# Mathematics Monster

## Welcome to Mathematics Monster

With a comprehensive mathematics glossary and hundreds of step-by-step lessons (all with tests, games or interactive widgets), **Mathematics Monster** is perfect for anyone who wants to be more confident with mathematics. There are no adverts, and it's all free. We just love mathematics!

## Mathematics Curriculum (by Lesson)

# Algebra Curriculum

## Algebra Definitions

Understanding terms in algebra

Understanding expressions in algebra

## Arithmetic with Letters

## Arithmetic with Terms

## Laws of Exponents in Algebra

Understanding the laws of exponents

Understanding an exponent of −1

## Like Terms

## Expanding Brackets

Expanding brackets using the grid method

Understanding the FOIL methods

Multiplying expressions in algebra

Expanding double brackets using the grid method

## Solving Equations with Brackets

Solving an equation with brackets

Solving an equation with two sets of brackets

## Factoring

Understanding factors in algebra

Understanding the greatest common factor in algebra

Finding the greatest common factor in algebra

## Algebraic Fractions

Understanding algebraic fractions

Subtracting algebraic fractions

Multiplying algebraic fractions

Simplifying algebraic fractions

Finding the reciprocal of an algebraic fraction

# Equations: Linear Equations Curriculum

## Equations and Linear Equations

Understanding linear equations

## Lines, Slopes and Y-Intercepts

Understanding linear equations in slope-intercept form

Finding the slope from a linear equation

Finding the y-intercept of a line

Finding the y-intercept from a linear equation

Finding the equation of a line

## Slope-Point Form

Understanding linear equations in slope-point form

Finding the slope from a linear equation in slope-point form

Finding the y-intercept from a linear equation in slope-point form

## General Form

Understanding linear equations in general form

Finding the slope from a linear equation in general form

Finding the y-intercept from a linear equation in general form

Converting a linear equation from general to slope-intercept form

## Equation of a Line Between Two Points

Finding the equation of a line between two points

# Equations: Quadratic Equations Curriculum

## Quadratic Equations

Understanding quadratic equations

## Solving Quadratic Equations

Solving quadratic equations using factoring

Solving quadratic equations using factoring (a ≠ 1)

Solving quadratic equations using the quadratic formula

Solving quadratic equations using a graph

## Difference of Squares

Understanding a difference of squares

Solving quadratic equations using a difference of squares

## Completing the Square

Understanding perfect square trinomials

Understanding completing the square

# Equations: Simultaneous Equations Curriculum

## Simultaneous Equations

Understanding simultaneous equations

## Solving Simultaneous Equations

Solving simultaneous equations

Solving simultaneous equations using elimination

Solving simultaneous equations using elimination (where coefficients differ)

Solving simultaneous equations using substitution

Solving simultaneous equations using a graph

# Equations: Functions Curriculum

## Functions

## Plotting Functions

Finding y-intercept of a function

Finding x-intercepts of a function

## Composite Functions

Understanding composite functions

Evaluating a composite function

## Inverse Functions

Understanding inverse functions

Finding the inverse of a function

Finding the inverse of a function using a graph

# Fractions and Percentages: Fractions Curriculum

## Fractions

## Types of Fractions

Understanding proper fractions

Understanding improper fractions

Converting mixed to improper fractions

Converting improper to mixed fractions

## Equivalent Fractions and Simplifying Fractions

Understanding equivalent fractions and simplest form

## Arithmetic with Fractions

Finding the reciprocal of a fraction

Finding the power of a fraction

## Using Fractions

Finding a fraction of a number

Expressing a number as a fraction of another number

## Converting Fractions

Converting a fraction to a percentage

Converting a fraction to a decimal

# Fractions and Percentages: Percentages Curriculum

## Percentages

Finding a percentage of a number

Expressing a number as a percentage of another number

## Percentage Changes

Understanding percentage changes

## Converting Percentages

Converting a percentage to a fraction

Converting a percentage to a decimal

# Geometry: Shapes Curriculum

## Plane Shapes

## Areas

Finding the area of an ellipse

Finding the area of a parallelogram

Finding the area of a rectangle

Finding the area of a trapezoid

Finding the area of a triangle

## Volumes

Finding the volume of a cylinder

Finding the volume of a sphere

## Circles

Understanding the circumference

Finding the length of an arc (degrees)

Finding the length of an arc (radians)

Finding the area of a sector (degrees)

Finding the area of a sector (radians)

## Radius of a Circle

Finding the radius from the diameter

Finding the radius from the circumference

Finding the radius from the area

## Diameter of a Circle

Finding the diameter from the radius

Finding the diameter from the circumference

Finding the diameter from the area

## Area of a Circle

Finding the area of a circle using diameter

## Circle Theorems

Understanding the circle theorems:

