Download Complete Math TAKS study Guide

Add/Subtract Mixed Numbers
Convert a fraction to a %
• Find LCD then +/- Fractions
• Multiply by 100 and use % symbol
• +/- Whole Numbers
3
1
3
1
3
2 3
Convert to a percent
•
Simplify
5 2
5 2
5
4
4
2
4
4
3
a
100
 100
Subtract Mixed Numbers w/Borrowing
5
b
• Find LCD
60
300
• Rename by Whole # then subtract
 5 300 60%
• Simplify
5
Multiply Fractions
1
3
Convert a decimal to a %
• Numerator x numerator
8 2
Convert a decimal to a fraction
2
4
• Move decimal to right twice or x by 100
• Denominator x denominator
2
3
• Simplify
0.8 = 80%
80
%
8 2
3
• Use the last digit of the decimal.
a c
ac 3 1
4
4
 
 
Convert a % to a decimal
4
b d b  d 4 5 20
0.abcd • Apply to place value fraction. • Move decimal to left twice or divide by 100 8  7  4 Divide Fractions
a ab abc
80% = 0.8
6
3 • Flip divisor
0.8
,
,
• Always simplify if possible.
7 2
10 100 1000
4
4 • numerator x numerator
Simplify fractions (Repeat the process)
Convert a fraction to a decimal Divide
numerator by denominator.
.
Los = a
0.75__
.
a
b
 b a.00 ¾ = 4 3. 00
b
-2 8
0.75
20
-20
0
L
• Divide the numerator and denominator by the
• denominator x denominator
3
58
5
same number.
• Simplify
3 1 3 2 6
4
9
4
 
a
c
a

d
a
8
100
 
7 2 7 1 7
29
 2 a, 2 b
 2 8 , 2 18
b d
bc
58 29
b
18
50

Order/Compare Fractions Decimals %’s
4
a
100 50

3
a
,
3
b
• Convert all values into fractions, decimals, or %’s
Convert a mixed # to an improper fraction.
9
b
• Then order or compare
b Ac  b
a
A 
Order from greatest to least.
 5 a, 5 b
c
c
23
b
1
0.8, ,10%,0.19
4
3 5 4  3
a
2
5 
 7 a, 7 b
80%, 50%, 10%, 19%
4
4
b
1
Convert an improper fraction to a mixed #. Add/Subtract Fractions
0.8, , 0.19, 10%
2
• Divide the numerator by the denominator.
• Find LCD then +/- numerators
Rounding Numbers
• keep like denominator
A
D
b
• Always look to the right of your rounding digit
D
A
c D
1
3
2
3
c
c
1
  
c
• If the digit is 0,1,2,3 or 4 do not change the rounding digit.
-(Axc)
1
2 4 4 4
• All digits that are on the right hand side of the requested rounding digit
4
b
5
1
3
will become 0
1
5
5
• Determine what your rounding digit is and look to the right of it. If the
4
4
4
23
digit is 5,6,7, 8 or 9, your rounding digit rounds up by one number. All
 4 23
digits that are on the right hand side of the requested rounding digit will
4
-20
become 0
3
Round nearest dollar 16.8 = $17
0.58 
Round nearest Penny 1.652 = $1.65
Add/Subtract Decimals
•Line up decimals
•Add/Subtract
12.3
12.3  5.8
+5.8
18.1
Multiply Decimals
•Line up the numbers on the right - do
not align the decimal points.
Divide with decimal divisors
•If the divisor is not a whole number,
move decimal point to right to make
it a whole number and move decimal
point in dividend the same number
of places.
• Put decimal point directly above
decimal point in the dividend.
•Divide as usual
•Multiply
•Place the decimal point in the answer
by starting at the right and moving a
number of places equal to the sum of
the decimal places in both numbers
multiplied.
Order/Compare decimals
•Line up decimals
•Then compare/order
> Greater than or < Less than
12.3
5.82
12.3
05.8
10.566
Divide decimals (dividends)
•Put decimal point directly
above decimal point in the
dividend.
424.9
•Divide as usual
Order of Operations PEMDAS
• () 1st
• Exponents 2nd
•Multiply & Divide Left to right
•Add/ decimal point in the
dividend.
•Divide as usual
12.3 > 5.82
Exponents
Scientific Notation
• Def. product of two factors where:
• 1st factor: 1 or more but less than 10
•2nd factor: a power of 10.
Write in scientific notation and vice versa.
1.5 103  1500
0.000128  1.28 10 4
Square Roots
•The square root of a number, n,
written below is the number that gives
n when multiplied by itself.+/- Whole
Numbers
•Finding the square root of a number
is the inverse operation of squaring
that number. Remember, the square
of a number is that number times
itself.
Find the sale price
• Find the % of original (discount)
• An integer is a whole number that can
be either greater than 0, called positive,
• Subtract discount from the original (sale price)
or less than 0, called negative. Zero is
Shirt reg. $16 for 20% off (convert 20% to a decimal & multiply)
neither positive nor negative.
20% of 16 = 3.20 (discount)
• Two integers that are the same
16-3.20 = $12.80 (sale price)
distance from zero in opposite
Find the discount rate
directions are called opposites.
75% times by ¾ or times by 0.75
• Every integer on the number line has
• original/regular – sale (discount)
50% divide by 2 or times by 0.5
an absolute value, which is its distance
• Discount divided by original times 100
33 1/3% divide by 3
from zero.
Shirt regular $20 on sale $12
25% divide by 4 or times by 0.25
reg  sale
20% divide by 5 or times by 0.2
100
original
10% divide by 10, times by 0.1, move left
20  12
decimal once
 100
1% divide by 100 or times by 0.01 or move
20
decimal left twice
Add/Subtract Integers
8 100

