Download 8th grade MN MCA-III Practice Packet

8th Grade Only …
NO CALCULATORS ON THIS PORTION…
Which
expression
results
in
a
rational
number?
1.
A)
1.5 + 1.5 THINK
Rational Numbers can be graphed on a number
line. They either terminate (end) or repeat and
CAN be written as fractions.
B)
12− 12 €
€
3 3
C)
•
4 4
D)
25÷ 25 €
€
Examples:
Simplify.
(4x)2
–
4x3
2.
A)
x -1
B)
12x -1
€
C)
16x 2 −4x 3 €
D)
16x 2 −64x 3 THINK
The exponent is like a
… he will “lasso” ONLY what he
is “touching.” REMEMBER: When in doubt, EXPAND IT OUT!
Example:
(3a)2 – 5a3
= (3a)(3a) – 5a3
= 9a2 – 5a3
Are they like terms? 
= __________
LIKE TERMS have the SAME BASE and the SAME POWER.
Example: 2a2 + 3a2 = 5a2
A number written
Part 1:
Part 2:
Part 3:
EXPONENT.
€
€
€
€
C)
2.5×10−10 D) 2.5×10 −11
THINK
in scientific notation has THREE parts:
A number greater than or equal to 1 and less than 10
A multiplication symbol – usually x.
The number 10 with a positive or negative
Dividing using scientific notation
A)
2.5×10−2 B)
2.5×10−9 €
14 = 3.74165… no pattern…
€
€
€
3.
Simplify.
1.2×10−6
4.8×104
5
, 9, …
6
Irrational Numbers are “mixed up decimals”
when simplified with no pattern. They never end
€ be written as
and never repeat and CAN’T
€
fractions.
Examples: 4, -2, 3.5, 0.3333,
KNOW IT!
1.
2.
3.
Group and decimals and MULTIPLY!
ADD the exponents when its MULTIPLICATION
SUBTRACT the exponents when it’s DIVISION.
4. Which
table
of
values
does
NOT
represent
a
function?
THINK
• In a function, there is ONE unique OUTPUT (y) value for
every INPUT (x) value.
• You do not have a function if the same input value results in
2 or more different output values.
• You do not have a function if the same “x” value results in 2
or more different y values.
Does each table represent a function? Why or Why Not?
5.
Example 1: YES
Example 2: YES
Each INPUT
has ONLY 1
OUTPUT.
Each INPUT
has ONLY 1
OUTPUT.
Example 3: NO
The 2 has MORE than
ONE OUTPUT.
The
number
of
cakes
needed
for
a
party,
c,
is
dependent
upon
the
number
of
guests
at
the
party,
g.
Which
equation
shows
the
number
of
cakes
as
a
function
of
the
number
of
guests?
THINK
“As a function of… guests (g)…” means ___________________
The dependent variable CAN’T be changed – not free.
The independent variable CAN change – it is free.
In this problem, the dependent variable is c. This means c
CAN’T change and is NOT included in the function. What CAN
change? Guests (g)
*You are looking for the function of guests (g) that shows the
number of guests as your independent variable (what will
CHANGE).
For example:
Guests (g)
Equation
Cakes (c)
12
1
24
2
36
?
Which equation/function matches?
6.
A
graph
is
shown.
Which
situation
is
represented
by
the
graph?
7.
THINK
Strategy: Use a ruler to
EXTEND the line.
Use the line to GUESS and
TEST each statement.
ONLY 1 is TRUE.
Ann
sells
bracelets
for
$4
each
and
necklaces
for
$8
each.
Which
inequality
shows
x,
the
number
of
bracelets,
and
y,
the
number
of
necklaces
Ann
must
sell
to
make
at
least
$100?
THINK
Math Talk…
“each” means
x or ÷
“at least” means more than or equal to $100
Where are numbers that are “at least” 100?
98
99
100
101
102
Word Equation:
Bracelets = x Bracelets and Necklaces = 100
Necklaces = y
__x + __y
___
100
8.
A
rectangle
is
drawn
on
a
coordinate
grid.
The
