EXPONENTS
BASIC
1. If
x
is
an
integer
and
x
<
0,
then
which
expression
is
the
least?
The
greatest?
x5
x‐5
x8 x‐8
‐x8
3
2. Which
of
the
following
expressions
is
equivalent
to
( 2x ) ?
A)
8x B)
2x 3 C)
5x 3 D)
6x 3 E)
8x 3 Explain
why
choice
B
is
incorrect:
3. Simplify
the
following
expressions:
a 8b −2
a3 m 2 m 2 n 3 n 3 n 3 14y −2
7y 4 1
2 2
(3 )
1
1
1
1
1
−2
 3a 7b −9 c 0 
 6a 3a 2b 3c −8  2
( 9x y )
(
1
b 3 ⋅ b 4 1
2 2
6
64x 9 y 24
)
1
3
4. Simplify
the
following
exressions.
Rationalize
as
needed.
3
40a 6b10 c (
)
2 5 3 10 − 6 20 + 8 − 16 2
4
9 24
3
1
−4 5
3 + 2
5
4+ 2
5.
9 ,
5 2 ,
32 ,
6 ,
and
10 2 are
the
five
sides
of
a
pentagon.
In
exact
simplified
form,
state
the
perimeter
of
this
pentagon.
FOCUS
( )
6.
If
x 2
3
= x p for
all
x ≥ 0 ,
then
p 2 = ? A)
36
B)
25
C)
6
D)
5
E)
12
7.
Rewrite
3 27x 2 y 2 in
simplified
exponent
form.
(
8.
Convert
64a 6b 3c 0
)
1
3
to
radical
form
and
simplify
completely.
1
9.
Simplify
 13
10 ⋅  64 2 


5
1
2
using
rules
of
exponents.
10.
What
expression
would
you
multiply
4x 2 y by
to
get
a
product
of
20x 7 y 3 ?
34x a y 7 z −3
11. If
72 can
be
simplified
in
the
form
a b ,
simplify
completely.
17x b y 0 z 9
12. If
2a3b ⋅5⋅7 = 2520 ,
what
is
the
value
of
(2a )b ?
NCP
605
–
MULTIPLY
TWO
COMPLEX
NUMBERS
BASIC
1. Find
the
product
of
(3
+
4i)
and
(‐2
–
6i).
 1 
3 
3.
Find
the
product
of
 − + i   2 − i  4 
4 

3
5
2.
Simplify
7i ⋅ 2i completely.
4.
Evaluate
−1
2
( )
−1
2
( −1)
FOCUS
4.
Find
the
product
of
the
solutions
of
the
following
equations:
‐2
=
x2
+
4x
and
2x2
=
3x
–
4
5. Two
complex
conjugates
have
a
product
of
25
and
a
sum
of
6.
What
are
the
two
numbers?
6. Simplify
3i + 6 + −49 − 5i + i 2 + 11i 7. If
f(x)
=
2x3
–
4x2
+
x
–
3,
find
f(2
+
i)
3
 1
3 
8. Show
that
 − +
i = 1 2 2 

