Topics by Skills

Dividing Numbers with Decimals

• Divide Numbers with Decimals to the Tenths 
• Divide Numbers with Decimals to the Hundredths
• Divide Numbers with Decimals to the Thousandths

Multiplying Numbers with Decimals

• Multiplying Numbers with Decimals to the Tenths
• Multiplying Numbers with Decimals to the Hundredths
• Multiplying Numbers with Decimals to the Thousandths

Prime Factorization

• Introduction to Prime Factorization
• Finding Prime factors of a number

GCF and LCM

• Introduction to GCF
• Finding GCF of two or more numbers
• Real-World Problems
• Introduction to LCM
• Finding LCM of two or more numbers
• Real-World Problems

Adding and Subtracting Integers

• Introduction
• Ordering & comparing integers
• Adding & subtracting integers with same signs
• Adding & subtracting interers with different signs
• Adding & subtacting multiple integers

Multiplying and Dividing Integers

• Multiplying & dividing integers with the same signs
• Multiplying & dividing  interers with different signs
• Multiplying & dividing multiple integers

Order of Operations with Integers

• Expressions
• Equations
• Inequalities

Absolute Values

• Introduction to the Absolute values
• Order & Compare absolute values
• Equations with Absolute Values
• Absolute values Inequalities
• Absolute values of Rational Numbers
• Real-world problems involving Absolute Values

Addition and Subtraction of Fractions

• Addition and Subtraction of Fractions with Like Denominators
• Addition and Subtraction of Fractions with Unlike Denominators
• Order and Compare Fractions with Like Denominators
• Order and compare Fractions with Unlike Denominators
• Word Problems involving Addition and Subtraction of Fractions

Multiplication and Division of Fractions

• Multiplication and Division of Fractions with Like Denominator
• Multiplication and Division of Fractions with Unlike Denominator
• Multiplication and Division of Mixed Fractions
• Word Problems involving Multiplication and Division of Fractions

Mixed Fractions

• Addition and Subtraction of Mixed Fractions
• Multiplication and Division of Mixed Fractions
• Order and Compare Mixed Fractions
• Word Problems involving Mixed Fractions

Fraction and Decimal Conversion

• Changing Decimal to Fraction
• Changing Fraction to Decimal

Adding and Subtracting Rational Numbers

• Add Rational Numbers
• Subtract Rational Numbers

Order and Compare Rational Numbers

• Order Rational Numbers
• Compare Rational Numbers

Multiplying and Dividing Rational Numbers

• Multiply Rational Numbers
• Divide Rational Numbers

Unit Rate

• Introduction to Unit Rate
• Real-World Problems

Ratios and Proportions

• Introduction to Ratios
• Equivalent Ratios
• Compare Ratios
• Ratios and Rates
• Ratios and Proportions
• Ratios, Rates and Proportions
• Real-World Problems

Percents

• Introduction to percents
• Converting decimals to percents
• Converting percents to decimals
• Converting fractions to percents
• Converting percents to fractions
• Finding percent of a number
• Putting percent to work

Algebraic Expressions & Properties

• Converting Real- World problems to Algebraic Expression
• Converting Algebraic Expression to Real-World Problem
• Converting Real-World description to Algebraic inequality
• Converting Algebraic inequality to Real-World Description
• Evaluate Algebraic Equations
• Use Algebraic properties to create equivalent Expressions
• One-Step Equations

Introductions to Equations

Coordinate Planes

• Introduction to four quadrants
• Plotting a point in coordinate plane
• Plotting polygons in coordinate plane
• Word problems

Area of Triangles

• Area of triangles
• Perimeter of triangles

Area of Paralleogram

• Area of parallelogram
• Perimeter of parallelogram

Area of Trapezoids

• Area of trapezoids

Area of Circles

• Radius & diameter
• Area of circles
• Area of semicircles
• Circumference of circles

Area of Composite Figures

• Introduction to composite shapes & figures
• Splitting composite figures into non overlapping parts/regions
• Finding area of composite figures

Introduction to Statistics

• Introduction to Statistics
• Statistical Questions
• Non-Statistical Question

Mean, Median, Mode & Range

• Introduction to statistics
• Mean
• Median
• Mode
• Range

Probability

• Probability of simple events
• Theoritical probability
• Experimental probability

Graphs and Charts

• Histograms
• Line plots
• Box plots
• Stem-and-leaf plots
• Circle graphs

Expressions and Equations

• Algebraic expressions
• Combining like terms
• Simple equations
• Solving one-step equations
• Solving two-step euations
• Solving multi-step euationas
• Solving equations with variables on both sides