equation
for
1
side
of
the
rectangle
is
3x
–
2y
=
12.
Which
could
be
an
equation
for
another
side
of
the
rectangle?
THINK
Graph given equation. REMEMBER:
y = mx + b
slope
y-intercept
• PARALLEL lines have EQUAL slopes.
• PERPENDICULAR lines have OPPOSITE RECIPROCAL
slopes.
(Calculators are ok from this point on…)
9.
Which
sequence
is
arithmetic?
A)
4
8
16
32
64
....
B)
11
12
14
17
21
....
C)
28
15
2
−11
−24
....
D)
30
−25
20
−15
10
....
THINK
An Arithmetic Sequence has a
COMMON DIFFERENCE.
This
means you can ADD or
SUBTRACT the SAME
number from one term to the
next.
10.
Jayda makes a graph to show the weight of a jar when it contains different
numbers of marbles.
THINK
An intercept is where the line
crosses an x or y-axis. LOOK
at the LABEL of the Y-AXIS
AND the TITLE to determine
the answer to this question.
What does the y-intercept represent?
A)
The
weight
of
each
marble
B)
The
weight
of
the
jar
by
itself
C)
The
number
of
marbles
when
the
weight
is
0
grams
D)
The
number
of
marbles
when
the
weight
is
10
grams
Explain WHY you chose this answer: _______________________________
_______________________________________________________________
11. An
equation
is
shown.
m
=
4p
+
3
When
p
is
increased
by
2,
how
much
does
m
increase?
A)
2
B)
4
C)
7
D)
8
THINK
1. What does m = __ when p = 1?
2. “Increase” means +. How much do
you add to 1? 1 + 2 = 3
3. What does m = ___ when p = 3?
4. How much did p increase (go up)?
12.
A
sequence
is
shown.
What
is
the
seventh
term
in
the
sequence?
1.5
4.5
13.5
40.5
…
THINK
Is this sequence Arithmetic or Geometric?
_______________
WHY? I have to MULTIPLY by 3 each
time to find the next term.
A)
121.5
B)
364.5
C)
1,093.5
Two Solution Methods
1. EXTEND the PATTERN to the 7th term
(you have 1-4 already).
D)
3,280.5
2. Formula: a • (r) n – 1
a = first #
n = # you want to find
r = ratio
13.
Which
property
is
used
in
the
equation:
mg
+
mh
=
m(g
+
h)?
A)
Associative
B)
Commutative
C)
Distributive
D)
Identity
THINK
Associative: You CHANGE the GROUP you hang out with (+ or •).
Examples:
(a + b) + c = a + (b + c)
(a • b) • c = a • (b • c)
Commutative: You MOVE to “commute” from school to home (+ or •).
Examples:
a+b=b+a
a•b=b•a
Distributive: You SHARE (MULTIPLY) the OUTSIDE with the (INSIDE). “Rainbow” property
Examples:
a(b + c) = ab + ac -OR- ab + ac = a(b + c)
Identity: The number keeps its “identity” (SAME #).
Examples:
a+0=a
a•1=a
14.
Which
equation
is
the
same
line
as
y
=
3x
−
8?
A)
3x
−
2y
=
8
B)
−3x
−
2y
=
−8
C)
6x
−
y
=
16
D)
6x
−
2y
=
16
15.
An
equation
is
shown.
|2x
–
4|
=
6
The
equation
has
2
solutions.
One
solution
is
x
=
5.
What
is
the
other
solution?
THINK
REWRITE each equation in slopeintercept form: y = mx + b
Which one is the SAME?
SHOW ALL WORK!!!
THINK
RULE: The expression INSIDE the
absolute value symbol can be either
positive or negative.
| ax + b | = c means
ax + b = c
OR
ax + b = -c
Positive
Negative
2x – 4 = 6
2x – 4 = -6
THINK
*Isolate the terms inside the | | and
make the ANSWER BOTH + and -. To
find the other solution just solve for x.
Lisa
has
5
more
green
marbles
than
blue
marbles.
She
has
a
total
of
40
green
and
blue
marbles.
Which
system
of
equations
represents
this
situation
if
x
is
the
number
of
green
marbles
and
y
is
the
number
of
blue
marbles?
16.
y= x +5
A)