9. Simplify
the
following:
3 + 2i
4 − 8i  1 
 − 4 + i 

3   2 − 4 i 
XEI
601
–
MANIPULATE
EXPRESSIONS
AND
EQUATIONS
BASIC
1. Write
the
following
in
slope
–
intercept
form:
a. 3x
–
5
(y
+
9)
=
14
2y − 4x
= −2 4
b.
2k
2. a.
Solve
Q = for
v.
v
d
b.
Solve
s = for
t.
t
kq q
c.
Solve
F = 12 2 for
r.
r
3. Solve
the
equation
v 2 = v02 + 2ax − 2ax0 for
a.
FOCUS
µI
4. The
magnetic
field
of
a
long
straight
wire
is
found
using
the
formula
B = 0 .
Solve
this
equation
for
r.
2π r
3 2
7
5. Solve
the
equation
− = − for
x.
2
x y
3
6. Solve
for
r
in
the
equation
r + 9 s = 21 .
7. Suppose
that
x
=
3
–
4t
and
y
=
5
+2t.
Find
x
in
terms
of
y.
b
b
8. Solve
for
c
in
terms
of
a
and
b
given
that
a + = a
.
c
c
9. If
the
ratio
of
2x
–
y
to
x
+
y
is
2
:
3,
find
the
ratio
x
:
y.
XEI
602
‐
WRITE
EXPRESSIONS,
EQUATIONS,
AND
INEQUALITIES
FOR
COMMON
ALGEBRA
SETTINGS
BASIC
1.
Lady
Gaga
is
4/5
as
old
in
2010
as
she
will
be
6
years
from
now.
a. Write
an
equation
to
model
the
situation.
b. Solve
the
equation
to
find
Lady
Gaga’s
current
age.
2.
Anthony
wanted
to
work
out
during
the
off‐season.
He
went
to
X‐Fitness
where
he
found
a
one
year
membership
that
cost
$360
for
the
year
plus
$1.50
for
each
visit.
He
then
went
to
Bally
Total
Fitness
who
offered
him
a
$250
membership
plus
$2
for
each
visit.
a.
Write
two
expressions
representing
each
gym’s
prices.
b.
How
many
times
would
Anthony
need
to
work
out
in
one
year
in
order
to
pay
the
same
amount
for
both
memberships?
c.
Anthony
chose
Bally
Total
Fitness.
He
worked
out
210
times
in
one
year.
Did
he
choose
the
right
gym?
3. In
Carlee’s
math
class,
only
five
chapter
exams
are
given
and
an
80%
average
must
be
achieved
in
order
to
pass
the
course.
Carlee
has
completed
the
first
four
exams
with
scores
of
73,
82,
79,
and
84.
Write
an
inequality
that
represents
the
minimal
score
m
Carlee
can
get
on
the
fifth
exam
in
order
to
pass
the
class.
FOCUS
4.
Each
element
in
a
data
set
is
multiplied
by
3
and
each
resulting
product
is
then
decreased
by
2.
If
m
is
the
mean
of
the
final
data
set,
write
an
expression
for
the
mean
of
the
original
set
in
terms
of
m.
5.
a.
Write
an
inequality
that
represents
the
diagram.
x + 12
3x
40
b.
Solve
the
inequality
for
x.
6.
If
the
perimeter
of
the
rectangle
is
at
least
62
cm.,
what
are
the
possible
values
of
its
area?
2x + 3
x-5
7.
The
following
table
shows
the
tolls
charged
at
exits
that
are
various
distances
from
the
eastern
end
of
a
tollway.
Exit
number
1
2
3
4
5
6
7
Miles
from
east
end
25
60
84
130
155
180
210
Toll
(dollars
1.25
3.75
4.00
6.00
7.25
8.50
9.75
a. Use
a
calculator
to
make
a
scatterplot
of
the
data.
Describe
any
correlation
in
terms
of
the
problem.
b. Use
your
calculator
to
determine
the
equation
of
the
best
fit
model.
c. A
new
tollway
exit
is
to
be
built
100
miles
from
the
east
end.
What
should
the
toll
at
that
exit
be?
XEI
603
‐
SOLVE
LINEAR
INEQUALITIES
THAT
REQUIRE
REVERSING
THE
INEQUALITY
SIGN
GRE
602
‐
MATCH
NUMBER
LINE
GRAPHS
WITH
SOLUTION
SETS
OF
LINEAR
INEQUALITIES
BASIC
1.
Solve
the
following
inequalities
and
graph
the
solutions
on
the
number
line.
5
1
>− p
a.
−2 ≤ 10 − 4x b.
3
6
c. −4 < −4(x + 5) < 8 d.
2. For
what
values
of
x
is
the
quantity
2 x − 3 between
7
and
2x + 3 > 6
or
3‐2x<7 21
?
2
3. Which
of
the
following
number
line
graphs
shows
the
solution
set
of
3(x + 2) + 1 ≤ 4x + 15 ?
4. Solve
the
following
inequality.
Express
your
answer
in
interval
notation
and
graph
the
solution
set:
2x − 1
−3 <
<0
4
FOCUS
5. Given
the
inequality
x 2 − 3x − 10 ≥ 0 ,
a. Solve
and
graph
the
inequality
on
the
number
line.
b. Write
the
solution
in
interval
notation.
6. Find
all
values
of
r
that
satisfy
the
inequality
r 2 − 4r < 12 .
7. Solve
and
graph
the
solutions
for
the
inequality
(2x
–
1)(x
+
1)(x
+
7)
>
0
8. If
a>b>c>d,
then
which
is
larger,
a
+
c
or
b
+
d?
XEI
604
–
SOLVE
ABSOLUTE
VALUE
EQUATIONS
BASIC
1. Define
absolute
value
in
terms
of
distance.
2. Explain
why
x = −x 3. Solve
the
equation
9 − x = 5 and
graph
the
solutions
on
a
number
line.
4. Solve
the
equation
− 3x + 5 = x − 9 for
x
and
graph
the
solutions
on
a
number
line.
3x
+ 12 − 16 = 14 ,
for
x.
5. Solve
3
4
6. Determine
which
of
the
following
are
always
true.
Write
TRUE
or
FALSE.
For
those
that
are
FALSE,
provide
a
counter‐example
(a
specific
example
that
proves
the
statement
false)
A.
a = a _________________
B.
a − b = b − a _________________
D.
ab = a i b _________________
F.
x − y = x − y _________________
G.
− a = −a _________________
H.
− a + b = −a − b _________________
C.
a + b = a + b _________________
2
E.
a = a 2 _________________
FOCUS
7.
Is
π 2 −10 equal
to
π 2 −10
or
10 − π 2 ?
8.
The
perimeter
of
triangle
ABC
is
88
meters.
Find
x.
6 x+1
2 x+1
3 x+1
B
A
C
9.
Solve
the
equation
x + 2 + x + 5 = 8 graphically.
10.
If
x − 2 = p where
x
<
2,
then
which
of
the
following
expressions
must
equal
x
–
p?
A) ‐2
B) 2
C) 2
–
2p
D) 2p
–
2
E)
2p − 2 XEI
605
–
SOLVE
QUADRATIC
EQUATIONS
BASIC
1.
What
is
a
quadratic
function?
2.
List
the
different
names
for
the
solutions
of
a
quadratic
equation.
Give
an
explanation
for
each
name.
3.
List
the
different
methods
you
know
to
solve
quadratic
equations.
4.
How
can
you
tell
how
many
real
solutions
a
quadratic
has
by
looking
at
its
graph?
Solve
the
quadratic
equations
using
any
method.
3
5.
x 2 + 3x = 18 6.
x 2 + x = 1 2
3r − 2 6r − 9
=
7.
8.
!2x 2 + 12x !16 = 0 2r + 1 4r + 3
9.
16x 2 ! 48x = !27 10.
5(x − 4)2 = 45 2
= 1
11.
41! (x + 6) 2 = 5 12.
5
3x +
x
FOCUS
13.
A
rectangle
has
an
area
of
60in2.
Find
the
value
of
x
if
the
length
is
2(x
–
1)
and
the
width
is
5(x
–
2).
14.
Given
square
GABE
inscribed
in
circle
S.
a. Write
simplified
expression
for
the
area
of
the
shaded
region.
A
G
4x
S
E
b.
If
the
area
of
the
shaded
region
is
30
square
units,
find
x
to
the
nearest
tenth.
B
15.
Given
f(x)
and
g(x)
graphed
below.
12
10
a. Write
the
product
of
f(x)
and
g(x)
in
standard
form.
6
g(x)
f(x)
4
2
Y Axis
8
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
b.
What
is
the
sum
of
the
roots
of
f (x)ig(x) 16.
At
the
EG
fireworks
show,
a
rocket
is
fired
from
a
50
ft.
tower.
The
rockets’
height
in
feet
after
s
seconds
is
given
by
the
equation
h(t) = 50 +100s −16s 2 .
a. Find
the
maximum
height
of
the
rocket.
Explain
the
method
you
used.
b. After
how
many
seconds
does
the
rocket
hit
the
ground?
-8
-10
X Axis
17.
Solve
the
equation
modeled
by
the
following
set
of
points.
Explain
the
method
you
used
to
solve
it.
x
‐15
‐7
‐2
3
8
13
y
204
36
‐4
6
66
176
6
= 5 .
18.
Find
all
solutions
to
x +10 −
x
+10
19.
A
quadratic
equation
has
solutions
x=‐4
and
x=7.
When
written
in
standard
form,
ax 2 + bx + c = 0 ,
the
equation
has
real
coefficients
a,
b,
and
c.
Find
the
product
abc.
20.
If
(x
+
6)
is
a
factor
of
3x 2 +16x + k ,
find
the
value
of
k.
XEI
606
–
FIND
SOLUTIONS
TO
SYSTEMS
OF
LINEAR
EQUATIONS
BASIC
1. Name
all
the
ways
you
know
how
to
solve
a
system
of
linear
equations.
2. Solve
each
system
by
hand.
 y = −5x + 4
a.

