Standardized Tests

SAT/ACT Standardized Test Prep

Linear Equations

Notes: Linear Equations

Linear Equations and Slope

Graphing Linear Equations

Slope Formula

Linear Equations- Standard Form

Net Change

Slope Intercept Form

Point Slope Form

Linear Equations- Direct Variation

Parallel and Perpendicular Slope

Distance between a point and a line

Isolating Variables

Fahrenheit and Celsius Conversions

Finding x- and y- intercepts

Solving Systems

Solving Systems (Substitution)

Solving Systems (Elimination)

Graphing Systems of Inequalities

3 Variable Systems

Nonlinear Systems

Polynomials

Irrational Numbers

Is it Rational or Irrational?

Exponents

Multiplying Monomials

Dividing Monomials

Scientific Notation

Intro to Polynomials

Is it a Polynomial?

Notes: Polynomials

Adding and Subtracting Polynomials

Multiplying Polynomials (FOIL)

Dividing Polynomials (Long Division)

Dividing Polynomials (Synthetic Division)

Synthetic Substitution

End Behavior- Polynomial Functions

Completing the Square

The Quadratic Formula and the Discriminant

Complex Numbers (Imaginary Numbers)

Polynomials- Roots & Multiplicity

Rational Zero Theorem

Descartes’ Rule of Signs

Roots and Zeroes

Polynomial Equation Given Roots

Linear Factored Form

Quadratic Inequalities

Polynomial Inequalities

Quadratic Word Problems

Complex Numbers

Adding and Subtracting Complex numbers

Multiplying Complex Numbers

Dividing Complex Numbers

Complex Conjugates

Factoring

Factoring out a GCF

Factoring Perfect Square Trinomials

Factoring Trinomials a=1

Factoring u-substitution

Factoring Trinomials a≠1

Factoring: Difference of 2 squares

Factoring: Sum/Difference of 2 cubes

Factor by Grouping

Solving Quadratic Equations by factoring

Solve by Factoring

Polar Coordinates

Notes- Complex Polar Numbers

Graphing Polar Coordinates

Roots of Complex Polar Numbers (de Moivres)

Conjugates

Radical Expressions & Equations

Adding and Subtracting Square Roots

Multiplying Square Roots

Dividing Square Roots

Radical Expressions

Radical Equations

Square Roots

Simplifying Square Roots

Cube Roots

Simplifying Cube Roots

Adding & Subtracting Cube Roots

Multiplying Cube Roots

Dividing Cube Roots

Radical Exponents

Rational Exponent Form

Zero Exponents

Negative Exponents

Word Problems

Word Problems- Linear Equations

Word Problems- Averages

Word Problems- Consecutive Integers

Word Problems- Distance, Rate and Time

Breakeven Word Problems

Word Problems- Ratios and Proportions

Word Problems- Ages

Word Problems- Mixtures and Concentration

Rational Expressions & Equations

Ratios and Proportions

Rational Expressions (Multiplying and Dividing)

Rational Equations

Rational Expressions (Adding and Subtracting)

Simplifying Rational Expressions

Domain of Rational Expressions

Direct, Inverse and Joint Variation

Complex Fractions

Rational Inequalities

Partial Fraction Decomposition

Data Analysis

Histograms

Circle Graphs (Pie Charts)

Stem and Leaf Plot (Stemplot)

Mean, Median and Mode

Mean Absolute Deviation

5 Number Summary-Quartiles and IQR

Box and Whisker Plot

Parameter vs Statistic

Scatterplots

Probability

Experimental and Theoretical Probability

Factorials

Combinations and Permutations

Complement of an Event

Probability “At Least One”

Mutually Exclusive Events (Disjoint)

Expected Value and Variance of a Random Variable

Independent Random Variables
Sums and Differences

Independent Events (Probability)

Conditional Probabilities

Marginal Frequencies and Distributions

Two-Way Tables (Probability)

Tree Diagrams

Probability- Marbles

Probability- Coin Tosses

Probability with Dice

Probability- Round Table

Probability- 5 card Poker Hands

Binomial Distribution Notes

Functions

Evaluating Functions

Set Builder Notation

Vertical Line Test

Is it a Function?

Operations of Functions

Notes- Functions

Composite Functions

Inverse Functions and Relations

Interval Notation

Domain and Range (Roots and Denominators)

Describing Transformations of Functions

Parent Functions

Graphing Square Root Functions

Graphing Quadratic Functions

Graphing Cube Root Functions

Graphing Absolute Value Functions

Vertical Asymptotes

Horizontal Asymptotes

Slant Asymptotes

Domain of Rational Functions

Graphing Rational Functions
(Horizontal and Vertical Asymptotes)

Even and Odd Functions

Evaluating Piecewise Functions

Graphing Piecewise Functions

Absolute Value Functions as Piecewise Functions

Transformations- |f(x)| and f|x|

Matrices

Notes: Matrices

Intro to Matrices

Operations with Matrices
(Adding, Subtracting, and Scalar multiplication)

Multiplying Matrices

Determinants

Cramer’s Rule

Identity Matrix

Identity and Inverse Matrices

Transpose of a Matrix

Rotation Matrix

Eigenvalues and Eigenvectors

Conic Sections

Notes: Conic Sections

Equation of a circle

Parabolas

Axis of Symmetry

Vertex & Axis of Symmetry

Ellipses

Area of Ellipses

Hyperbolas

Conic Sections- Completing the Square

Eccentricity

Degenerate Conics

Parametric Equations

Parametric to Rectangular

Parametric Equations (Conic Sections)

Exponential and Logarithms

The number e

Notes: Logarithms

Growth or Decay?

