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MATH RESOURCE GUIDE
Increase/decrease % = subtract the two #s and divide by 1st # given
D = RT distance = rate or speed x time
CELSIUS ℃ = ( ℉ − 𝟑𝟐 ) 𝟓/𝟗
Unit or Each or per unit = $ / amount
I = PRT (simple): interest $ = $ put in x % x time (yrs)
I = PRT (compounded): interest $ = (1 + rate %)™ x $ Put in
c² * b² = c * b = z ²
𝒃² ∗ 𝒃³ = 𝒃 ³ + ² = 𝒃 ⁵
(𝒂)³
(b)
𝒂³
b³
(𝑪² )³ = 𝑪 ² ∗ ³ = 𝑪 ⁶
b⁵
b ²
(𝒂 𝒃)³
= 𝒂³ 𝒃³
b⁵ - ² =b ³
(𝒇 𝑶𝑭 𝒙) 𝒇 (𝒙) = 𝟑 𝒙 + 𝟗
𝒇(𝒙) = 5 𝒚 = 𝟑 (𝟓) + 𝟗 … 𝒚 = 𝟏𝟓 + 𝟗
𝒚 = 𝟐𝟒 Coordinate Pair would be ( 𝟓 , 𝟐𝟒 )
Scientific Notation: MUST have one digit __. X 10 to a power ? ; The power
is the movement of the decimal to the first digit. 345, 000 = 3.45 x 10 ⁵; positive
power moves to right; negative power moves to left .000078 = 7.8 x 10
Absolute Value: distance from zero; MUST be positive when leaving the |
| 5 |= 5
| -7 + 5 | = |-2 | = 2
| 9 + -23| = |-14 | = 14
|
REAL NUMBERS: all numbers that exist.
 Rational Numbers: Integers, fractions, or decimals that Terminate (end) OR a
Repeat decimal… 12, ½, .363636.. , 2 ¾ , -15, 0
Integers: Positive and Negative Whole Numbers
Integer Rules:
Multi or Divide: − 𝑥 − = +
+ 𝑥 += +
− 𝑥 + = −
+ 𝑥 − = −
Add or Subtract: Change to addition and PUT ON the correct side of Alge
mat and Zero pair off; record what is left on the mat on which side.

Irrational Numbers:
Anything that doesn’t end or repeat… √2 , √3 , √ 5 ,
√7 , √ 8 , π, etc……….
ORDER OF OPERATIONS (Please Excuse My Dear Aunt Sally)
Step 1 Do Parentheses (
)
Step 2 Do Exponents / Powers / Square Roots
Step 3 Do Multiplication or Division
MUST DO In order from left to right
Step 4 Do Addition or Subtraction
MUST DO In order from left to right
SOLVING EQUATIONS:
1. Change ALL subtraction to addition (if need)
2. Do the Distributive Property (If needed)
3. Combine Like TERMS on EACH side
4. Get the VARIABLE on one side (do the INVERSE to remove)
5. SOLVE
6. CHECK your answer (substitute in problem)
SOLVING RATIOS/ PROPORTIONS/ FRACTIONS & PROBABILITY
1. Look for a RULE BETWEEN Fractions/Ratios/Proportions
2. REDUCE fraction/ratio/proportion to LOWER TERMS to get RULE
3. CROSS MULTIPLY and solve using steps above for SOLVING EQUATIONS
FRACTION RULES:
Addition and Subtraction: May Change to same denominator or
Butterfly Method
⅚ + or - ⅞ =
Multiplication: multiply straight across
Division: Flip / Reciprocal/Inverse of 2nd fraction THEN multiply across or
ZIG/ZAG by multiplying.
Improper fraction: 24/4 = 6; 36/7 = 5 1/5 (divide)
Mixed Fraction: 5 ¾ = 5.75 = 575% = 23/4
SLOPE
Line rises to Rt = positive slope
Line horizontal = 0 slope
** m is the slope
Line rises to Lt = negative slope
Line vertical = undefined slope
b is the y- intercept (hits the y axis)**
Standard Equation:
Ax + By = C
𝐲 = 𝐦𝐱 + 𝐛
Slope-Intercept Equation:
Slope of a line using points:
Point/Slope form:
𝒚₂ − 𝒚 ₁
x₂ − 𝒙₁
m=
y - y1 = m( x – x1)
Slope of a Line: rise (y)
run (x)
Table: In (x) Out (y)
-2
-4
-1
-2
0
0
Slope = 2 (Y)
1 (X)
To find the y-intercept (b): (x , y) put a zero in for x (0, y) and solve the equation given;
will get y =
To find the x-intercept: (x , y) put a zero in for y (x, 0) and solve the equation given; will
get x =
Perpendicular Slope Equations MUST have OPPOSITE AND FLIPPED slope and may have
the same y- intercept or b
Parallel Slope Equations MUST have SAME SLOPE, BUT different y-intercept or b
(𝒇 𝑶𝑭 𝒙) 𝒇 (𝒙) = 𝟑 𝒙 + 𝟗
𝒇(𝒙) = 5 𝒚 = 𝟑 (𝟓) + 𝟗 … 𝒚 = 𝟏𝟓 + 𝟗
𝒚 = 𝟐𝟒 Coordinate Pair would be ( 𝟓 , 𝟐𝟒 )
Arithmetic Sequence
Geometric Sequence
f(x) = mx +b
f(x) = a(b) or f(x) = a²
PROPERTIES OF OPERATIONS
Commutative Property: Numbers can change order 3 +* 4 = 4 +* 3 and problem
answer doesn’t change.