3x − 4 y = 12

1
 y − 4 = x − 21
b.

3
 x + 3y = 3

(
)
(
)
.25x − y = 16.5
c.
 1 1
 x+ y=2
6
3
d.
€
 3x −11y = 4

 3x −11y = 22
4x + y + 3z = 2

5x − y − 2z = −3

e.
3x + 2 y + 5z = 5 
a + b − c = 1

1
1
 a− b+ c = 3
2
3

f.
 1 2 1
 3 a + 3 b − 6 c = 2
3.
The
admission
fee
at
a
small
fair
is
$1.50
for
children
and
$4.00
for
adults.
On
a
certain
day,
2200
people
enter
the
fair
and
$5050
is
collected.
How
many
children
and
how
many
adults
attended?
1

4.
The
graphs
of
the
equations
−3ax + 5by = 14 and
2ax − 4by = −4 intersects
at
 , −1 .
Find
a and
b .
3 
5.
Mr.
Cannon
invested
$2500,
part
at
3%
interest
and
the
rest
at
2.4%
interest.
If
he
earned
$69.15
in
interest
the
first
year,
how
much
did
he
invest
at
each
rate?
FOCUS
6.
A
passenger
jet
took
three
hours
to
fly
1800
miles
in
the
direction
of
the
jetstream.
The
return
trip
against
the
jetstream
took
four
hours.
What
was
the
jet's
speed
in
still
air
and
the
jetstream's
speed?
7.
Suppose
you
are
flying
an
ultra‐light
aircraft.
You
fly
to
a
nearby
town,
18
miles
away.
With
a
tail
wind,
the
trip
takes
20
minutes.
Your
return
flight
with
a
head
wind
takes
3/5
hour.
Find
the
average
wind
speed
in
miles
per
hour.
8.
Marina
had
$24,500
to
invest.
She
divided
the
money
into
three
different
accounts.
At
the
end
of
the
year,
she
had
made
$1,300
in
interest.
The
annual
yield
on
each
of
the
three
accounts
was
4%,
5.5%,
and
6%.
If
the
amount
of
money
in
the
4%
account
was
four
times
the
amount
of
money
in
the
5.5%
account,
how
much
had
she
placed
in
each
account?
9.
A
circular
forested
area
is
bounded
by
the
equation
x2
+
y2
=
17.
A
straight
ATV
trail
running
through
the
forested
area
is
represented
by
x
+
y
=
5.
Graphically,
at
what
points
does
the
trail
enter
and
exit
the
forested
area?
10.
A
rectangle
has
a
perimeter
of
14
feet,
and
twice
its
length
(l)
is
equal
to
1
less
than
4
times
the
width
(w).
Write
and
solve
a
system
of
linear
equations
to
find
the
length
and
the
width
of
the
rectangle.
11.
Find
a,
b,
and
c
so
that
the
following
ordered
triples
will
be
solutions
of
the
given
equation
ax + 2 y − bz = c; (1,5,3) , ( 3,3,5) , ( 0, −3, −4 ) 12.
The
sum
of
the
length,
width,
and
height
of
a
rectangular
box
is
17
cm.
The
length
is
one‐third
the
height.
The
sum
of
the
length
and
height
exceeds
twice
the
width
by
2
cm.
Find
the
length,
width,
and
height
of
the
box.
13.
The
sum
of
three
numbers
is
12.
One
of
the
numbers
is
twice
the
sum
of
the
other
two
numbers.
This
same
number
is
also
equal
to
one
of
the
other
numbers
decreased
by
triple
the
third
number.
What
are
the
three
numbers?
GRE
603
–
USE
THE
DISTANCE
FORMULA
1. Show
that
the
points
(4,
7)
and
(7,
4)
are
equidistant
from
the
origin.
2. Determine
if
PB ≅ HI .
Assume
lattice
points.
3. What
kind
of
triangle
is
determined
by
the
points
(10,6),
(‐1,
2),
(13,
‐1)?
FOCUS
(x1, y2)
4. Write
an
expression
for
the
length
of
the
hypotenuse:
(x1, y1)
5. Given
AB as
shown
below
A
(2c, 9)
a)
Find
AB
B
(-2c, 5)
b)
Find
AB
if
c
=
2.
c)
Find
c
if
AB
=
4 37 (x2, y1)
6. The
point
(5,
y)
is
equidistant
from
(1,
4)
and
(10,
‐3).
Find
y.
7. Find
all
x
such
that
the
point
(x,
3)
is
5
units
away
from
(‐1,
7).
8. Find
the
distance
between
the
line
3x
–
4y
+
6
=
0
and
the
point
(‐6,
2).
(
)
(
)
9. Find
the
exact
distance
between
3 2,8 3 and
6 2,5 3 .
GRE
604
‐
USE
PROPERTIES
OF
PARALLEL
AND
PERPENDICULAR
LINES
TO
DETERMINE
AN
EQUATION
OF
A
LINE
OR
COORDINATES
OF
A
POINT
BASIC
1. What
is
the
slope
of
a
line
perpendicular
to
the
line
with
equation
16
=
‐5y
+
3x
?
2. Given
1 is y = −
1
x − 3
3
a. Write
the
equation
of
the
line
parallel
to
1 passing
through
(3, −2) .
b. Write
the
equation
of
the
line
perpendicular
to
1 passing
through
the
point
(3, −2) FOCUS
3. Find
the
value
of
k
so
that
the
graphs
of
8y
=
kx
–
4
and
6x
+
24y
=
12
are
perpendicular.
4. John
and
Nick
marked
the
locations
of
their
respective
offices
on
a
map.
John
marked
(‐15,
86)
and
Nick
marked
(25,
206).
a. Write
an
equation
in
slope‐intercept
form
that
models
the
line
between
the
offices
of
John
and
Nick.
b. A
new
shopping
complex
is
being
built
on
the
line
that
is
the
perpendicular
bisector
of
the
line
joining
the
offices
of
John
and
Nick.
Write
the
equation
of
the
line
on
which
the
shopping
complex
is
being
built.
(Leave
exact
numbers,
not
decimal
approximations).
c.
Who
is
closer
in
distance
to
the
shopping
complex,
John
or
Nick?
5.
The
tangent
line
to
a
circle
is
defined
as
a
line
that
intersects
a
circle
at
one
point
and
is
perpendicular
to
2
(
) (
)
2
the
radius
segment
to
the
point
of
tangency.
Given
the
equation
x − 4 + y − 6 = 100 ,
write
the
equation