Evaluating Exponential Functions

Exponential Models

Combining or Condensing Logarithms

Logarithmic Form & Exponential Form

Evaluating Logarithms

Exponential Decay (Half Life)

Compounded Interest Problems

Annuities

Exponential Functions Given 2 Points

Solving Exponential Equations

Logarithms

Expanding Logarithms

Decibel Notes

Earthquake Problems- Richter Scale

Graphing Exponential Functions

Domain and Range of Logarithmic Functions

Graphing Logarithmic Functions & State the Domain

Solving Logarithmic Equations

Inverse of Exponential Functions

Inverse of Logarithmic Functions

Logistic Function

Sequences and Series

Arithmetic Sequences

Geometric Sequences

Arithmetic Series

Geometric Series

Infinite Geometric Series

Arithmetic Means Between 2 Terms

Summation Notation (Sigma Notation)

Product Notation (Pi Notation)

Finite Sums Formulas

Recursive Sequences

Fibonacci Sequence

Golden Ratio

Pascal’s Triangle

Binomial Theorem

Trigonometry

Right Triangle Trigonometry

Word Problems- Trigonometry

Converting Radians and Degrees

Degrees Minutes Seconds Form

Coterminal Angles

Reference Angles

Find all 6 Trig Functions

Unit Circle

Law of Sines

Area of triangle SAS formula

Law of Cosines

Heron’s Formula- Area of Triangle

Area of Oblique Triangles

Geometric Mean

Similar Right Triangles

Inverse Trigonometric Functions

Sum and Difference of Angles Formulas

Double-Angle and Half-Angle Formulas

Trigonometry- Pythagorean Identities

Product-Sum Identities

Cofunction Identities

Trigonometric Identities

Graphing Trig Functions (sin and cos)

Graphing Trig Functions (tan and cot)

Solving Trigonometric Equations

Vectors

Displacement Vectors

Magnitude of Vectors

Unit Vectors

Direction of a Vector

Dot Product

Orthogonal Vectors

Parallel and Perpendicular Vectors

Scalar and Vector Projections

Cross Product

Converting Polar Coordinates

Euler’s Formula

Equation of a Plane

Is this point on this plane?

Equation of a Plane given 3 Points

Coplanar Points

In Summary

Algebra 2 is a branch of mathematics that builds upon the concepts introduced in Algebra 1. It includes the study of advanced algebraic concepts such as equations, functions, and graphing techniques.

One of the main goals of Algebra 2 is to teach students how to solve quadratic equations, which are equations in the form of \(ax^2 + bx + c = 0\). Quadratic equations can be solved using a variety of techniques, including factoring, completing the square, and using the quadratic formula.

In addition to quadratic equations, Algebra 2 also covers the study of polynomial functions, which are functions of the form \(f(x) = a_nx^n + a_{n-1}x^{n-1} + … + a_1x + a_0\). These functions can be graphed using techniques such as finding the zeros (or roots) of the function and using the end behavior of the function. Polynomial functions can also be used to model real-world situations, such as the height of a ball thrown into the air or the velocity of a car.

Another important topic in Algebra 2 is the study of conic sections, which are curves formed by the intersection of a plane and a cone. There are four types of conic sections: circles, ellipses, hyperbolas, and parabolas. These conic sections can be graphed using standard equations, and can also be used to model real-world situations, such as the path of a projectile or the shape of an antenna dish.

In addition to graphing conic sections, students in Algebra 2 will also learn about transformations of functions, which involve changing the graph of a function by stretching, shifting, or reflecting it. These transformations can be useful for understanding the behavior of a function and for solving real-world problems.

Algebra 2 also introduces students to matrices, which are arrays of numbers used to represent linear transformations. Matrix operations, such as matrix addition and multiplication, can be used to solve systems of linear equations and perform other mathematical tasks.

Another important concept in Algebra 2 is the study of exponential and logarithmic functions, which are used to model situations where there is rapid growth or decay. These functions can be graphed and transformed in a similar way to polynomial functions, and can be used to model real-world phenomena such as population growth, radioactive decay, and compound interest.

In addition to these topics, Algebra 2 also includes the study of sequences and series, which are used to represent patterns and trends in data. Students will learn about arithmetic and geometric sequences and series, and will use these concepts to solve real-world problems.

One application of Algebra 2 is the study of probability and statistics. Students will learn about probability distributions, such as the binomial and normal distributions, and will use statistical techniques, such as hypothesis testing and regression analysis, to analyze data and draw conclusions.

Another application of Algebra 2 is the study of trigonometry, which is the study of triangles and the relationships between the sides and angles of triangles. Trigonometry is used to solve problems in fields such as physics, engineering, and astronomy.

In addition to these topics, Algebra 2 also includes the study of complex numbers, which are numbers that include a real part and an imaginary part. Complex numbers can be represented in the complex plane and can be manipulated using algebraic techniques similar to those used for real numbers.

Overall, Algebra 2 is a crucial subject for students interested in pursuing careers in science, engineering, or other fields that require advanced mathematical skills. By mastering the concepts of Algebra 2, students will be well-prepared to tackle more advanced math courses and apply their skills to real-world problems.

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