Linear Inequalities in One Variable

• Introduction to Linear Inequalities in One Variable
• Solving Simple Linear Inequalities
• Graphical Representation of Linear Inequalities in One Variable

Application of Percentage

• Percent of a number
• Finding a number based on percent of its own
• Percent change - increase or decrease
• Tips, tax, discounts & interests
• Real-life percents problems

Angles & Triangles

• Sum of interior angles in a triangle
• Sum of exterior angles in a triangle
• Interior angles sum of a ploygon
• Finding missing angle in a triangle

Adjacent & Vertical Angles

• Introduction to adjacent & vertical angles
• Idenfifying adjacent & vertical angles
• Finding adjacent or vertical angle measues

Complementary & Supplementary Angles

• Introduction to complementary & supplementary angles
• Identifying complementary & supplementary angles
• Finding missing angle measure
• Parallel lines & traversals
• Angles formed by parallel lines & traversals

Cylinders

• Volume of cylinders
• Surface area of cylinders

Cones

• Volume of cones
• Surface area of cones

Pyramids

• Volume of pyramids
• Surface area of pyramids

Spheres

• Volume of spheres
• Surface area of spheres

Prisms

• Volume of prisms
• Surface area of prisms

Laws of Exponents

• Introduction
• Negative exponents
• Adding & subtracting exponents
• Multiplying & dividing exponents
• Power of exponents
• Scientific notations

Square Roots and Cube Roots

• Exact square & cube roots
• Approximating square & cube roots
• Simplifying square & cube roots

Introduction to Systems of Equations

• Introduction to Systems of Equations 
• Types of Linear Systems in Two Variables
• Consistent and Dependant Equations
• Consistent and Independant Equations
• Inconsistent Equations
• Graphs of Systems of Linear Equations
•  

Algebraic Fractions

• Fractions in Algebra
• Adding and Subtracting Algebraic Fractions
• Multiplying and Dividing Algebraic Fractions
• Simplifying/Reducing Algebraic Fractions

Linear Equations

• Writing Equations in Slope-Intercept Form
• Writing Equations in Point-Slope Form
• Scattered Plots & Lines of Fit
• Parallel and Perpendicular Lines

Inequalities & Graphing

• Properties of Inequealities
• Solving Inequalities by Addition and Subtraction
• Solving Inequalities by Multiplication and Division
• Multi-Step Inequalities
• Multiple Inequalities
• Graphing Inequalities
• Intervals

Systems of Equations and Inequalities

• Systems of Equations in Two Variables
• Graphing Systems of Equations
• Solving Systems of Equations using Substitution
• Solving Systems of Equations using Elimination (Addition, Subtraction and Multiplication)
• Graphing Systems of Linear Inequalities
• Applications of Systems of Equations

Adding and Subtracting Radical Expressions

• Adding and Subtracting Radical Expressions with Like Radicand
• Adding and Subtracting Radical Expressions with Unlike Radicand

Multiplying and Dividing Radical Expressions

• Product and Quotient Rule
• Multiplying Radical Expression
• Rationalizing the Denominators

Simplifying Radical Expressions

• Simplifying Radicals using the Product and Quotient Rules
• Simplifying Radicals with Variables
• Rationalize a Denominator using Conjugates
• Simplifying Square and Cube Roots
• Simplifying Higher Roots
• Solving Equations with Radicals

Monomials

• Introduction to Monomials
• Adding and Subtracting Monomials
• Multiplying Monomials
• Dividing Monomials

Polynomials and Operations

• Understanding Polynomials
• Adding and Subtracting Polynomials
• Multiplying Polynomial with Monomial
• Multiplying Polynomial with Polynomial
• Dividing Polynomial with Monomial
• Dividing Polynomial with Ploynomial

Factoring Polynomials

• Introduction
• Factoring Out a Common Factor
• Factoring the Difference of Squares
• Factoring Trinomials of Form: $x^2 + bx + c$
• Factoring Trinomials of Form: $a{x}^2 + bx + c$
• Factoring by Grouping
• Factoring Perfect Square Trinomials

Quadratic Equations

• Solving Quadratic Equations by Factoring
• Solving Quadratic Equations by Completing the Square
• Solving Quadratic Equations by the Quadratic Formula

