Algebra I SOL Topics and Formulas
SOL 1: Equations, Inequalities, Expressions
Use Opposite operation Inverse
Divide/Multiply by a negative switch the symbols**
SOL 2: Verbal Expressions
Oder of Operations PEMDAS
Two less than x = x-2
Remember these key words:
ADDSUBTRACTMULTIPLY
more thanless than (switch the numbers)product
increased by how much more? twice
total ofdifferenceof (like half of)
sumhow much farther?
at least → ≥
DIVIDEis – equalsno more than → ≤
shared equallyis less than → <at most → ≤
quotientis greater than → <no less than → ≥
“times the sum of” or “times the difference of – you need parentheses
So “Five less than three times the sum of a number and seven” means 3(n+7) - 5
Example: Omar wants to have a party. He will pay $300 for a DJ and $10 per person for food. If his bill was $650, how many people are coming to the party?
Omar has to pay $300 for the DJ no matter what, that is the thing that doesn’t change. His cost for food changes according to how many people he invites. $650 is his total, so this is the equation:
300 + 10x = 650
You can use solver to get x = 35 people.
SOL 3: Properties
Distributive Property: Multiply a number outside of a parenthesis to every term inside.
6x – 12 = 6(x – 2)
3(n – 7) = 3(n) + 3(-7)
a(x + b) = ax + ab
Identity Property of Multiplication – if you multiply any number by 1 you get the original number
Identity Property of Addition – if you add zero to any number you get the original number
Commutative Property :the numbers can change places.
3 + 5 = 5 + 3
ab = ba
(ab) + 3 = (ba) + 3
(7a + 9 ) +5a = 5a + (9 + 7a)
There is no commutative property of division or subtraction
Reflexive
SymmetricIf, then
Associative Property:move the parentheses around , the numbers have to stay in exactly the same order.
3x + (5x + 9) = (3x + 5x) + 9
7(xy) = (7x) y
Again – there is no associative property of subtraction or division
Transitive Property of Equality – if two number both equal the same thing then they equal each other (it
always says if…and…then)
If, and, then
Addition Property of Equality – if you add the same thing to both sides of an equation, the two sides are still equal)
Subtraction Property of Equality – if you subtract the same thing from both sides of an equation, the two sides are still equal)
Multiplication Property of Equality – if you multiply both sides of an equation by the same thing, the two sides are still
equal)
Division Property of Equality – if you divide both sides of an equation by the same thing, the two sides are still equal)
Inverse Property – any number plus its opposite = 0 ( 4 + (-4) = 0)
any number times its inverse =1 (2 * ½ = 1)
SOL 4: Matrices
Rows x Columns
Add, Subtract, Multiply
SOL 5: Function, Patterns
Function: x does not repeat (domain is all different numbers)
Graphs use vertical line test can only cross at one point
Functions and Graphing A.5
The coordinate plane is made up of an x-axis and a y-axis. To find a certain point on the coordinate plane, you need an x and a y coordinate that are listed together like this (x, y). The x and y axes are always labeled on the SOL.
A relation is any set of ordered pairs. The domain is the set of all x values or first coordinates and the range is the set of all y values or second coordinates. A relation is a function if all of the x-values are different. See examples below.
EX1: {(3, -4), (3, 5), (4, 6)} EX2: {(7,1), (8,1), (9,1)}EX3 EX4
not a function – the x’s repeat function
111
EX5: EX6:
this is a function not a function – the x
D = { 1, 2, 3,} is used twice
R = { 4, 5, 6}
not a function – the x’s repeat this IS a function
x is reused with the same y
functionnot a function – use the vertical line test not a function – use the vertical line test
D = { all real numbers}
R = { all real numbers greater than 0}
SOL 6: Slope, X, Y, Intercepts
y=mx+bm=slopeb=y-intercept
Ax + By = C standard form
Slope= m=
Horizontal line y=2 slope = 0 (HOY)
Vertical line x=2 slope is undefined (VUX)
SOL 7: Slope, Graph of a line
Types of slope
Positive Negative Zero Undefined
SOL 8: Write Linear Equations
Y=mx+b slope intercept (where it crosses the y axis)
(m is your slope () , b is the y-intercept)
Ax+By=C Standard
(A, B, and C cannot be fractions; A cannot be negative)
SOL 9: Systems of Equations: 2 equations, 2 variables, 2 answers
Elimination
**now plug y=5 into either equation
Substitution
Graphing- where 2 lines intersect is the solution (x,y)
SOL 10: Monomials, Exponents, Scientific Notation
A. Add exponents when multiplying polynomials
B. Multiply Exponents when raising a polynomial to a power
C. Subtract Exponents when dividing polynomials
Scientific Notation 2.53 x = 253,000
3.06 x= 0.0000306
SOL 11: Polynomials
Add/Subtract like terms
(The same variables with the same exact exponents)
Multiply/Distribute, FOIL (First Outer Inner Last)
SOL 12: Factoring Binomial/Trinomial Equations
Signs Trinomial= 2 binomials
(+ +)=(+)(+) =
(- +)= (-)(-) =
(+ -)=(+)(-) =
(- -)= (+)(-) =
Different of Squares
SOL 13: Radicals
Adding/Subtracting:
Reduce: look for a perfect square(4,9,25,36,etc)
Only add like terms (same radian and index)
Reduce the radicals by looking for perfect squares
Add the leading coefficients only!
SOL 14: Solve Quadratic Equation
Set trinomial =0
Factor Polynomial like normal
Set each factor (set of parenthesis) equal to zero
Solve for the variable
You should have two answers!
**This is also called zeros or solutions**
Graphs Parabola Answers is where graph crosses the x-axis
X-intercepts, Function
SOL 16: Functional Value
=substitute a value in for the variable
Plug in value for x
f(x) = 3x – 5 f(x) means the same thing as y. It is just the name of the function
f(7) = 3(7) – 5 = 16 f(7) means take out x, put in 7
EX for f(x) = x2 – 1 find the range if the domain is { -2, -1, 0, 1}
this means put all of those numbers in for x and get an answer for each one. Put all of the negative numbers in parentheses to square them.
Answer {-1, 0, 3} – in order from smallest to biggest. You got 0 twice but you don’t have to list it twice.
SOL 17: Line of Best Fit
Draw line that goes through most points.
Write Equation use slope, y-intercept y=mx+b
SOL 18: Statistics
Mean- averages (add up all the data and then divide by # of objects)
Mode- Most
Medium- middle # put in order first to last
Range- subtract the lowest value from the highest value
Stem-leaf, Box-whisker read directions, look at graphs
SOL 19: Direct Variation, Graphs
Varies Directly Proportion cross multiply
Varies Inversely Proportion inverse y’s and cross multiply
Graph: Goes through origin positive slope
Direct variation y=mx+0