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
  • 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

    • 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

    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 & 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

    • Volume of cylinders
    • Surface area of cylinders

    • Volume of cones
    • Surface area of cones

    • Volume of pyramids
    • Surface area of pyramids

    • Volume of spheres
    • Surface area of spheres

    • 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
  • Monomials, Polynomials & Factoring

    • 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: x2 + bx + c
    • Factoring Trinomials of Form: ax2 + 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

    • 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

  • 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
  • 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 nthterm
    • 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 nthterm
    • Finding the Sum of the First n Terms
    • Finding the Sum using Summation Notation
    • Finding the Sum Based on Given a1, an, and r
  • Statistics & Probability

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

    • 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

    • 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

    • 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

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

    • 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

    • 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