of
a
line
tangent
to
the
circle
at
(10,
‐2).
6.
Point
P
has
coordinates
(7,
5);
Q
has
coordinates
(‐2,
8).
If
M
has
coordinates
(a,
2)
and
N
has
coordinates
(5,
2a),
what
is
the
value
of
a
for
which
the
line
MN
is
perpendicular
to
the
line
PQ?
7.
In
the
diagram,
AD ⊥ BC .
A (4, 5)
a. Find
the
value
of
k.
B (6, 3)
b. Find
the
area
of
triangle
ABC.
C (-2, 1)
D: (k, -2)
8. Given
that
P
=
(−1,−1),
Q
=
(4,
3),
A
=
(1,
2),
and
B
=
(7,
k),
find
the
value
of
k
that
makes
the
line
AB
a)
parallel
to
PQ;
b)
perpendicular
to
PQ.
6
4
2
-5
5
-2
-4
10
GRE
605
‐
RECOGNIZE
SPECIAL
CHARACTERISTICS
OF
PARABOLAS
AND
CIRCLES
(E.G.,
THE
VERTEX
OF
A
PARABOLA
AND
THE
CENTER
OR
RADIUS
OF
A
CIRCLE)
BASIC
1.
Explain
how
to
find
the
vertex
and
line
of
symmetry
for
each
of
the
following
forms
of
a
quadratic
function:
Vertex
form:
f(x)
=
a(x
–
h)2
+
k
Standard
form:
f(x)
=
ax2
+
bx
+
c
Factored
form:
f(x)
=
a
(x
–
x1)
(x
–
x2)
2.
Given
the
function
f (x) = x 2 − 6x − 7 ,
find
the
line
of
symmetry
and
the
vertex.
3.
What
is
the
absolute
maximum
of
the
function
f (x) = −2x 2 − 9x + 24 ?
4.
Write
the
equation
of
the
quadratic
function
in
standard
form
whose
vertex
is
at
(3,
‐4)
and
goes
through
the
point
(4,‐1).
5.
Find
the
center
and
the
radius
of
the
circle
given
by
the
equation
(x − 3)2 + (y + 5)2 = 36 .
6.
Write
the
equation
of
a
circle
that
is
centered
at
(5,0)
with
a
radius
of
4.
7.
Write
the
equation
of
a
circle
that
is
centered
at
(‐3,4)
and
goes
through
the
point
(2,1).
8.
Write
the
equation
of
the
quadratic
function
with
a
vertex
at
(2,
3)
and
a
y‐intercept
of
(0,7).
(
2
) (
)
2
9.
What
is
the
length
of
the
diameter
of
a
circle
modeled
by
the
equation
x − 2 + y + 3 = 9 ?
CONTEXT
10.
A
volleyball
is
hit
upward
by
a
player
in
a
game.
The
height
h
(in
feet)
of
the
volleyball
after
t
seconds
is
given
by
the
function
h = −16t 2 + 30t + 6 .
a)
What
is
the
maximum
height
the
volleyball
reaches?
b)
At
what
time(s)
does
the
ball
reach
15
ft?
c)
After
how
many
seconds
does
the
volleyball
hit
the
ground?
11.
The
minimum
of
f (x) = 2x 2 − 8x − 11 and
the
point
(6,13)
form
the
diameter
of
a
circle.
Find
the
equation
of
the
circle.
12.
Given
the
rectangle
ABCD
find
the
value
of
x
that
forms
the
max
area.
16 - x
What
is
the
max
area?
A
B
x-1
D
C
13.
Dan
is
planting
a
vegetable
garden.
He
wants
to
plant
six
different
vegetables
so
he
will
put
5
partitions
in
the
garden.
If
he
has
exactly
350
feet
of
fencing
to
use,
what
is
the
maximum
area
of
the
garden
he
can
plant?
14.
Write
the
standard
form
equation
of
the
circle
given
by
x 2 + 8x + y 2 − 12y − 10 = 2 PPF
601
‐
APPLY
PROPERTIES
OF
30°‐60°‐90°,
45°‐45°‐90°,
SIMILAR,
AND
CONGRUENT
TRIANGLES
BASIC
1. Find
the
value
of
each
variable.
Write
answers
in
simplest
radical
form.
a.
b.
c.
2. The
altitude
of
an
equilateral
triangle
is
10.
Find
the
exact
perimeter
of
the
triangle.
3. Find
the
value
of
x
in
the
figures
below.
4. A
building
that
is
8.5
meters
tall
casts
a
shadow
that
is
20
meters
long.
At
the
same
time,
a
flagpole
casts
a
shadow
that
is
6.5
meters
long.
Find
the
height
of
the
flagpole.
5. PENTA~QUICK.
Find
the
values
of
x
and
y.
Be
careful!
21
P
84°
E
K
136°
90°
20
16 3y+8°
N
Q
C
14
2x+12
118°
A
18
112°
T
U
I
!"#
6. Dexter
is
standing
4
ft
away
from
a
tree
that
is
12
ft.
tall.
Dexter
is
5
½
ft.
tall.
!
a. How
long
is
Dexter’s
shadow?
!"#
!
!"#$
b. How
long
is
the
tree’s
shadow?
#
!
!"#
!"#
$
$
%
"#$!%&
!"#
!"#$
7. Triangles
OMG
and
RAT
are
similar.
The
perimeter
of
the
smaller
triangle
OMG
is
135.
The
lengths
of
two
corresponding
sides
on
the
triangles
are
45
and
270.
What
is
the
perimeter
of
RAT?
!
!"
CONTEXT
!
!"#
8. Find
the
coordinates
of
point
G
in
each
figure.
(Note:
circles
and
angles
are
graphed
in
the
standard
x‐y
!
"
coordinate
plane)
"
A
!
#
A
G (?, ?)
!"#
G (?, ?)
!"#$%&
D
C
10. Find
the
perimeter
of
the
isosceles
trapezoid
shown
below.
J
!"#$
D
B
B
9. Sketch
the
largest
45°‐45°‐90°
triangle
that
fits
in
a
30°‐60°‐90°
triangle
so
that
the
right
angles
coincide.
What
is
the
ratio
of
the
area
of
the
30°‐60°‐90°
triangle
to
the
area
of
the
45°‐45°‐90°
triangle?
H
!"#
"#$%&'(
!"#$%&
D
!"
!"#
#$
I
K
!"
11. One
of
the
angles
of
a
rhombus
has
a
measure
of
120°.
If
the
perimeter
of
the
rhombus
is
24,
find
the
length
of
each
diagonal.
!"#
#$
!"#
!"#$%&
!"#$
12. Find
the
area
of
the
regular
hexagon.
(HINT:
split
the
hexagon
into
6
triangles.
What
kind
of
triangles
N
are
these?
Why?)
M
!"
13. ABCD
is
a
trapezoid
with
DC  AB .
Find
DC
and
BC.
#
C
D
!"#
!
A
!"#
B
!
A
!"
H
I
14. If
a
=
13,
and
b
=
5,
find
the
exact
values
of
x,
y,
and
z.
!"#
G (?, ?)
J
#$
!"#
C
"#$!%&
K
D
L
!"#$
B