 40%
Proportions
• Use the number line for adding and
20 1
A
proportion
is
a
statement
subtracting integers:
where two ratios are equal. It can
Find the regular price
• Add a positive integer by moving to the right
be
written
in
two
ways:
• 100% - n% Off (%paid)
on the number line
a c

• Add a negative integer by moving to the left
• Sale price x 100
b d
on the number line
• answer divided by %paid (regular price)
Find the Percent of a number
• Subtract an integer by adding its opposite
Sale price $15 at 20%off
Convert % to a decimal
Add Integers Rule
100-20=80(80%paid)
• Same sign: add & keep sign -8+-5 = -13 Multiply the decimal by the number 15x100=1500
16% of 50 = 0.16 x 50 = 8
• Different signs: Subtract & keep sign of
1500/80=18.75 =>$18.75 = regular price
Using the Percent Equation
largest absolute value. – 8 + 5 = -3
Find % off
• identify each component of the
Subtract Integers Rule
• Find the % of the original (discount) is
equation
%
• To subtract a number, add its opposite.

•
Subtract
discount
from
original
(sale)
•
“is”
part
of
the
whole
or
the
result
• Leave Change Change /KFC
of 100
• “of” is the total or original amount Find % Mark Up
-8-5 = -8+-5 Keep Flip Change
• Find % of the original (profit)
• “%” is the percent (always over 100)
= -13
Change= 2
• Add profit to original
17 is what percent of 51?
Multiply/Divide Integers
Original
=10
New = 12
Percent of change
is
%
• Same signs: multiply/divide as usual
1700
1

• Find the difference of original and new
 33 %
of 100
answer is positive
51
3
• Divide the difference by the original
17 %
2
%
• Different signs: multiply/divide as usual
change
%

• Multiply by 100


51 100
answer is negative
Raise from $10/hr to $12/hr original 100 10 100
17 %
-4 x -3 = 12
-8/2 = - 4
20% increase

51 100
Integers
Percents = means per hundred
¾ = 75%
2/3 = 662/3%
½ = 50%
1/3 = 33 1/3%
¼ = 25%
1/5 =20%
1/6 =16 2/3%
1/7 = 14%
1/8 =12.5% 1/10 = 10%
Find popular %’s (drop % sign)
Circumference
Around a circle
Trigger Words In Word Problems
Add
increased by, more than
combined, together
total of, sum
added to, in all, altogether
total amount, Perimeter
Plus, Mix
Subtrac
t
decreased by
minus, how many more, less
difference between/of
less than, fewer than
Multiply
Of, times, multiplied by
product of, area,
each/ per,
increased/decreased by a
factor of (this type can
involve both addition or
subtraction and
multiplication!)
Note: if confused whether to
multiply or divide, set up a
proportion.
Divide
Per /each, a ratio of, quotient
find the unit rate, out of,
Share, distribute, Average
Note: if confused whether to
multiply or divide, set up a
proportion.
Equals
is, are, was, were, will be,
gives, yields, sold for…
Perimeter
Around the Base
Area
1
Cover a
S  Pl
3
Base figure
1
S  Pl  B
3
Lateral Surface Area
1
V  Bh
3
V  Bh
S  Ph
S  Ph  2B
Cover sides
of a 3D figure
Total Surface Area
Cover all of a 3D
figure
Volume
Fill a 3D figure
c2  a2  b2
P represents the perimeter of the base shape of a
3D figure.
V  Bh
S  Ph
S  Ph  2B
1
3
¼
8
8
½
5
8
0.1 0.2 0.3 0.4
7
1
3
1 1¼1
8
8
¾8
1
0.5 0.6 0.7
½
B represents the area of the Base of a 3D figure.
7
5
1 1¾ 1 8
8
1½
Inch Ruler
0.8
2
0.9
2
1.1 1.2 1.3 1.4
1
1
3
2
2¼
8
8
1.5
1.6
Centimeter Ruler
1.7
2
2½
1.8
5
7
2
8 2¾ 8
3
1.9
2.1 2.2 2.3 2.4
2
2.5
2.6
2.7
2.8 2.9
3
Type of Graph
Common Use
Line graph
Shows change in data over time.
Bar graph
Shows relationships or comparisons
between groups.
Circle graph
Compares parts to a whole.
Histogram
Shows the frequency of data divided
into equal parts.
• Independent means with replacement
Box-andwhisker plot
Shows the distribution and spread of
data.
• Multiply the two events
Line plot
Shows the distribution of data.
Scatter plot
Shows the relationship of two data
sets.
Simple Probability
Venn Diagram
p(event) 
Only
about
item 1
Ways
they’re
the
same
Only
about
item 2
p (blue ) 
9
20
•Find the probability of both events
• Simplify if possible
20 Marbles: 5 red, 6green, 9 blue
P (blue 1st ) then p(green 2nd)
with replacement
9 6
54


