Math Exercises

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Algebra 1
- Numbers
  - Classify numbers
  - Compare and order integers
  - Compare and order rational numbers
  - Absolute value and opposites
  - Number lines
  - Convert decimals to fractions
  - Convert fractions to decimals
  - Square Roots
  - Cube Roots
- Operations
  - Add Integers
  - Subtract Integers
  - Multiply Integers
  - Divide Integers
  - Order of operations with integers
  - Evaluate variable expressions involving integers
  - Add and subtract rational numbers
  - Multiply rational numbers
  - Divide rational numbers
  - Order of operations with rational numbers
- Ratios and proportions
  - Identify equivalent ratios
  - Equivalent ratios: fill in the missing number
  - Unit rates
  - Unit prices
  - Solve proportions
  - Solve proportions: word problems
  - Scale drawings and scale factors
- Percents
  - Convert a percent to a decimal
  - Convert a percent to a fraction
  - Convert a decimal to a percent
  - Convert a fraction to a percent
  - Solve percent equations
  - Percent word problems
  - Percent of change
  - Percent of change: word problems
  - Percent of a number: tax, discount, and more
  - Find the percent: tax, discount, and more
  - Multi-step problems with percents
- Measurement
  - Convert rates and measurements: customary units
  - Convert rates and measurements: metric units
  - Unit prices with unit conversions
  - Precision
  - Greatest possible error
Algebra 2
- Arithmetics
  - Comparing whole numbers
  - Addition
  - Subtraction
  - Multiplication
  - Division
  - Order of operations
- Divisibility
  - Prime numbers
  - Factoring
  - Multiples
  - Divisibility rules
  - Prime factorization
  - GCF
  - LCM
- Decimals
  - Addition
  - Subtraction
  - Multiplication
  - Division
- Fractions
  - Identify fractions
  - Equivalent fractions
  - Reducing fractions
  - Reducing to least common denominator
  - Comparing fractions
  - Reciprocals
- Exponents
  - Multplication properties
  - Division properties
  - Power of a power
- Proportional reasoning
  - Ratio
  - Proportion
  - Direct proportion
  - Inverse proportion
  - Mixture problems
  - Uniform motion problems
  - Equal shares
- Radical expressions
  - Adding and subtracting
  - Rationalizing
  - Radical equation
- Graphs
  - Plotting points and naming quadrants
  - Definition of slope
  - Positive or negative slope
- Monomials
  - Addition
  - Subtraction
  - Multiplication
  - Division
- Polynomials
  - Polynomial Vocabulary
  - Addition
  - Subtraction
  - Multiplication (FOIL)
  - Multiplication
  - Special products
  - Long division
  - Synthetic division
  - Remainder theorem
  - Roots and factors
  - Polynomial Function
- Factoring
  - Factoring
  - Factoring Trinomials a=1
  - Factoring trinomials a not equal to 1
  - Difference of Perfect Squares
  - Perfect Trinomial Squares
  - Factoring by grouping
  - Factoring the Sum or Difference of Cubes
  - Factoring Complicated Expressions
  - Solving equations by Factoring
- Variable expressions
  - Write variable expressions
  - Write variable expresions to represent diagrams
  - Identify terms and coefficients
  - Evaluate single-variable expressions
  - Evaluate multi-variable expressions
  - Add like terms
  - Subtract like terms
  - Simplify variable expressions
- Linear Equations
  - Solving equations
  - Equations with parentheses
  - Equations with fractions
  - Radical equations
  - Word problems
  - Mixture problems
  - Time and distance problems
  - Equal shares
- Linear Functions
  - Evaluate Linear Functions
  - Does (x,y) satisfy the linear equation?
  - Complete a function table
  - Write a rule for a function table
  - Find points on a function graph
  - Linear function word problems
  - Identify proportional relationship
  - Find the constant of variation from graph
  - Find the constant of variation from a table
  - Find the constant of variation: word problems
- Graphs of linear equations
  - Rectangular Coordinate System
  - Midpoint Formula
  - Definition of Slope
  - Positive and negative slope
  - Determine the slope of a line
  - Find the slope from two points
  - Find the slope from an equation
  - Slope of parallel and perpendicular lines
  - Find the slope of parallel lines
  - Find the slope of perpendicular lines
  - Equations of lines
    - Slope-Intercept Form
    - Point-Slope Form
    - Standard Form
  - Equation of lines (from graph)
  - Applications of linear equations
- Inequalities
  - Linear inequalities
  - Multistep inequalities I
  - Multistep inequalities II
- Quadratic equations
  - Quadratic formula
  - Solve factoring
  - Solve completing the square
  - Incomplete quadratic equation (b=0)
  - Incomplete quadratic equation (c=0)
  - The discriminant
  - Applications
  - Quadratic function
  - Equations in quadratic form
- Graphs of quadratic equations
  - Exploring Quadratic Graphs
  - Graphing Quadratic Equations
  - Using a table to graph a Quadratic Equation
  - Vertical and Horizontal Shifts of Quadratic Graphs
  - Vertical Stretching and Shrinking of Quadratic Graphs
  - Vertex and Intercepts of a Quadratic Graph
  - Applications
- Absolute Value
  - Definition
  - Absolute Value Equations
  - Absolute Value Inequalities
  - Absolute Value Graphs
- Radical expressions
  - Adding and subtracting
  - Rationalizing
  - Radical equations
- Exponential equations
- Logarithmic equations
- System of equations
  - Introduction
  - Substitution
  - Elimination
  - Graphing
  - Using the augmented matrix
  - Using the inverse matrix
  - Word problems
  - System of 3 variables
- Graphs and functions
  - Plotting points and naming quadrants
  - Interpreting Graphs
  - Relations and Functions
  - Function Notation
  - Writing a Linear Equation from a Table
  - Writing a Linear Equation to describe a Graph
  - Direct Variation
  - Indirect Variation
  - Domain and range
  - - Definitions
    - Polynomial function
    - Rational function
    - Radical function
    - Trigonometric function I
    - Trigonometric function II
    - Trigonometric function III
- Sequences and series