!
N
!"
M
15. A
If BD is parallel to CE, find the
value of x.
!
3x-15
B
x+3
C
!"#
D
3x - 6
5x - 10
"
#
E
!
!
!
16. Given
ABC DEF ,
mA = 50, mD=2x+5y,
mF=5x+y,
mB=102‐x .
Find
the
measure
of
angle
F.
0
PPF
602
–
USE
THE
PYTHAGOREAN
THEOREM
BASIC
1. Which
of
the
following
sets
of
lengths
of
the
sides
of
triangles
that
can
represent
a
right
triangle?
3,
4,
5
24
10,
12,
15
3.4,
5.6,
5.9
4, 5,3 How
do
you
know
which
ones
represent
right
triangles?
2.
Find
the
length
of
the
missing
side.
a.
60
b.
c.
10
32
21
75
14
13
13
26
14
3. If
one
leg
of
a
right
triangle
measures
10
and
the
hypotenuse
measures
8 135 ,
find
the
length
of
the
other
leg
to
the
nearest
tenth.
4. In
the
figure
below,
MO
is
perpendicular
to
LN,
LO
=
4,
MO
=
ON,
and
LM
=6.
What
is
the
exact
length
of
MN?
5. A
submarine
travels
an
evasive
course
trying
to
outrun
a
destroyer.
It
travels
1
km
north,
then
1
km
west,
then
1
km
north
,
then
1
km
west
and
stops
because
it
has
reached
safety.
How
many
kilometers
is
the
sub
from
the
point
at
which
it
began?
M
N
L
O
6. An
explorer
hikes
4
miles
east,
7
miles
south,
then
3
miles
east,
then
1
mile
north,
and
finally
2
miles
west.
How
far
is
he
from
his
original
position?
7. Find
the
perimeter
of
an
isosceles
triangle
whose
base
is
16
cm
and
whose
height
is
15
cm.
8. Andrew’s
mom
drives
him
to
school
every
day
and
picks
up
Michael
on
the
way
on
some
days.
How
much
farther
does
Andrew’s
mom
have
to
drive
when
she
picks
up
Michael
on
the
way
than
if
she
just
drove
straight
to
school?
Michael
3 mi.
9 mi
School
2.5 mi
9. In
polygon
ABCDE
shown
below,
the
angles
at
A,
B,
and
E
are
right
angles.
What
is
the
perimeter
of
the
polygon,
in
feet?
10. Find
all
the
possible
side
measures
of
the
triangle
shown
below.
4x + 2
x+4
Andrew
4x
11. Two
horseback
riders,
Jackie
and
Katie,
set
out
to
ride
at
noon.
Jackie
leaves
at
a
bearing
of
140°
and
travels
at
an
average
speed
of
24
mph.
Katie
leaves
at
a
bearing
of
N50°E
and
travels
at
an
average
speed
of
32
mph.
How
far
apart
are
Katie
and
Jackie
at
1:30pm?
MEA
601
‐
USE
RELATIONSHIPS
INVOLVING
AREA,
PERIMETER,
AND
VOLUME
OF
GEOMETRIC
FIGURES
TO
COMPUTE
ANOTHER
MEASURE
BASIC
1. The
radius
of
a
circular
race
track
is
234
feet.
How
many
times
must
a
car
go
around
the
track
to
travel
10
miles?
2. A
square
has
a
perimeter
of
96
feet.
A
rectangle
with
the
same
area
has
a
base
with
length
20
feet.
What
is
the
rectangle’s
width
to
the
nearest
tenth
of
a
foot?
3. The
height
of
a
cylinder
is
30
cm.
Find
the
surface
area
of
the
cylinder
if
its
volume
is
750π cm3 .
4. A
cylindrical
glass
that
has
a
diameter
of
8
cm
and
a
height
of
15
cm
is
full
of
water.
The
water
is
poured
into
a
rectangular
pan
that
measures
15
cm
by
10
cm
by
5
cm.
Will
the
pan
overflow?
If
so,
by
how
much?
If
not,
how
much
space
is
left
in
the
pan?
5. The
diagonal
of
one
of
the
faces
of
a
cube
is
6
in.
long.
Find
the
total
surface
area
and
volume
of
the
cube.
6. The
sum
of
the
lengths
of
all
the
edges
of
a
cube
is
60
inches.
What
is
the
length
in
inches
of
the
diagonal
of
the
cube?
FOCUS
7. Given
cube
A
with
an
unknown
side
length,
find
the
ratio
of
the
volume
of
cube
A
to
cube
B
if
the
length
of
the
sides
of
cube
B
are
double
those
of
cube
A.
8. ABC
is
an
isosceles
right
triangle.
The
hypotenuse
AB
of
this
triangle
is
a
leg
of
a
second
coplanar
isosceles
right
triangle
ABD,
with
C
and
D
on
opposite
sides
of
AB .
If
AB
=
5 2 ,
find
the
area
of
quadrilateral
ACBD.
9. One
triangle
has
sides
13,
13,
and
10.
A
second
triangle
has
sides
12,
20,
and
16.
Find
the
ratio
of
their
areas.
10. A
plane
intersects
a
sphere,
forming
a
circle.
Find
the
exact
radius
of
the
circle
if
the
radius
of
the
sphere
is
6
and
the
center
of
the
sphere
is
3
units
away
from
the
plane.
11. A
circle
is
inscribed
in
a
square,
then
a
square
is
inscribed
in
this
circle,
and
finally,
a
circle
is
inscribed
in
this
square.
What
is
the
ratio
of
the
area
of
the
smaller
circle
to
the
area
of
the
larger
square?
12. A
cube
is
inscribed
in
a
sphere.
Find
the
ratio
of
the
surface
area
of
the
sphere
to
the
surface
area
of
the
cube.
FUN
601
‐
EVALUATE
COMPOSITE
FUNCTIONS
AT
INTEGER
VALUES
BASIC
1.
CONTEXT
2.
Given
the
following
functions,
f (x) = −2x 2 + 3 and
g(x) =
a. ( f g)(3) b.
(g  f )(−1) ( )
x
‐2
‐1
0
1
2
3
f(x)
1
2
3
4
5
6
g(x)
4
1
0
1
4
9
a.
( )
f g(3) (
h(x)
2
1
0
‐1
‐2
‐3
If
p(x) = 3x + 1 ,
find
5.
€
The
graphs
of
f(x)
and
g(x)
are
shown
below.
f(x)
Find:
4.
c.
f ( f (1)) )
Given
the
table
below,
find
f g(1) and
p h(−2) .
3.
€
x+3
,
find
each
of
the
following:
2
p(x)
9
5
4
5
9
13
g(x)
( )
b.
g f (4) f (3)
in
simplest
form.
f
(−2)
2x 2 − 6
if
x
<
6