Associative Property: Parentheses change order or one set leaves:
( 3+*6) +* ( 4 +*9) = 3 +*( 6 +* 4 ) + * 9 =
Distributive Property: a letter or # is given to the inside (): 6 ( 4a + 5b) = 24a +
30b OR a letter or # is removed to the outside of ( ): 6x + 8x = x (6+8)
RANGE: Maximum - Minimum
MEAN: (Average) Add up data and divide by # of data
MODE: Most repeated data
MEDIAN: Put data in order and find the MIDDLE
< is less than or equal .
> is greater than or equal .
< is less than o
> is greater than o
CAPACITY OR FLUID OUNCE
8 fl oz = 1c
32 fl oz = 4c = 2 pt = 1 qt
128 fl oz = 16c = 8pt = 4 qt = 1 gal
WEIGHT
16 oz = 1 pound (lb)
2,000 lb = 1 ton
DISTANCE
12 in. = 1 ft
36 in. = 3 ft = 1 yd
5,280 ft = 1 mi
TIME
60 sec = 1 min; 60 min = 1 hr; 24 hrs = 1 day 365 days = 1 year
10 years = 1 decade
100 years = 1 century
TEMPERATURE
F = Fahrenheit C = Celsius
Water Freezes
32 ⁰
0⁰
Normal Body
98.6 ⁰
37 ⁰
Water Boils
212 ⁰
100 ⁰
CONVERSIONS
1 oz ≈ 28g
1.06 qt ≈ 1 L
1 gal ≈ 3.79 L
1 in. ≈ 2.54 cm
1 K ≈ .62 mi
1 tsp ≈ 5mL
2.2 lb ≈ 1 Kg
1 mi ≈ 1.6 Km
METRIC
k = kilo = 1,000 meters, grams, Liters
h = hecto = 100 meters, grams, Liters
da = deca = 10 meters, grams, Liters
d = deci = 0.1 meters, grams, Liters
c = centi = 0.01 meters, grams, Liters
m = milli = 0.001 meters, grams, Liters
GEOMETRY
POLYGONS
Line = 180°
Triangle 3 SIDES = 180 ⁰
Quad 4 SIDES= 360 ⁰
Perpendicular Lines make a 90◦
Total Degrees in Polygon RULE = 180 ( n – 2) n = number of sides
Scalene = NO sides same
Isosceles = 2 sides same
Equilateral = 3 sides same
Acute ∆ = ALL angles acute
Obtuse ∆ = 1 angle obtuse
Rt ∆ = 1 angle right
ANGLES
Supplementary Angles = 180°
Complementary Angles = 90°
Adjacent Angles = share a side
Vertical Angles = are diagonal from each other and have = degrees
PERIMETER (unit) = ADD all the sides of polygon;
CIRCUMFERENCE (Circle perimeter) C = d 𝜋 or 2r𝜋
(d=diameter: across full circle through the center; r=radius: from center to one side
of circle)
AREA (sq unit or unit 2)
Triangle
A = 1/2hb or hb/2
Rectangle / Parallelogram / Square A = bh
Trapezoid
A = ½ h (b + b)
Circle
𝐴 = 𝜋𝑟 2
SURFACE AREA (sq. unit or unit 2)
Find the AREA of EACH Shape …. then ADD together
Cylinder SA = (𝜋𝑟 2 ∗ 2) + (d𝜋 ∗ ℎ)
VOLUME (cubic or unit 3)
Cube 𝑉 = 𝑠³
1
Triangular Prism 𝑉 = 𝐵 ℎ (B = lw)
2
Rectangular Prism 𝑉 = 𝐵ℎ
(B=lw)
2
Sphere V = 𝜋 𝑟 4/3
Cone
𝑉 = 𝜋 𝑟 2 ℎ 1/3
Cylinder V = 𝜋 𝑟 2 h
Pyramid 𝑉 = 𝐵ℎ1/3 (B=lw)
Pythagorean Theorem:
RIGHT TRIANGLE ONLY; Also, DISTANCE of two points on a GRAPH
𝒂𝟐 + 𝒃𝟐 = 𝒄𝟐
a & b Must be the legs/sides that form RT ANGLE!