  - Introduction to sequences
  - Series and Summation Notation
  - Arithmetic sequences
  - Arithmetic series
  - Geometric sequences
  - Geometric series
  - Recursion Sequence
- Matrices
  - Concept of matrix
  - Definitions
  - Addition and subtraction
  - Multiplication
  - Multiplication properties
  - Solve linear systems (augmented matrix)
  - Solve linear system (inverse matrix method)
  - Matrix equations
- Inverse of a matrix
- Determinants
- Inner product
Geometry
- Triangles
  - Classify triangles
  - Find the unknown angle
  - Area of a triangle
  - Isosceles Triangle
  - Triangle Side Inequality
  - Side and Angle Inequalities
  - Remote Interior Angles
  - SSS and SAS
  - ASA and AAS
  - HL
  - CPCTC
  - Isosceles Triangle Property
- Quadrilaterals
  - Classifiy quadrilaterals
  - Find the missing angle in quadrilaterals
- Points, lines, and segments
  - Lines, line segments, and rays
  - Lengths of segments on number lines
  - Distance formula
- Angles
  - Types of angles
  - Measure angles with a protractor
  - Complementary and supplementary angles
- Lines in the coordinate plane
  - Find points on a coordinate plane
  - Quadrants
  - Coordinate Graphs Review
- Polygons
  - Interior Angles Sum
  - Equiangular Polygon Sums
  - Exterior Angles
  - Kite Properties
  - Triangle Midsegment
  - Trapezoid Midsegment
  - Parallelogram Properties
  - Rhombus Properties
  - Rectangle Properties
  - Square Properties
- 2-D Figures
  - Polygon vocabulary
  - Interior angles of polygons
  - Area of a Triangle
  - Area of a Square
  - Area of a Rectangle
  - Area of a Rhombus
  - Area of a Trapezoid
  - Area of a Parallelogram
  - Area of Regular polygon
  - Area of a Circle
- 3-D Figures
  - Types of solids
  - Prism
  - Pyramid
  - Cylinder
  - Cone
  - Sphere
- Areas
  - Triangle I
  - Triangle II
  - Square
  - Rectangle I
  - Rectangle II
  - Parallelogram I
  - Parallelogram II
  - Kite and Rhombus I
  - Kyte and Rhombus II
  - Trapezoid I
  - Trapezoid II
  - Regular polygon
  - Circe
  - Sector
  - Annulus
  - Segment
  - Regions between circles and squares
- Surface Area
  - Cube
  - Rectangular Prism
  - Pyramids
  - Cylinder
  - Cones
  - Spheres
  - Joined Solids
- Volume
  - Volume of prisms
  - Volume of pyramids
  - Volume of cylinders
  - Volume of cones
  - Volume of spheres
- Pythagorean Theorem
  - Pythagorean theorem
  - Proofs
  - Solve right angles (find hypotenuse)
  - Solve right angles (find missing legs)
  - Word problems
  - Space Diagonals
  - Converse of the Pythagorean Theorem
  - Pythagorean Triples
  - 45-45-90 Triangles
- Building Blocks
  - Lines, line segments, and rays
  - Congruent segments and midpoints
  - Midpoint
  - Parallel and skew lines
  - Parallel lines and planes
  - Angles
  - Complementary and supplementary angles
  - Using a protractor
  - Angle bisector
  - Polygons
  - Regular polygons
  - Concave and convex polygon
  - Congruent polygon
  - Vertex and diagonal
  - Perimeter
  - Parts of a circle
  - Concentric circles
  - Congruent circles
- Geometry Transformations
  - Transformations and Isometries
  - Identify translations, reflections and rotations
  - Translations
  - Reflections
  - Rotations
  - Symmetry
  - - - Reflectional symmetry
    - - Rotational symmetry
  - Dilations
- Parallel, coincident and intersepting lines
- Distances in the plane
  - Between two points
  - From a point to a line
  - Between two lines
- Lines in space
  - Lines in space
  - Intersection 2 lines
- Plane in space
  - Planes in the Space
  - Line-Plane Intersection
  - Intersection of Two Planes
  - Intersection of Three Planes
  - Sheaf of Planes
- Angles in the space
  - Line-Line angle
  - Line-Plane angle
  - Plane-Plane Angle
  - Exercises
- Distances in the space
  - Point-Line Distance
  - Point-Plane Distance
  - Line-Line Distance
  - Plane-Plane Distance
- Similarity
Precalculus
- Sequences and series
  - Introduction to sequences
  - Series and Summation Notation
  - Arithmethic sequences
  - Arithmetic series
  - Geometric sequences
  - Geometric series
  - Recursion Sequences
- Graphs
  - Graphs
  - Definition of slope
  - Positive or negative slope
  - Determine the slope of a line
  - Equation of a line (slope-intercept form)
  - Equation of a line (point slope form)
  - Equation of a line from graph
  - Domain and range
  - - Definitions
    - Polynomial function
    - Rational function
    - Radical function
    - Trigonometric function I
    - Trigonometric function II
    - Trigonometric function III
  - Quadratic function
  - Limits (approaches a constant)
  - Limits (approaches infinity)
  - Asymptotes
  - Continuity and discontinuities
- Parallel, coincident and intersepting lines
- Introduction to Functions
  - Seven Basic Functions
- Limits
  - Limit of a function
  - Limits approaches a constant
  - Limits approaches infinity
  - Evaluating limits
  - One-Sided Limits
- Continuity
  - Continuity
  - Discontinuities
- Asymptotes
  - Vertical Asymptote
  - Horizontal Asymptote
  - Slant Asymptote
Trigonometry
- Trigonometric ratios
  - Sine
  - Cosine
  - Tangent
- The reciprocal trigonometric ratios
  - Cosecant
  - Secant
  - Cotangent
  - Elemento sin tÃtulo
- Trigonometric ratios of related angles
  - Complementary angles
  - Supplementary angles
  - Angles that differ by 180º
  - Opposite angles
- Trigonometric identities
- Solving right angles
  - Two sides knowed
  - One side and one angle
- Law of sines
- Law of cosines
- Domain of trigonometric functions
Statistics
- Mean
- Median
- Mode
- Quartiles
- Deciles
- Percentiles
- Mean deviation
- Variance
- Standard Deviation
- Coefficient of variation
- Skewness
- kurtosis
- Frequency distribution
  - Previous concepts
  - Ungrouped data
  - Grouped data
- Graphing statistics & Data
  - Bar chart
  - Histogram
  - Pie chart
  - Frequency Polygon
  - Pictogram
  - Cartogram
- Factorial
- Variations without repetition
- Variations with repetition
- Permutations without repetition
- Permutation with repetition
- Circular permutation
- Binomial coefficient
- Combinations without repetition
- Combinations with repetition