Two radii make an isosceles triangle

Perpendicular bisector of a chord

Angle at the center is twice the angle at the circumference

Angles in the same segment are equal

Angles in a cyclic quadrilateral

Tangents from the same point are the same length

## Triangles

Understanding the types of triangles

Understanding equilateral triangles

Understanding isosceles triangles

Understanding scalene triangles

Understanding the interior angles of a triangle

Finding a missing angle in a triangle

Finding a missing angle in an isosceles triangle

## Angles

Understanding the types of angles

## Angle Properties

Understanding complementary angles

Understanding supplementary angles

Understanding explementary angles

## Polygons

Understanding the interior angles of a polygon

Finding the interior angle of a regular polygon

Finding the sum of the interior angles of a polygon

Understanding the exterior angles of a polygon

Finding the exterior angle of a regular polygon

Understanding the sum of an interior and exterior angle of a polygon is 180°

# Geometry: Transformations Curriculum

## Transformations

## Translations

## Rotations

Understanding the radial coordinate

Understanding the common rotations

## Reflections

Understanding the common reflections

## Enlargements

Understanding the scale factor

Enlarging a shape with a fractional scale factor

Enlarging a shape with a negative scale factor

Describing an enlargement with a negative scale factor

# Graphs and Coordinate Geometry Curriculum

## Graphs

Understanding the parts of a graph

## Cartesian Coordinates

Understanding Cartesian coordinates

Understanding the x-coordinate

Understanding the y-coordinate

Drawing a point from Cartesian coordinates

Reading off a point from Cartesian coordinates

## Polar Coordinates

Understanding polar coordinates

Understanding the radial coordinate

Understanding the angular coordinate

Drawing a point from Cartesian coordinates

Reading off a point from polar coordinates

Converting from Cartesian to polar coordinates

Converting from polar to Cartesian coordinates

## Coordinate Geometry of Points and Lines

Finding the distance between points

Finding the slope between points

Finding the midpoint between points

## Transformations in Coordinate Geometry

Reflecting shapes in the x-axis

Reflecting shapes in the y-axis

Reflecting shapes in the line y = x

Reflecting shapes in the line y = −x

## Equation of a Circle

Understanding the basic equation of a circle

Understanding the equation of a circle

Finding the center and radius from the equation of a circle

Understanding the equation of a circle in general form

Converting an equation of a circle from general to standard form

# Numbers and Arithmetic: Numbers Curriculum

## Types of Numbers

Understanding the types of numbers

## Positive and Negative Numbers

Understanding positive numbers

Understanding negative numbers

Arithmetic with negative numbers

## Even and Odd Numbers

Arithmetic with even and odd numbers

## Prime Numbers

Understanding composite numbers

The fundamental theorem of arithmetic

## Square Numbers and Square Roots

## The Number Line

Subtracting on the number line

# Numbers and Arithmetic: Arithmetic Curriculum

## Operations and Their Order

Understanding inverse operations

Understanding the order of operations

## Advanced Arithmetic

Understanding long subtraction

Understanding long multiplication

Understanding long multiplication with decimals

Understanding long division with a remainder

Understanding long division with decimals

## Factors

Understanding the greatest common factor

Finding the greatest common factor

## Multiples

Understanding the least common multiple

Finding the least common multiple

## Powers

## Laws of Exponents

Understanding the laws of exponents

## Reciprocals

Understanding an exponent of −1

# Numbers and Arithmetic: Notation Curriculum

## Scientific Notation

Understanding scientific notation

Converting a number to scientific notation

Converting a number less than 1 to scientific notation

Converting scientific notation to a number

Converting scientific notation with a negative exponent to a number

## Engineering Notation

Understanding engineering notation

Converting a number to engineering notation

Converting a number less than 1 to engineering notation

Converting engineering notation to a number

Converting engineering notation with a negative exponent to a number

# Probability and Statistics: Probability Curriculum

## Probability

## Combined Events

Understanding independent events

Understanding the multiplication rule

Understanding dependent events

Understanding mutually exclusive events

Understanding the addition rule

Understanding complementary events

## Tree Diagrams

Multiplication rule on a tree diagram

Addition rule on a tree diagram

Understanding dependent events on a tree diagram

# Probability and Statistics: Statistics Curriculum

## Data

Understanding the types of data

Understanding quantitative data

Understanding qualitative data

## Averages

## Measures of Spread

Understanding the lower quartile

Understanding the upper quartile

Understanding the interquartile range

Finding the interquartile range

## Frequency Tables

Understanding frequency tables

Finding the mean from a frequency table

Finding the median from a frequency table

Finding the mode from a frequency table

Finding the range from a frequency table

## Cumulative Frequency Tables

Understanding cumulative frequency tables

Making a cumulative frequency table

## Grouped Frequency Tables

Understanding grouped frequency tables

Making a grouped frequency table

Finding the mean from a grouped frequency table

Finding the median group from a grouped frequency table

Finding the mode group from a grouped frequency table

## Cumulative Grouped Frequency Tables

Understanding cumulative grouped frequency tables

Making a cumulative grouped frequency table

## Bar Charts

Bar charts and the types of data

# Trigonometry Curriculum

## Right Triangle

## Pythagoras' Theorem

Understanding Pythagoras' theorem

Finding the hypotenuse using Pythagoras' theorem

Finding a shorter side using Pythagoras' theorem

## Sine Function

Understanding the sine function

Finding the angle using the sine function

Finding the opposite using the sine function

Finding the hypotenuse using the sine function

## Cosine Function

Understanding the cosine function

Finding the angle using the cosine function

Finding the adjacent using the cosine function

Finding the hypotenuse using the cosine function

## Tangent Function

Understanding the tangent function

Finding the angle using the tangent function

Finding the opposite using the adjacent function

Finding the adjacent using the tangent function

## Area of a Triangle Using Trigonometry

## Mathematics Curriculum (by Subject)

Our mathematics curriculum is shown below.

**Click on a box below to find out more about the mathematics topics!**

# Algebra

Algebra is a branch of mathematics that uses letters and other symbols to represent numbers.

# Equations

Equations show us that two things are equal using the equals sign =.

# Fractions and Percentages

Fractions and percentages show a part of a whole.

# Geometry

Geometry is a branch mathematics that studies shapes and their properties.

# Graphs and Coordinate Geometry

# Numbers and Arithmetic

Numbers are used to count. Arithmetic is the study of numbers and their operations.

# Statistics and Probability

Probability concerns the likelihood of events. Statistics concerns the study of data.

# Trigonometry

Trigonometry is a branch of mathematics that studies the angles and lengths of the sides of triangles.