Diploma in Mathematics
Want to improve your math skills? This course will guide you through math’s most important concepts and principles.
Description
The course covers a comprehensive range of key subjects in mathematics. Starting with calculus and geometry, the course guides you through the mathematics behind shapes and design principles. Next, the course moves through functions, vectors, and data distributions. These are highly important principles used in rocket science, the military, and aerospace engineering. The course will then introduce you to algebra and trigonometry, which are core to a future in any mathematicsoriented career.
Next, you’ll learn how to confidently create graphs and make advanced calculations such as straightline calculations, kinematics, motion, and quadratic functions. Finally, for the gamblers amongst you, you will learn about probability and statistics, including an overview of the relationship between the graphs of functions and their antiderivatives. This section will also show you how to use binomial expansions for problem solving, so the next time you play poker you will have a real edge over your competitors.
By the end of this course, you will have gained math skills that can open up a range of careers, and will be much better prepared for your next math exam. Math skills are in great demand from international employers, and almost every student in the world needs to learn them. Despite this, very few people have strong math skills. With this free course, and less than 5 hours of work, you’ll stand above the crowd. So why wait? Make Math easier, today.
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Modules
Introduction to triangles

Introduction to triangles

Triangle letter names

Equilateral triangles

Isosceles triangles

Scalene triangles

Acuteangled triangles

Rightangled triangles

Obtuseangled triangles

Quiz on triangle names
Angle types

Angle types

Angles in a circle

Angles as numbers

Measuring angles with a protractor

Complementary and supplementary angles

Angles in circles, rectangles and triangles

Vertically opposite angles
Angle sizes and sums in triangles

Angle sizes and sums in triangles

Angle sum demonstration

Practice questions on sum of angles in a triangle

Quiz on sum of angles in a triangle

Exterior angles of a triangle

Quiz on exterior angles of triangles
Triangles  Similiarity and congruence
Corresponding angles

Corresponding angles

Parallel lines

Alternate and cointerior angles

General angles quiz

Quiz on angles and parallel lines
Introduction to quadrilaterals

Introduction to quadrilaterals

Equal sides, equal angles and parallel lines

Properties of a square

Properties of a rectangle

Properties of a parallelogram

Properties of a rhombus

Properties of a trapezium

Properties of a kite

Properties of basic quadrilaterals

Quiz on properties of quadrilaterals

Properties of an isosceles trapezium

Properties of a rectangle

Properties of a parallelogram

Properties of a rhombus

Properties of a trapezium

Properties of an isosceles trapezium

Properties of a kite

Properties of basic quadrilaterals
Quadrilaterals
Introduction to polygons

Introduction to polygons

What are polygons?

Regular polygons

Naming of polygon types

Rotational symmetry in polygons

Line symmetry in polygons

Quiz on polygons
Polygons

Polygon interior angle sum

Regular polygon interior angle sizes

Sum of exterior angles of polygons

Regular polygon exterior angle sizes

Quiz on polygon angle sizes
Geometrical solids

Geometrical solids

Prisms

Prisms quiz

Pyramids and cones

Spheres, hemispheres and toruses

Quiz on geometrical solids
Transformations

Introduction to transformations

Translations, reflections and rotations

Translations and coordinate geometry

Translations and coordinate geometry quiz

Reflections

Reflections

Reflections and coordinate geometry

Rotations

Rotations and coordinate geometry

Quiz on transformations
Univariate data
Univariate data 2
Bivariate data

Introduction

Dependent and independent variables

Percentaged tables

Parallel boxplots

Backtoback stemplots

Graphical display of bivariate data – in summary
Summary statistics

Summary statistics

The mean

The median – definition

Cumulative frequency

Cumulative frequency graph

The mode

Advantages and disadvantages of the mean

The median for even data sets

Advantages and disadvantages of the median

The mean  example

The median  example
Range

The soccer activity

The range

The interquartile range

The interquartile range  example 1

The interquartile range  example 2

The standard deviation

Boxplots

Boxplots  example

Using your calculator
Symmetry

Symmetry and skew of a distribution

Negative skew

Positive skew

Probability intervals

Probability interval examples

Comparing sample and population
Calculating a seasonal index

Calculating a seasonal index

Interpreting seasonal indices

Seasonal movements

Deseasonalising the data

Deseasonalising the data – example
Coefficient

Scatterplots

Scatterplots: using your calculator

Pearson's product moment correlation coefficient, r

Calculating r

The coefficient of determination

Practice question

Strength of association
Regression line

Introduction

Finding the equation of a regression line

Interpretation of slope and intercept

Practice question

The threemedian regression line

Using your calculator

The threemedian regression example

The threemedian regression practice questions

The least squares regression line

Making predictions from a regression line
Nonlinear data

Nonlinear data

Square transformation

Log transformations

Reciprocal transformation

Example 1

Example 2
Residual analysis

Introduction

Residual analysis  part 1

Plotting the residuals

Residual analysis  part 2

Residual analysis  part 3
Trends

Trends

Cyclic patterns

Random patterns

Describing patterns in time series data

Seasonal patterns

Smoothing a time series

Median smoothing

Smoothing using moving averages

Smoothing  example 1

Smoothing  example 2
Arithmetic sequences

Arithmetic sequences

Find a particular term in an arithmetic sequence

How many terms in this arithmetic sequence?

Show that the sequence is arithmetic

Solving arithmetic sequences simultaneously

Summing up arithmetic sequences

Is this an arithmetic sequence?

