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THE quick guide to MATH-7 TEST SUCCESS!!
A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z
Fraction  Decimal
“Take the top #, divide
by the bottom #!”
Decimal to Percent (D to P): “to the right, to the right”
1 = 8I1
8
.125 = 12.5%
Percent to Decimal (P to D): “to the left, to the left”
(turn the fraction clockwise)
5% = .05
1) P arenthesis
2) E xponent
3) M ultiply OR
D ivide
4) A dd OR
S ubtract
Perfect Squares:
12 = 1
112 = 121
22 = 4
122 = 144
32 = 9
132 = 169
42 = 16 142 = 196
52 = 25 152 = 225
62 = 36 162 = 256
72 = 49 172 = 289
82 = 64 182 = 324
92 = 81 192 = 361
10²= 100 20² = 400
Scientific Notation:
3.95 x 105 = 395,000
3.12 x 10-4 = .000312
You
MATH!
Negative exponents do
NOT make the answer
negative!!
Exponents:
10 3 = 10 x 10 x 10 = 1,000
10 -3 =
1
1
1
x x
10 10 10
=
1
1000
= 0.001
Properties (MEMORIZE these!):
Commutative (ORDER switches): a + b = b + a
Associative (GROUPING): (a + b) + c = a + (b + c)
Distributive: a (b + c) = a(b) + a(c)
Identity of Addition: a + 0 = a
Identity of Multiplication: a x 1 = a
Multiplicative Property of Zero: a x 0 = 0
Inverse of Multiplication: (a/b) x (b/a) = 1
Inverse of Addition (zero pair) : -a + a = 0
Square Root Ex.:
Absolute Value is ALWAYS
positive!! It measures the
𝟐𝟓 = 5
distance from zero on a
Both have the
𝟑𝟔 = 6
SAME absolute
number line.
value!
𝟒𝟗 = 7
I -3 I = 3
I 3 I=3
Integers and Algebra
Subtracting Integers:
Adding Integers:
DIFFERENT
SIGNS
ADD
KCC
4 - 7 = ___
SUBTRACT
KEEP SIGN OF
LARGER
ABSOLUTE VALUE!!
KEEP
SIGN!!
3+4=7
-3 + -4 = -7
4 + -7 = -3
coefficient
-3 + 4 = 1
3 + -4 = -1
3x + 5
Multiplying/Dividing Integers:
Neg. x Neg. = Pos.
+ Pos. x Neg. = Neg.
x
y
Domain
Range
Independent
Dependent
- +
Neg. x Pos. = Neg.
You’re the
BEST and
will rock
the test!
Inequalities:
>
<
≥
≤
constant
Solving an Equation:
2x + 4 = -6
A. 1
If you forget
B. -1
steps, PLUG
IT IN!!
C. -5
Add
Subtract
Multiply
Divide
Sum
Difference
Product
Quotient
Does the bird
get the worm?
When multiplying or
dividing by a negative
#, we switch the
inequality sign!
-3x > 15 – Switch Sign!
Expression– x + 5
Equation–
x+5=8
Inequality– x + 5 < 8
Percent Proportions:
%
𝒑𝒂𝒓𝒕
=
𝟏𝟎𝟎
Equation
> becomes <
variable
- -
+ +
Pos. x Pos. = Pos.
“Seven less than a number is five”
x–7=5
“Seven less a number is five”
7–x=5
SAME
SIGNS
y = 3x + 2
Plug in the “x”
values from
the table!
Table
x
y
-1
-1
0
2
1
5
2
8
𝒘𝒉𝒐𝒍𝒆
Graph
All ordered
pairs must fit
on line!
Measurement and Geometry
Transformations:
Translate – Slide
Rotation – Turn
Reflection– Flip
Dilation– Re-size
Coordinate Plane:
Volume:
Fill
Hold
Cubic Units3
Plot point-- over left or right (x),
then up or down (y).
II
Rotations:
(-3,1)
Here is a clockwise
rotation about the origin
(the x and y switch places
with each turn):
Original: (-3,1)– Q II
90˚:
(1, 3)– Q I
180˚:
(3,-1)– Q IV
270˚:
(-1,-3)– Q III
360˚:
(-3,1)– Q II
I
Changing an Attribute:
If ONE attribute (l, w, h)
of a prism is changed
(doubled, tripled, halved),
then the VOLUME will
also change by the same
amount!
C
III
IV
If we triple the length, the
volume will also triple,
etc.!
Surface Area:
RIGHT or LEFT changes X !
UP or DOWN changes Y !
Cover
Wrap
Square Units2
Quadrilaterals:
Parallelogram
Trapezoid
 Opposite sides parallel (2 pairs)
 One pair of parallel sides
 Opposite sides congruent
Rhombus
Rectangle
 Opposite sides
parallel
 Opposite sides parallel
 4 equal sides
 Must have 4 right angles
 4 equal sides
 4 right angles
SAME shape, DIFFERENT
size, CONGRUENT angles,
PROPORTIONAL sides!
𝒙
𝟏𝟎.𝟓
= 𝟏𝟏.𝟐𝟓
𝟏𝟕.𝟓
Height on top
and shadow on
bottom!!
Square:
ALWAYS UP,
SOMETIMES
DOWN, NEVER
SIDE-TO-SIDE!!
Similar Figures:
A square is
ALWAYS a
rectangle,
rhombus, &
parallelogram!
Probability
Theoretical Probability:
what “should” happen
Experimental Probability:
what “actually” happens
Probability:
𝒇𝒂𝒗𝒐𝒓𝒂𝒃𝒍𝒆 𝒐𝒖𝒕𝒄𝒐𝒎𝒆𝒔
𝒕𝒐𝒕𝒂𝒍 𝒐𝒖𝒕𝒄𝒐𝒎𝒆𝒔
P(roll a 5) =
As the # of trials increase, the
experimental probability will come
closer and closer to the theoretical
probability!!
𝟏
𝟔
Tree Diagram:
Fundamental
Counting
Principle:
1) 3 shirts, 2 belts, 3 shorts:
3 x 2 x 3 = 18 possible outfits
2 cone choices x 4 flavors = 8 possible outcomes
Independent
Events
Dependent
Events
with
without
replacement
replacement
Finding the
probability of
picking a king,
putting it back,
and picking a
king again . . .
Finding the
probability of
picking a king,
keeping it, and
picking a king
again . . .
4
52
x
4
52
4
52
x
2) Roll one die and flip one
coin:
6 x 2 = 12 possible outcomes
REMEMBER:
With replacement– put it back!!
Without replacement– keep it !!
3
51
Number/ Letter Codes . . .
A code consists of three numbers. The
choices for each number range from 0 – 9.
How many unique codes?
10 x 10 x 10 = 1,000
Ms. Dyson
knows that the
odds will be ever in
your favor on the
SOL test!!