x +y= 40
x = y +5
B)

x +y= 40
€
€
y= x +5
C)

y= x +40
€
x = y +5
D)

x=y+40
€
“Total” means =
Word Equation:
Green = x
Blue = y
Green and Blue = 40
_ + _ = 40
THINK of the pattern…
Blue
Green
1
6
2
7
3
__
What is the equation?
Blue + _ = Green
y + _=x
(Assign x and y)
What
is
the
distance
between
(4,
7)
and
(­3,
9)
on
a
coordinate
grid?
17.
A)
5 B)
45 €
€
THINK
“More” means +
C)
53 D)
305 THINK
Two Solution Methods
“Distance” means distance formula:
2
(x − x ) + (y
2
1
2−
OR
Plotting on a coordinate plane and using the Pythagorean
Theorem (a2+ b2= c2)
€
€
€
y1
)
2
18.
Which
function
forms
a
geometric
sequence
when
x
=
1,
2,
3,
…?
A)
f(x)= x +2 B)
f(x)= x 2 €
€
THINK
Geometric Sequences have a COMMON
RATIO (MULTIPLY by the SAME
number) to extend the pattern.
Formula:
f(x) = a(b)x
C)
f(x)= x 2 + 2
D)
f(x)= 2 x €
€
19.
A
sequence
is
shown.
What
is
the
function
rule
for
the
sequence?
­1
­7
­13
­19
­25
…
THINK
A)
f(x)= x - 6 B)
f(x)= -6x C)
f(x)= 5x - 6 €
D)
f(x)= -6x - 5
€
€
Arithmetic Sequences have a COMMON DIFFERENCE
(Add or Subtract the SAME number) to extend the
pattern….
Formula:
f(x) = mx + b
The common difference IS the slope (m).
Find what came BEFORE -1 (the ZERO term #) – this
IS the y-intercept (b).
*Because the y-intercept
is the value of y when x = 0.
€
20.
What
is
the
value
of
­3|­2x
–
y|
when
x
=
­4
and
y
=
5?
SHOW
YOUR
WORK!
THINK
Substitute for x
A)
‐27
B)
‐9
C)
9
D)
27
and y then solve.
21.
Leon
plants
3
rows
of
tomatoes
with
n
plants
in
each
row.
He
also
plants
1
row
of
beans
with
5
plants
in
the
row.
Which
equation
can
be
used
to
find
t,
the
total
number
of
plants
Leon
planted?
A)
t = n+8
THINK
B)
t = 3n+1
€
“each” means • or ÷
C)
t = 3n+5
D)
t = 5n+3
€
€
€
22.
What
is
the
value
of
p
when
2p
+
10
=
24?
SHOW
YOUR
WORK!
A)
p = 7
B)
p = 12
C)
p = 17
TIP Draw a picture
THINK
This is a 2-Step
equation. What comes
first? ___
D)
p = 28
23.
A
number
line
is
shown.
Which
inequality
has
the
solution
shown
on
the
number
line?
A)
-4 > x > -2 B)
4 <-2x <8 €
€
€
€
C)
4 > -2x > 8 D)
-4 <2x <-8 THINK
Steps:
1. Isolate the variable (x) in each
inequality.
2. Remember…
< means numbers that are LESS than
> means numbers that are MORE than
24.
A
triangle
is
shown.
THINK
We use the PYTHAGOREAN THEOREM
What
is
AC? to find the length of LEGS (AB and BC)
or the HYPOTENUSE (AC) of RIGHT
triangles.
Formula:
a2 + b2 = c2
Steps:
1. Formula
2. Substitute
3. Solve
4. Remember to find the
!
25.
The
graph
of
a
line
is
shown.
What
is
the
equation
of
a
line
that
is
perpendicular
to
the
line
shown
and
goes
through
the
point
(3,
­1)?
4
A)
y= - x −5
3
4
B)
y= - x +3
3
€
4
C)
y= x −5
3
€
4
D)
y= x +3
3
€
€
THINK
1. Find the slope of the line.
2. What is the slope of a line perpendicular to
that? ______
3. Starting at the given point, draw in your NEW
slope. What is your y-intercept? __________
Slope-intercept form:
y = mx + b
slope
y-intercept
26.
The
scatterplot
shows
the
heights
of
Ferris
wheels
and
the
years
they
were
built.
THINK
Base your decision
solely on the given data
and the trend of the
data line.
Which
statement
is
true
about
the
scatterplot?
A)
All
Ferris
wheels
build
before
1980
must
have
been
less
than
60
meters
high.
B)
Based
on
the
line
of
best
fit,
Ferris
wheel
heights
increase
about
25
meters
every
10
years.
C)
Each
Ferris
wheel
is
taller
than
all
Ferris
wheels
that
were
built
earlier.
D)
Each
year,
more
Ferris
wheels
were
built
than
the
year
before.