# 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
• Real-World Problems
• Introduction to LCM
• Finding LCM of two or more numbers
• Real-World 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
• Real-world 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
• 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 Reasoning

##### 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

• #### 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
• Non-Statistical 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
• Stem-and-leaf plots
• Circle graphs
• #### Expressions, Equations & Inequalities

##### 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
• #### 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
• Real-life 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
• #### Volumes & Surface Areas

##### 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
• #### 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 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
• #### 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:
• Factoring Trinomials of Form:
• 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
• Point-Slope form
• Slope-Intercept 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
• #### 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
• Bell-Shaped 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 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
• #### 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 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
• #### 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