Let
h(x)
be
defined
by
the
piecewise
function
h(x) =  1
.
if
x ≥ 6

x −5
( )
Find
h h(8) .
d.
g(g(−2)) 9
FUN
602
‐
APPLY
BASIC
TRIGONOMETRIC
RATIOS
TO
SOLVE
RIGHT‐TRIANGLE
PROBLEMS
BASIC
1. Find
each
missing
side
length
below.
60°
a.
60°
b.
15
c.
33°
x
21°
8
12
x
x
H
40
H
40
40
F
2.
Find
each
indicated
angle
measure
to
nearest
tenth.
G
a.
b.
7 c.
x°
45
8
25
4
19
x°
3. Solve
the
following
right
triangles:
a.
a
=
12,
b
=
15,
C
=
90 ° b.
b
=
10.2,
A
=
35.2 ° ,
C=
90 ° FOCUS
4.
Find
the
length
of
AB
in
the
figure
below.
21°
x°
5.
A
boat
is
2000
meters
from
a
cliff.
If
the
angle
of
depression
from
the
top
of
the
cliff
to
the
boat
is
25°,
how
tall
is
the
cliff?
Round
your
answer
to
the
nearest
tenth.
6.
A
42‐ft
tree
casts
an
18‐ft
shadow.
Find
the
measure
of
the
angle
of
elevation
to
the
sun
to
the
nearest
degree.
7.
Find
the
area
of
a
regular
pentagon
with
side
length
10.
8.
An
octagon
is
inscribed
in
a
circle
with
radius
16.
Find
the
perimeter
of
the
octagon.
9.
A
fire
is
sighted
due
west
of
lookout
A.
The
bearing
of
the
fire
from
lookout
B,
8.6
miles
due
south
of
A,
is
N
42.43 ° W.
How
far
is
the
fire
from
B
(to
the
nearest
tenth
of
a
mile)?
10.
A
ship
is
sailing
due
west.
The
captain
sees
a
large
iceberg
ahead
of
the
ship
at
an
angle
of
38°
to
the
right
of
the
path
of
motion.
By
radar,
the
captain
determines
that
the
iceberg
is
10
miles
from
the
ship.
a. Draw
a
horizontal
line
representing
the
path
of
the
ship.
Draw
the
position
of
the
iceberg.
What
is
the
closest
distance
the
ship
will
come
to
the
iceberg?
b. How
far
must
the
ship
go
to
reach
its
closest
point
to
the
iceberg?
c. If
the
ship
sails
2.5
miles
from
its
initial
point,
calculate
the
angle
to
the
path
at
which
the
captain
must
look
to
see
the
iceberg.
11.
Find
the
equation
of
a
line
passing
through
the
origin
so
that
the
sine
of
the
angle
between
the
line
in
3
quadrant
I
and
the
positive
x‐axis
is
.
2
12.
Find
h
in
the
figure
below.
h
56.2 ° 24.4 ° |‐‐‐167ft‐‐‐‐
|
FUN
703
–
Exhibit
knowledge
of
unit
circle
trigonometry.
BASIC
1. Find
the
exact
value
for
each
of
the
following.
No
calculator!
7π
3π
π
13π
a. sin
b.
tan
c.
sin
d.
csc
6
4
2
3
5π
3π
23π
e.
sin
−
f.
cot
g.
sec
h.
cot
‐2π
6
2
6
2. Find
the
exact
value
of
θ in
the
given
interval
that
has
the
given
trig
function
value.
Do
not
use
a
calculator!
3
1
π 
 3π