20 20 400
54  2
27

400  2 200
• Outliers – a data value that’s much higher or much lower than the other
data values in a set
•Mean – average (when you have no outliers)
This is a coordinate
plane. It has two axes
and four quadrants. The
two number lines form
the axes. The horizontal
number line is called the
x-axis and the vertical
number line is called the
y-axis.
• Median – middle of an ordered set (when outliers influence the mean)
• Mode –occurs the most (when data isn’t numerical)
Find the Measures of Central Tendency
• Mean-Add each item, then divide the total by the # of items
• Median-order the set, then choose the middle number. If there are two
numbers, find their average
• Mode-the number that occurs the most in a set of data (most popular)
27,32, 30,31,11,30
Probability of Dependent Events
The center of the coordinate
plane is called the origin. It
has the coordinates of (0,0).
• Dependent means no replacement
Locations of points on the
plane can be plotted when one
coordinate from each of the
axes are used. This set of x
and y values are called
ordered pairs.
• Find the probability of 1st event
• Find probability 2nd event after
removing the item from the 1st event.
• Multiply the two events
• Simplify if possible
20 Marbles: 5 red, 6green, & 9 blue
Sequences
Find the mean, median, & mode. Identify any outliers.
Outlier:11
20 Marbles: 5 red, 6green, 9 blue
Probability of Independent Events
Measures of Central Tendency & When To Use Them
Mean = 27+32+30+31+11+30 => estimate 26.8
60
Median = 32, 31, 30, 30, 27, 11
 30
2
Mode = 30
favorable outcomes
possible outcomes
Position
1
2
3
n
Value
5
7
9
2n + 3
p(blue 1st ) then p(green 2nd)
without replacement
Tables & Function Rules 9
6
54

20 19 380
X
Y
2
5
0
-1
Common difference (term) 54  2
-3
-10
+/- Constant
y = 3x - 1

380  2

27
190
p(blue 1st ) then p(blue 2nd)
without replacement
9 8
72
 
20 19 380
72  4 18

380  4 95
Pythagorean Theorem
a, b, c
3, 4, 5
9 + 16 = 25
5, 12, 13
25 + 144 = 169
7, 24, 25
49 + 576 = 625
8, 15, 17
64 + 225 = 289
9, 40, 41
81 + 1600 = 1681
11, 60, 61
121 + 3600 = 3721
12, 35, 37
144 + 1225 = 1369
16, 63, 65
256 + 3969 = 4225
20, 21, 29
400 + 441 = 841
Example
Finding Square Roots
Example
Hypotenuse missing
1.
Square given
sides
2.
Add squares
3.
Find the square
root
A ramp was constructed to load a
truck. If the ramp is 9 feet long and
the horizontal distance from the
bottom of the ramp to the truck is 7
feet, what is the vertical height of
the ramp?
Leg missing
1.
Square given sides
2.
Subtract squares
3.
Find the square root
About 6 ft
REMEMBER: The Pythagorean Theorem ONLY works for
Right Triangles!
a, b are legs.
c is the hypotenuse
(c is across from the right angle).
Perfect Squares
8th Grade Math TAKS April 6, 2010
Score back April 27, 2010**
7th Grade LAT Math April 26, 2010
Scores Back May 19-26, 2010
7th Grade Math April 26, 2010
Scores Back May 19-26, 2010
8th Grade LAT Math May 17, 2010
8th Grade Math TAKS Retest May 18, 2010
Scores Back June 8, 2010***
Scores Back June 8, 2010***
8th Grade Math TAKS Retest June 29, 2010
Scores Back July 16, 2010
** 10 working days after the testing contractor receives the scorable materials † Includes TAKS (Accommodated) only
*** Tests administered over two days, May 18 and May 19
TAKS
Objectives
7th Grade
Questions
8th Grade
Questions
Objective 1
10
10
Objective 2
10
10
Objective 3
7
7
Objective 4
5
5
Objective 5
7
8
Objective 6
9
10
Total
48
50