Summary Algebra 1 Full Year Formula and Equations Guide by Cute Calculus

Algebra
ALGEBRA 1 1, Sheet 1 See also Pre-Algebra, Algebra II, Geometry, Precal, Calculus Sheets

Adding & Subtracting 5 + 3 same sign add = 8 5 - (-3) same sign add = 8
positive and negative numbers 5 + +3 same sign add, equals positive 8

-5 - 3 same sign add = - 8 5 - 3 different sign subtract = 2
SAME SIGN ADD (the sign on the bigger number = sign of answer)

-5 + (-3) same sign add = - 8 -5 - (-3) different sign subtract= - 2
-5 + +3 diff sign subtract, larger number (-), ans (-)
DIFFERENT SIGN SUBTRACT
-5 + 3 different sign subtract = - 2 5 + -3 different sign subtract = 2
(the sign on the bigger number = sign of answer) (the sign on the bigger number = sign of answer)

Multiplying & Dividing 6 x 7 same sign + = + 42 42 ÷ 7 same sign + = + 6
positive and negative numbers
-6 x -7 same sign + = + 42 -42 ÷ -7 same sign + = + 6
SAME SIGN POSITIVE +
6 x -7 different sign - = - 42 42 ÷ -7 different sign - = - 6
DIFFERENT SIGN NEGATIVE -
-7 x 6 different sign - = - 42 42 ÷ -6 different sign - = - 7

|Absolute Value| Distributive Property Order of Operations
DISTANCE from ZERO PEMDAS
Distribute (or multiply) the term outside
the parentheses times EACH TERM Please (Parentheses)
ALWAYS POSITIVE +++ Multiplication and
INSIDE THE PARENTHESES. Excuse (Exponents)
|8| = +8 |125| = +125 Division are done
5(x +1) = 5•x + 5•1 = 5x + 5 My (Multiplication) left to right.
|- 8| = +8 The only possible |- 125| = +125
negative outcome 2
y(2y - 3) = y•2y - y•(-3) = 2y - 3y Dear (Division)
- |8| = - 8 is if it is out in - | 125| = -125 Aunt (Addition)
Addition and
FRONT of the
12(a2 + 5b)= 12•a2+12•5b = 12a2 + 60b Sally (Subtraction) Subtraction are
- | - 8| = - 8 absolute value - |- 125| = -125 done left to right.

Evaluate Algebraic Expressions Adding and Subtracting Variables 4x - 10x = -6x
Plug in the given variables, solve! Only add and subtract LIKE TERMS
4x -10y = NOT POSSIBLE
Examples of “like terms”:
2
Evaluate x - 5y for x = 2 and y = -1 4ab + 100ab = 104ab
“like term”
x - 5y =
2
(2)2 - 5(-1) = 4 - (-5) = 9 4x, -10x, 100x, -3x x 4y - 10y + 100y = 94y
4ab, -10ab, 100ab, -3ab ab
Evaluate 3x2 + 2y for x = 5 and y = -4 4x2 + 100x = NOT POSSIBLE
4y, -10y, 100y, -3y y
3x2 + 2y= 3(5)2 + 2(-4) =75 - 8=67 4x2 - 3x2 = 1x2
4x2, -10x2, 100x2, -3x2 x2
Slope m = slope Mulitplying and Dividing Variables 2x • 3x2 = 2 • 3 • x1+2 = 6x3
m = y2 - y1 4 2 3 2 4+3
=30x2y7
x2- x1 UNlike terms can be multiplied and divid- 5y • 6x y = 5 • 6 • x • y
b = y-intercept
ed. Multiply and divide whole numbers
Slope-Intercept Form separate of the variable. 3 2 3-2 1
(x1, y1) (x2, y2) 4a ÷ a = 4a = 4a
y = mx + b
ADD exponents when multiplying 5
8x ÷ 2x = 4x 3 5-3
= 4x2
Point-Slope Form = given points
SUBTRACT exponents when ÷
y - y1 = m(x - x1) 18x2y3 ÷ 3y= 6x2y3 - 1 = 6x2y2

Simplifying Fractions Multiplying Fractions Dividing Fractions
Find a number that can be divided evenly in both nu- Multiply top • top, bottom • bottom. Flip the second fraction and multiply.
merator and denominator. Keep doing this until you
can no longer divide, that’s when it is simplified.

5zx 240
2 Eye x5z 3 4 17
8 y
5 I I z 34 24 8 3
g oq 31 4 41 15
9x4 6 9
Exponents Exponents Raised to Exponents NEGATIVE Exponents
If a term has a negative exponent and is in
ADD exponents, → multiplying MULTIPLY exponents when raised to the numerator, move it to the denominator to
SUBTRACT exponents → dividing another exponent. become positive. If the term with the negative
exponent is in the denominator, move it to the
C273 27.1 2 C2 8 302
numerator to become positive.

8 2.3 5 83 x 5
24 7 4 3
16 6
47 t s s


t2a 4a 4a3 oy5K83 y5.3 51255 j.az I4Ia
FOR MORE HELP DM @CuteCalculus www.20MinTutor.com
CuteCalculus.com
Tutoring in Pre-Algebra, Algebra I & II, Geometry, Precal, Calculus - DM @CuteCalculus