 3π 
a.
 , π  ;
sin
θ =
b.
 , 2π  ;
cos
θ =
c.
π ,  ;
tan
θ =
3 2
2
2 
 2

 2 
CONTEXT
3. Solve
the
following
trigonometric
equations
over
the
interval
[ 0, 2π ] :
a. tan
x
=
‐1
d. 2 cos x = − 3 b.
2 cos 2 x + 3cos x = −1 2
e.
2 cos x − 3 cos x = 0 c.
2 cot x = −2 f.
sec x tan x = 2 tan x 4. Explain
why
sin 2 θ + cos 2 θ = 1 for
all
θ .
5. Show
that
the
left
side
is
equal
to
the
right
side
(in
other
words,
verify
the
identity)
cot θ
= cosθ csc θ
2
ANSWER
KEY
BOA
601:
1.
21:1
2.
75
3.
2.08
x
1023
4.
a.
35.731
miles
/
hr
b.
8.35
liters
5.
$1097.48
6.
21
teachers
7.
1:24
8.
2424.04
mL
PSD
601
1. 81
%
2. 57.29
miles/hr
3. 91.5%
4. 2:5
5. 178.55
g/mol
PSD
602/
GRE
601
1. a.
45/664
b. 49/166
2. a.
20
mph
b. slope
c. 5
miles/second
3. a.
1580
c. 8:00‐8:30
d. 7:30‐8:30
4. D
5. Various…
did
not
make
AYP
in
2009,
2010
6. Various
7. a.
(0,
1.5),
(2,3),
(4,6)
c. exponential
d. y=1.5(b)2
8. a.
10
b. 6
solutions;
‐8,
‐5,
‐1.7,
2,
6.1,
8.3
c. f(‐6)=
9,
f(2)
=
0
PSD
603
1. 900
2. 6561
3. 5040
4. 1/91
5. 1/(3.707x1011)
6. 421,
200
7. 1035
PSD
604
1. 13/18
2. a.
π/4
c. 5/17
d. (25π
‐
48)/
25π
3. 17/36
4. ¼
5. ¼
6. ¾
7. ¼
8. 2/3
9. 5/9
NCP
601
1. 6
x
6
x
2
2. c
3. 2
4. 7
5. 7
NCP
602
1. even
2. 4
3. 2
and
3
4. 24b
5. I
and
II
6. 2
7. even
8. 6(2q+3p)
9. odd
10. even
11. 5
or
7
12. 2
NCP
603
1. ‐18
2. 7
3. y
<
1
4. 12
5. negative
6. sometimes
7. c,
a,
b
8. i
only
NCP
604
1. least:
x5
;
greatest:
x8
2. E.
a5
4b 24
3. 3,
2 ,
4 16 ,
3x3y
b
a c
mn,
b.
t =
c.
r =
11
12
,
2
,
b ,
4x3y8
6
y
4.
2a 2b 3 3 5bc ,
16 2 − 120 ,
4 5
5
− 30
3− 2
−42 2 + 168
,
,
27
7
14
5.
9 + 19 2 6.
A
7.
3 3 x 2 y 2 8.
4a2b
9.
4 5 10.
5x5y2
2x 4 y 7
11.
12 z
12.
64
NCP
605
1. 18
–
26i
2. 14
1 35i
+
3.
4 16
4. –i
5. (3
+
4i)
and
(3
–
4i)
6. 2i
+
5
7. ‐9
+
7i
8. show
by
expanding
1 2
20 29
+ i ,
+ i
9. −
20 5
73 73
XEI
601
3
59
1. a.
y = x −
5
5
b.
y = 2x − 4 2k
2.
a.
v =
Q
d
s
kqq q2
F
v − v2
3.
a = 1 0 2x − 2x0
µI
4.
r = 0 2Bπ
−6y
5.
7y − 4
6.
r = 9261 − 729 s 3 7.
x
=
13
–
2y
−b
8.
c =
a − a 2b
9.
x:y
=
5:4
XEI
602
4
1. a.
x + 6 = x 5
c. 24
2. a.
360+1.5x
and
250
+
2x
c. 220
d. yes
3. m≥8
m+2
4.
3
5. a.
4x
+
12
<
40
b.
x
<
7
6.
A
≥
150
7.
a.
linear
b.
toll
=
.044
(miles)
+
.459
c.
4.86
XEI
603
/
GRE
502
1.
x≤3,
p
>
‐5/2
;
‐7
<
x
<
‐4;
2.
25
<
x
<
729/16
3.
B
4.
‐11/2
<
x
<
½
5.
(‐∞,
‐2)
U
(5,
∞)
6.
(‐2,
6)
(r
is
between
‐2
and
6)
7.
(‐7,
‐1)
U
(1/2,
∞)
8.
a
+
c
x
>
‐2
XEI
604
1. Distance
from
0
on
a
number
line
2. You
are
looking
at
distance.
3. x
=
4,
14
4. x
=
1,
‐7
5. x
=
‐8/3,
88/3
6. a.
F;
b.
T;
c.
F;
d.
T;
e.
T;
f.
F;
g.
F;
h.
F
7. 10
–
π2
8. x
=
‐9,
7
9. x
=
‐15/2
10. D
XEI
605
1. Function
with
degree
2
2. Roots,
solutions,
zeroes,
x’s
3. Quadratic
formula,
graphing,
factoring,
square
roots
4. Look
at
how
many
times
it
crosses
x‐axis
5. ‐6,
3
6. ½,
‐2
7. ‐3/13
8. 2,
4
9. 9/4,
¾
10. 7,
1
11. 0,
12
12. no
real
solutions.
13. x
=
4
14. a.
8x2π
–
16x2
b.
1.8
15.
a.
2x2+13x+18
b.
9
16.
a.
206.25
ft.
b.
6.7
seconds.
17.
‐3,
2
18.
111
19.
84
20.
‐12
XEI
606
2.
a)
x
=
28/23,
y
=
‐48/23
b)
(6,
‐1)
c)
(38/3,
‐40/3)
d)
no
solutions
e)
(0,
5,
‐1)
f)
(
104/19,
35/19,
120/19)
3.
1500
children,
700
adults
4.a
=
‐54,
b
=
8
5.
1525
at
3%,
975
at
2.4%
6.
jet:
525,
jetstream:
75
7.
12
mph
8.
8000,
2000,
14,500
9.
(1,4)
and
(4,
1)
10.l
=
4.5
w
=
2.5
11.
a
=
5,
b
=
3,
c
=
6
12.
l
=
3,
w
=
5,
h
=
9
13.
8,
5,
‐1
GRE
603
2.
no
3.
scalene
4.
(y2 − y1 )2 + (x2 − x1 )2 5.
a.
16 + 16c 2 b.
4 5 6.
‐1/7
7.
‐4,
2
8.
4
9.
3 5 GRE
604
1.
‐5/3
2.
a.
y=
(‐1/3)x
‐
1
b.
y
=
3x
‐
11
3.
32
4.
a.
y
=
3x
+
131
b.
y
=
(‐1/3)x
+
(443/3)
c.
same
distance.
5.
y
=
(3/4)x
‐
(19/2)
6.
a
=
17/5
7.
a.
23/4
b.
10.82
8.
a.
34/5
b.
‐11/2
c.
c=
6
GRE
605
 −b  −b  
1.
Vertex:
given
as
(h,
k).
Standard:
 , f     2a  2a  
2.
v:
(
3,
‐16),
LOS:
x
=
3
3.
(‐9/4,
34
1/8
)
4.
y=3x2‐18x+23
5.
(3,
‐5)
r
=
6
6.
(x
‐
5)2+y2=16
7.
(x
+
3)2+(y‐4)2=34
8.
(x
‐2)2
+
3
=y
9.
6
10.
a.
20.0625
b.
.375
sec
and
1.5
sec.
d.
2.06
11.
(x‐4)2+(y+3)2=260
12.
56.25
13.
2187.5
ft2
14.
(x+4)2+(y‐6)2=64
PPF
601
1. a.
x
=
6;
y=
6
b.
x
=
12,
y
=
8 3 8 3
c.
x
=
4,
y
=
3
2.
20 3 3.
9/4,
1
4.
2.7625
meters
2
5.
x
=
9,
y
=
36 3
6.
a.
3.38
b.
7.38
7.
810
 2 2   1 3
,
8.