Student :Check over the exercises you have completed

Teacher: monitor the progress of each individual student.

Pre-algebra

Algebra

Monomials
Polynomials
- Addition
- Subtraction
- Multiplication FOIL
- Multiplication
- Special products
- Long Division
- Synthetic division
- Remainder theorem
Factoring
- Greatest Common Factor
- Difference of Perfect Squares
- Perfect Trinomial Squares
- Factoring Trinomials a=1
- Factoring Trinomials
ax²+bx+c
- Factoring by grouping
- Factoring the Sum or Difference of Cubes
- Factoring Complicated Expressions
- Solving Equations by Factoring
Variable Expressions
-Write variable expressions
- Write variable expresions to represent diagrams
-Identify terms and coefficients
- Evaluate single-variable expressions
- Evaluate multi-variable expressions
- Add like terms
- Subtract like terms
- Simplify variable expressions
Linear Equations
- Solving equations
- Mixture problems
- Distance problems
Graphs of Linear Equations
Rectangular Coordinate System
Midpoint Formula
Definition of slope
Positive or negative slope
Determine the slope of a line
Equation of a line:
- Slope-intercept form
- Point Slope form
- Standard Form of a Line
Equation of lines (from graph)
Applications of Linear Equations
Quadratic equations
- Solve by factoring
- The quadratic formula
- Completing the square
- Incomplete equations
- The discriminant
- Equations in quadratic form
- Applications
Quadratic Graphs (Parabola)
- Exploring Quadratic Graphs
- Graphing a Quadratic Equation
- Using a table to graph a Quadratic Equation
- Vertical and Horizontal shifts
- Vertical Stretching and Shrinking
- Vertex and intercepts
- Applications
Inequalities
- Basic Inequalities
- Multisteps inequalities I
- Multisteps inequalities II
Radical expressions
- Adding and subtracting
- Rationalizing
- Radical equations
Exponential equations
Logarithmic equation
Systems of equations
- Substitution
- Elimination
- Graphing
- Using the augmented matrix
- Using the inverse matrix
- Word problems
System of 3 variables equations
Graphs and Functions
-Plotting points and naming quadrants
- Interpreting graphs
- Relations and Functions
- Function Notation
- Writing a Linear Equation to Describe a Table
- Writing a Linear Equation to Describe a Graph
- Domain and range
- Direct Variation
- Indirect Variation

