Topics by Skills
Based on MathPrep’s extensive research MathPrep has listed math topics by skills. Browse through the Mathprep notes before you start the practice to brush up on the concepts. You can practice your chosen skill by selecting from either the relaxed practice mode or timed practice mode.

Decimals
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

Properties of Numbers
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
 RealWorld Problems
 Introduction to LCM
 Finding LCM of two or more numbers
 RealWorld Problems

Integers
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
 Realworld problems involving Absolute Values

Fractions
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

Rational Numbers
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

Ratios, Rates and Percents
Unit Rate
 Introduction to Unit Rate
 RealWorld Problems
Ratios and Proportions
 Introduction to Ratios
 Equivalent Ratios
 Compare Ratios
 Ratios and Rates
 Ratios and Proportions
 Ratios, Rates and Proportions
 RealWorld 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 Reasoning
Algebraic Expressions & Properties
 Converting Real World problems to Algebraic Expression
 Converting Algebraic Expression to RealWorld Problem
 Converting RealWorld description to Algebraic inequality
 Converting Algebraic inequality to RealWorld Description
 Evaluate Algebraic Equations
 Use Algebraic properties to create equivalent Expressions
 OneStep Equations
Introductions to Equations

Areas and Perimeter
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

Data Analysis
Introduction to Statistics
 Introduction to Statistics
 Statistical Questions
 NonStatistical Question
Mean, Median, Mode & Range
 Introduction to statistics
 Mean
 Median
 Mode
 Range

Data Analysis & Probability
Probability
 Probability of simple events
 Theoritical probability
 Experimental probability
Graphs and Charts
 Histograms
 Line plots
 Box plots
 Stemandleaf plots
 Circle graphs

Expressions, Equations & Inequalities
Expressions and Equations
 Algebraic expressions
 Combining like terms
 Simple equations
 Solving onestep equations
 Solving twostep euations
 Solving multistep 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

Percents, Rates & Proportions
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
 Reallife percents problems

Polygons
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

Angle Pairs
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

Exponents and Indices
Laws of Exponents
 Introduction
 Negative exponents
 Adding & subtracting exponents
 Multiplying & dividing exponents
 Power of exponents
 Scientific notations

Irrational Numbers
Square Roots and Cube Roots
 Exact square & cube roots
 Approximating square & cube roots
 Simplifying square & cube roots

Expressions, Equations & Inequalities
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
Algebraic Fractions
 Fractions in Algebra
 Adding and Subtracting Algebraic Fractions
 Multiplying and Dividing Algebraic Fractions
 Simplifying/Reducing Algebraic Fractions

Linear Equations & Inequalities
Linear Equations
 Writing Equations in SlopeIntercept Form
 Writing Equations in PointSlope 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
 MultiStep 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

Radical Expressions
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, Polynomials & Factoring
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 Systems
Quadratic Equations
 Solving Quadratic Equations by Factoring
 Solving Quadratic Equations by Completing the Square
 Solving Quadratic Equations by the Quadratic Formula

Relations and Functions
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

Congruence & Similarity
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

Coordinate Geometry
Distance and Midpoint Formulas
 The distance formula
 The midpoint formula
Equation of a Line
 Equations of line
 Linear equation
 Standard form
 PointSlope form
 SlopeIntercept form

Circles
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

Rational Expressions
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

Complex Numbers
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

Matrices and Determinants
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

Sequence and Series
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 ${a}_{1},{a}_{n},\text{andr}$

Statistics & Probability
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
 BellShaped Curve
 Properties of Normal Distribution
 Converting Normal Scores to Standard Scores

Statistics & Probability
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

Conic Sections
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 Covertices 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

Trignometric Functions
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

Trignometric Identities and Equations
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

Applications of Trignometry
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

Limits and Continuity
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 Onesided Limits
 Evaluating Onesided Limits
 Lefthand Limit (LHL)
 Righthand Limit (RHL)
Limits Involving Infinity
 Introduction to Limits Involving Infinity
 Horizontal Asymptotes
 Vertical Asymptotes

Differential Calculus
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

Integral Calculus
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