 ,
 − ,

 2 2   2 2 
9.
3 :1 10.
80 3 11.
6,
6 3 12.
4 3 13.
DC = 4 + 4 3 ;
BC = 4 6 14.
x = 65; y = 3 26; z = 3 10 15.
13,
2
16.
33°
PPF
602
1.
3,4,5,
and
4, 5, 3 2.
a.
68,
b.
72,
c.
365 3.
92.4
4.
2 10 5.
2 2 6.
61 7.
50
8.
1.9
9.
38
10.
6,
8,
10
and
10,
24,
26
11.
60
miles
MEA
601
1.
37.2
times
2.
28.8
ft.
3.
350π
4.
will
overflow
by
3.98
cm3
5.
SA
=
108,
V
=
76.37
6.
5 3 7.
1:8
8.
37.5
9.
5:16
10.
3 3 11.
π:8
12.
π:8
FUN
601
1.
a.
‐15
b.
2
c.
2
d.
7/4
2.
f(g(1))
=
4,
p(h(‐2))=
9
3.
a.
3
b.
3.7
4.
126/5
5.
‐52/9
FUN
602
1.
a.
4.3
b.
9.741
c.
16
2.
a.
63.4
b.
68.4
c.
16
3.
a.
c
=
19.2,
B
=
51.3,
A
=
38.7
b.
c
=
12.5
B
=
54.8
a
=
7.2
4.
21
5.
932.6
meters
6.
66.8°
7.
172
8.
97.6
9.
11.7
10.
a.
6.16
b.
7.8
c.
49.3°
11.
y = 3x 12.
h=
108.87
FUN
703
1.
a)
‐1/2
b)
‐1
c)1
d)1
2 3
e)‐1/2
f)0
g)
h)
undefined.
2
5π
11π
7π
2.
a)
b)
c)
6
6
6
3π 7π
2π 4π
,
,π 3.
a)
,
b)
4 4
3 3
3π 7π
5π 7π
,
c)
,
d)
4 4
6 6
π 3π π 11π
π 7π
e)
, , ,
f)
,
2 2 6 6
4 4