High School Math Prep

Practice general math problems with Aberdeen Academy's free program designed for teens and adults who require online continuing education. To find out more about Aberdeen's course and what it entails, go to High School Diploma.

Introduction to statistics

Welcome to our new statistic section. Get ready to have a fun practicing the most important topics in statistics. Calculate the mean, mode and median of a set of data. Find the quartiles, deciles and percentiles of a set of data (include formulae for grouped data). Provides problems, explanations, and solutions. Central Tendency and Dispersion measures are introduced.

Sequences and series

Revise your understanding of arithmetic and geometric sequences and series. Provides problems, explanations, and solutions.

Exponents: Rules of exponents

Revise your understanding of exponents and powers. Here you will find activities to cover the basic exponent rules. Provides problems, explanations, and solutions.

Pythagorean Theorem

Solve right angled triangles by using the Pythagorean Theorem. Solve real life word problems using the Pythagorean Theorem. Use Pythagorean Triples to save your time on any test. Find the relationships between the sides of a 45-45-90 triangle or a 30-30-60 triangle. There are many applications for the Pythagorean Theorem: it can be used to find the distance between two points, to find the length of a space diagonal,... Provides problems, explanations, and solutions.

Proportional reasoning

Revise your understanding of proportional reasoning in maths. Here you will find exercises on ratios and proportions, direct proportions, inverse proportions, equal shares, time and distance and mixture word problems. You will learn to solve problems using real life situations. Provides problems, explanations, and solutions.

Distances

Find the distance between two points in the plane. Find the distance from a point to a line or the distance between two lines in the plane. Provides problems, explanations, and solutions.

Quadratic equations

Revise your understanding of quadratic equations. Solve complete and incomplete quadratic equations. Solve problems about real life using quadratic equations. Provides problems, explanations, and solutions.

Variations, permutations and combinations

Revise your understanding of variations, permutations and combinations. Solve exercises about variations, permutations and combinations with and without repetition. Provides problems, explanations, and solutions.

Matrices

Revise your understanding of matrices. Solve exercises about addition, subtraction and multiplication of matrices. Provides problems, explanations, and solutions.

Factorial

Revise your understanding of factorials. Enter any number you want and the computer will calculate its factorial for you. Provides problems, explanations, and solutions.

Precalculus

Graphs
Plotting points and naming quadrants
Definition of slope
Positive or negative slope
Determine the slope of a line
Equation of a line
Equation of a line (from graph)
Domain and range
Quadratic function
Parallel, coincident and intersecting lines
Limits
Asymptotes
Continuity and discontinuities
Distances
Angles in space

Trigonometry

Trigonometric ratios
- Sine
- Cosine
- Tangent
The reciprocal trigonometric ratios
- Cosecant
- Secant
- Cotangent
Trigonometric ratios of related angles
- Complementary angles
- Supplementary angles
- Angles that differ by 180º
- Opposite angles
Trigonometric identities
Solving right triangles
- Two sides knowed
- One side and one angle
Law of sines
Law of cosines

Statistics

Mean
Median
Mode
Quartiles
Deciles
Percentiles
Range
Mean Deviation
Variance
Standard Deviation
Coefficient of variation
Skewness
Kurtosis
Frequency distribution
- Previous concepts
- Ungrouped data
- Grouped data
Graphing statistics & Data
- Bar chart
- Histogram
- Pie chart
- Frequency polygon
- Pictogram
- Cartogram
Factorial
Variations without repetition
Variations with repetition
Permutations without repetition
Permutation with repetition
Circular permutations
Binomial coeffient
Combinations without repetition
Combinations with repetition
Exercises

Equations

Quadratic Equations

System of equatons

Special products

Special products

Radicals

Inner product

Inner product

Exponential and logarithmic equations

Geometry

Pythagorean Theorem
Polygons and areas
Similarity

Sequences and series

Links