Composite Functions

• Introduction to composite functions
• Notations and properties of composite functions
• Functional powers
• Decomposition of functions

Functions

• Introduction to functions and relations
• Types and key features of functions
• Interval notation
• Graphs of functions
• Absolute value functions
• Piecewise functions
• Real life applications of functions

Exponential Functions

• Exponential Functions
• Exponential Growth
• Exponential Decay
• Exponential Equations

Quadratic Functions

• Introduction to quadratic functions
• Forms of quadratic functions
• Properties of quadratic functions
• Graphs of quadratic functions

Continuous Function

• Introduction to continuous functions
• Discontinuous functions
• Types of discontinuities
• Removable discontinuity
• Jump discontinuity
• Infinite discontinuity

Inverse Functions

• Introduction to inverse function
• Inputs & outputs of the inverse function
• Graphs of inverse functions
• Finding inverse of a function
• Real world examples of inverses

Congruent Triangles

• Congruent figures
• Corresponding parts
• Test for congruence
• Congruence by SSS and SAS
• Congruence by ASA and AAS
• Congruence in Isosceles, Equilateral and Right triangles
• Triangle inqualities

Similar Polygons

• Ratios and proportions
• Properties of proportions
• Similar polygons
• Proportional parts and lengths

Distance and Midpoint Formulas

• The distance formula
• The midpoint formula

Equation of a Line

• Equations of line
• Linear equation
• Standard form
• Point-Slope form
• Slope-Intercept form

Equation of a Circle

• The standard equation of a circle
• Graphs of circles

Sector, Arc Length & Radian Measure

• Arc length and radian measure
• The radian measure of an angle
• Relationship and conversion between degrees and radians
• Area of a sector

Chords, Secants and Tangents

• Arcs and chords
• Angles by Chords, Secants, or Tangents
• Segments of Chords, Secants, and Tangents

Central and Inscribed Angles

• Central angles
• Arcs
• Inscribed angles
• Intercepted arcs
• Angles forrmed by a tangent and a chord

Logarithms

• Laws of Logarithms
• Properties of Logarithm
• Logarithmic Functions
• Logaritmic Equations
• Changing Exponential Equations to Logarithmic Form or Vice Versa
• Change of Base Formula
• Properties and Graphs of Logarithmic Functions

Polynomial Functions

• Introduction to Polynomial Function
• Linear Factors
• Remainder Theorem
• Zeros of a Function
• Rational Zeros Theorem
• Graphing and Transformation of Polynomial Functions

Simplifying Rational Expressions

• Simplying rational expressions

Multiplying and Dividing Rational Expressions

• Multiplying rational expressions
• Dividing rational expressions

Adding and Subtracting Rational Expressions

• Adding rational expressions
• Subtracting rational expressions

Complex Fractions

• Introduction to complex fractions
• Simplifying complex fractions
• Simplifying complex fraction as rewriting it as division
• Simplifying complex fration using least common denominator (LCD)

Rational Functions

• Introduction to rational functions
• Identifying a rational function
• Domain and range of a rational function
• Properties and representaion of a rational function
• Intercepts, asymptotes and graphs of a rational function

Adding and Subtracting Complex Numbers

• Adding and subtracting complex numbers
• Operations with complex number

Multiplying and Dividing Complex Numbers

• Complex conjugates
• Multiplying and dividing complex numbers

Simplifying Complex Numbers

• Operations with complex number
• Simplifying complex numbers

Matrix Operations

• Adding and subtracting matrices
• Scaler multiplication (multiplying a matrix by a number)
• Multiplying a matrix by another matrix
• Matrix row operations
• Transpose of a matrix

Determinants & Cramer's Rule

• Determinants
• Order of determinants
• Evaluating determinants
• Properties of determinants
• Minors and cofactors
• Determinants of a 2 x 2 matrix
• Determinant of a square matrix
• Cramer's rule
• Berzen's layer reduction method

Identity & Inverse Matrices

• Introduction to indentity matrix
• Properties of identity matrix
• Inverse of a matrix
• Finding inverse of a matrix by elementary operations
• Finding inverse of a matric by the adjoint method

Arithmetic Sequences & Series

• Identifying Arithmetic Sequence
• Figuring Out the First x Terms of a Sequence
• Expression/Rule for the $n^{th}$term
• Finding the Sum of the First n Terms
• Finding the Sum using Summation Notation

