Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)

Chapter 1: Solving Linear Equations Property/Postulate/Formula Example

Solving Linear EquationsHere are several steps you can use to solve an equation. Depending on the equation, you may not need to use some steps.

Rewriting Literal equationsAn equation that has two or more variables is called a literal equation. So rewrite a literal equation, isolate one variable in terms of the other variable(s).

Chapter 2: Solving Linear Inequalities Property/Postulate/Formula Example

InequalityA mathematical sentence comparing expressions

Representing Linear InequalitiesThe graph of an inequality shows the solution set on a number line

Multiplying/Dividing Inequalities by NegativesThe direction of the inequality must be “switched” in order to make the inequality true

Compound InequalitiesFormed by joining two inequalities with the words “and” or “or”

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Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)Chapter 3: Graphing Linear Functions

Property/Postulate/Formula ExampleFunctionsA relation that pairs one input with exactly one output (x-values CANNOT repeat)

Domain and RangeDomain: all possible input values (x-values)Range: all possible output values (y-values)

Linear vs. Nonlinear FunctionsLinear functions have a constant rate of change

Discrete vs. Continuous DomainDiscrete Domain: only certain numbers in an intervalContinuous Domain: all numbers within an interval

Function NotationInstead of writing as y = , write as f(x) =

Evaluating a FunctionSubstitute the given values for x in the function to determine the output

Using Intercepts to graph functionsPlot the x- and y-intercepts to graph the linear function

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Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)Slope

Slope-Intercept formy = mx + b

Absolute Value Function

Chapter 4: Writing Linear Functions Property/Postulate/Formula Example

Point-Slope FormLinear equation written in a different form than y = mx + b

Slopes of Parallel LinesTwo lines are parallel if and only if they have the same slope

CorrelationRelationship between Data Sets

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Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)Line of Best Fit (Linear Regression Equation)A Line drawn on a scatter plot that best represents the data

To get the line of best fit on the calculator:1. STAT EDIT2. Type data into L1 and L2

3. STAT CALC 4: LinReg (ax + b)4. ENTER5. Down to calculate6. ENTER

ResidualsThe difference of the y-value of a data point and the corresponding y-value found using the line of best fit

REMEMBER – The line is a good fit if the residuals do not follow a pattern and are evenly distributed above/below the x-axis

Correlations CoefficientTells whether the correlation is strong, weak, positive, negative.

REMEMBER – the Diagnostic must be turned on in order for the calculator to give you this value. Go to 2nd 0, down to DiagnosticOn, ENTER, ENTER.Arithmetic SequenceA sequence in which the difference between each term is the same

*Graphed as a straight line*Piecewise FunctionA function represented by 2 or more equations

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Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)Chapter 5: Solving Systems of Linear Equations

Property/Postulate/Formula ExampleSystems of Linear Equations – Graphing

Systems of Linear Equations – Substitution

Systems of Linear Equations – Elimination

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Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)Solutions of Systems of Linear EquationsSystems of linear equations can have one, zero, or infinitely many solutions

Graphing a System of Linear Inequalities

Chapter 6: Exponential Functions & SequencesProperty/Postulate/Formula Example

Rules of Exponents

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Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)Exponential FunctionA nonlinear function in the form y=abx

Exponential Growth Function

Exponential Decay Function

Compound Interest

Geometric SequenceThe ratio between each pair of consecutive terms is the same (has a common ratio)

*Graph is a curve that approaches x=0, but never touches it*Recursively Defined SequencesGives you the beginning term in a sequence and a Recursive Equation that tells you how an is related to the preceding term

Chapter 7: Polynomial Equations & Factoring7

Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)

Property/Postulate/Formula ExampleStandard Form of a PolynomialWhen the exponents of the terms decrease from left to rightAdding/Subtracting PolynomialsCombine all like terms

*When subtracting, don’t forget to distribute the subtraction sign to all terms in the second polynomial*

Addition:

Subtraction:

Multiplying Binomials1. FOIL2. Distributive Property3. “Box” Method

1.

2.

3. Factoring 1. Greatest Common Factor

2. Difference of Two Squares3. Factor Nice and Easy4. AC Method

Chapter 8: Graphing Quadratic Functions Property/Postulate/Formula Example

Characteristics of Quadratic Functions

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Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)Graphing f ( x )=a x2+bx+c

Graphing f ( x )=a(x−h)2

Vertex Form of a parabola

Average Rate of Change

Chapter 9: Solving Quadratic EquationsProperty/Postulate/Formula Example

Adding/Subtracting RadicalsAdd and subtract radicals only when the radicand is the same

Solving Quadratics Using Square Roots

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Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)Completing the Square

Quadratic Formula

Graphing Nonlinear Systems

METHODS FOR SOLVING QUADRATIC EQUATIONS

Chapter 10: Radical Functions & Equations Property/Postulate/Formula Example

Graphing Square Root Functions

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Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)Graphing Cube Root Functions

TRANSFORMATIONS OF FUNCTIONS

*REMEMBER: these rules apply for all functions, not just square root function*

Chapter 11: Data Analysis & DisplaysProperty/Postulate/Formula Example

Measures of Center

Standard DeviationThe measure of how much a typical data value differs from the mean.

Plug all data into STAT EDIT, STAT CALC 1 Var Stats

σ=¿ standard deviation

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Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)Box & Whisker Plot

To get the 5 Number Summary:Plug all data into STAT EDIT, STAT CALC 1 Var Stats

Min:Q1:Med:Q3:Max:

Shapes of Box & Whisker Plots

Shapes of Histograms

Two-Way TablesData collected from one source that belong to two different categories

Qualitative DataConsists of labels or non-numerical data that can be separated into categories

Examples: Zip codes of students in the class, hair color, etc.

Quantitative DataConsists of numbers that represent counts or measurements

Examples: Lengths of songs played at a concert, Prices of cars at a dealership, etc.

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Common Core Algebra I: Things I Need to KnowFrom Big Ideas Math (by chapter)

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