Geometric Sequence & Series

• Identifying geometric Sequence
• Finding the Common Ratio
• Expression/Rule for the $n^{th}$term
• Finding the Sum of the First n Terms
• Finding the Sum using Summation Notation
• Finding the Sum Based on Given $a_1, a_n, \text{and r}$

Permutations

• Fundamental counting principle
• Introduction to permutations
• Formula
• Finding the number of permutation
• Difference between permutation and combination

Combinations

• Introduction to combination
• Relationship between permutation and combination
• Formula
• Finding the number of combination
• Difference between permutation and combination

Normal Distributions

• Introduction to Normality of Data
• Bell-Shaped Curve
• Properties of Normal Distribution
• Converting Normal Scores to Standard Scores

Binomial Distributions

• Introduction to Binomial Distribution
• Binomial probability distribution, binomial theorm, and other related concepts
• The Mean, Variance, and the Standard Deviation of a binomial probability distribution
• The Binomial Theorem

Parabolas

• Finding the Direction of a Parabola
• Finding the Vertex, Focus and Directrix of a Parabola
• Possible Parabola Options
• Equations of Parabolas
• Finding the Axis of Symmetry
• Properties of Parabolas
• Graphing Parabolas

Circles

• Finding the Center of a Circle
• Finding the Radius and/or Diameter of a Circle
• Equation of a Circle in Standard Form
• Circles Centered at the Origin
• Circles Not Center at the Origin
• Finding a Tangent Line

Ellipses

• Finding the Center, Vertices and Co-vertices of Ellipses
• Finding Axes and Foci of Ellipses
• Equation of Ellipses
• Graphing Ellipses

Hyperbolas

• The Center, Foci and Vertices of a Hyperbola
• The Transverse and Conjugate Axis of a Hyperbola
• The Equation of Asymptote Lines
• The Equation of a Hyperbola in Standard From
• Graphing the Hyperbolas

Degree & Radians

• Relationship between degree and radians
• Converting the measure of an angle from degree to radians 
• Converting the measure of an angle from radians to degree

Right Triangle Trigonometry

• Six Trigonometric Ratios
• Relationship between trigonometric ratios
• Trigonometric Ratios of Complementary Angles

The Unit Circles

• Introcution to the Unit Circles
• Trignometric (Circular) Functions
• The Unit Circle
• Properties of the Unit Circles and Special Angles
• Trinometric Functions of any Angle
• Reference Angle

Trigonometric Identities

• Reciprocal Identities
• Pythagorean Identities
• Sign Identities
• Cofunction Identities
• Verify an Identity

Trigonometric Equations

• Introduction to Trignometric Equations
• Finding Principal Solution of Trigonometric Equations
• Finding General Solution of Trigonometric Equations

The Law of Sines

• Introduction
• The Law of Sines
• Applications of the law of sines

The Law of Cosine and Area

• Introduction
• The Law of Cosines
• Applications of the Law of Cosines
• Area Formulas

Vectors

• Representation of a Vector
• Vector Operations - Addition and Scalar Multiplication
• Unit Vectors
• Horizontal & Vertical Components of a Vector
• Dot Product of Vectors
• Angle Between Two Vectors

Introductions to Limits

• Introduction to Limits
• Properties of Limits
• Sum Rule
• Difference Rule
• Product of Two Functions Rule
• Product of a Function with a Constant Rule
• Division Rule
• Evaluating Limits by Direct Substitution Method
• Evaluating Limits by Factorization Method
• Evaluating Limits by Rationalization Method
• Evaluating Limits by Reducing to Standard Form
• Evaluating Limits by L’Hospital’s Rule

One Sided Limits

• Introduction to One-sided Limits
• Evaluating One-sided Limits
• Left-hand Limit (LHL)
• Right-hand Limit (RHL)

Limits Involving Infinity

• Introduction to Limits Involving Infinity
• Horizontal Asymptotes
• Vertical Asymptotes

Introduction to Derivatives

• Introduction to Derivatives
• Differentiation Rules
• Derivative of a Constant
• Derivative of a Power
• Derivative of a Sum or Difference
• Derivative of Quotient
• Derivative of a Product
• Chain Rule
• Derivative of Exponential and Logarithmic Functions
• Derivative of Trigonometric Functions
• Higher Order Derivatives

Area and the Definite Integrals

• Introduction
• Fundamental Theorem of Calculus
• Properties of Definite Integrals
• Evaluation of Definite Integral by Substitution
• Computing Areas by Definite Integral
• Computing Area under a Curve
• Computing Area Between Two Intersecting Curves