Example (b)

Example (c)

Example (d)
Arithmetic series
Geometric sequences

Geometric sequences

Is this a geometric sequence?

Find a term in an increasing geometric sequence

Find a term in a decreasing geometric sequence

Which term has that value?

Example (b)

Example (c)

Example (d)
Geometric series

Geometric series

Infinite geometric series

Find the sum of an increasing geometric sequence

Find the sum of a decreasing geometric sequence

How many terms until the sum exceeds 2000?

Find the sum of an infinite geometric series

Sum a geometric series to infinity
Difference equations 1
Difference equations 2

Difference equations

Generating a sequence from a difference equation

Difference equations that represent arithmetic sequences

Difference equations that represent geometric sequences

Generate the first 4 terms of a sequence

Generate the first 4 terms of another sequence

Find a general expression for the nth term

Find a general expression for the nth term
Difference equations 3

Other first order difference equations

Solving difference equations

Find a general expression for the nth term

Find the first term from a given term

Find the first term from the second term
Geometry

Intersection of half planes

Finding maximum and minimum values

Solving linear and programming problems

Solving linear programming problems  example

Example part (b)
Straight lines

Straight line graphs

The general equation of a straight line

Finding the equation of a line

Simultaneous equations

Method 1  elimination

Method 2  substitution

Sketching linear equations

Break even analysis

Straight line graphs  gradient

Finding the gradient given the coordinates of two points

Elimination examples

The break even example

Sketching linear equations  example 1

Sketching linear equations  example 2

Straight line graphs  gradient example
Graphs
Power graphs
Trigonometry 1

Trigonometry introduction

Rightangled triangles

Solving non rightangled triangles

The sine rule

The cosine rule

The area of a triangle

Example

Example 2

Cosine rule – Example 1

Cosine rule – Example 2
Trigonometry 2

Pythagoras' theorem

Pythagoras in 3 dimensions

Similar figures

Surface area and volume

Similar figures example

Surface area and volume: example 1

Surface area and volume: example 2
Pythagoras and bearings

The tomb of Pythagoras activity

Angles of elevation and depression

Directions and bearings

Contour maps

Traverse surveys

Compass bearings

True Bearings

Bearings application example

Field survey example

Field survey example continued

Bearings yachting example
Ratio and proportion

Ratio and proportion

Simplifying ratios

Expressing ratios as a percentage

Dividing quantities in a given ratio

Applications of ratio and proportion

Map scales

Dilution factors

Photography

Gears

Finding x values in ratios

Map scales: how far is that?

Dilution: drug strength

Photographing a tree

Gearing up... gearing down
Ratio and proportion gears
Discrete random variables

Random variables

Discrete probability distribution

The mean and variance of a discrete random variable

Standard deviation as a measure of spread
Normal distribution

The normal curve

Continuous random variables and the normal distribution

Calculation of probabilities for a normal distribution

Approximating the binomial distribution with normal distribution
Binomial distribution

Binomial probability function and distribution

The number of successes in a given number of trials

The effect of changing the parameter p

The effect of changing the parameter n

The mean and variance of a binomial random variable
Hypergeometric distribution

Sampling without replacement

The mean of a hypergeometric random variable

The variance of a hypergeometric random variable

The mean and variance of a hypergeometric random variable example

The mean and variance of a hypergeometric random variable example 2

The formula for calculating probabilities

Calculating probabilities

Relationship between hypergeometric and binomial distributions
Rules of integration

Antidifferentiation

Antiderivatives of basic functions

Finding specific functions based on given information

Indefinite integral

Using related derivatives to find an integral
Integration applications
Rules of differentiation

Basic functions

Functions

Rules of differentiation

Rules for finding derivatives

Linear combination of functions

Product of two functions

Quotient of two functions

Function of a function
Applications of differentiation

Applications of Differentiation

Stationary Points

Maximum or Minimum

Maximum/Minimum Problems

Equations of Tangents and Normals

Examples
Factors of polynomials

Factorising polynomials

Polynomial notation and function manipulations

Factorising polynomials

Factorisation process for cubics

Factorisation process for quartics

Factor and remainder theorems

Long division

Synthetic division

Factorising polynomials: example
Straight line graphs

Activity

Graphs of polynomial functions: the garden activity

Introduction

Graphs of polynomial functions

Graphs derived from standard graphs

Other standard graphs

Certain special graphs

Transformations

Reflections

Dilations

Combinations of transformations

Addition of ordinates

Important graphs

Important graphs: Type 1

Important graphs: type 2

Important graphs: type 3

Important graphs: type 4

Graphs of inverse functions

Graphs of polynomial functions: examples
Graphs of ciruclar functions

Introduction

Graphs of the form y=Asin(a(x+b))+B and y=Acos(a(x+b))+B

Solution of trigonometric equations

Graphs of the form y = tan(ax)

Equations of the form sin(ax)=B and cos(ax)=B

Equations of the form sin(ax)=kcos(ax)
Inverse functions

Inverse functions  manytoone and onetomany

Inverse functions

Further inverse functions

Examples
Logarithms and index laws
The binomial theorem
Creating a frequency table from data

Frequency and graphs  overview

Nominal data

Discrete data

Continuous data

Frequency tables with nominal data

Frequency tables with discrete data

Frequency tables  discrete data and summary statistics

Mean from frequency tables  discrete data

Interpreting column graphs

Family size cumulative frequency
Differentiation  Product rule
Antiderivatives

Review of Standard Antiderivatives

Standard Antiderivative Types

Type 2  Hyperbolic Functions

Type 3  Partial Fractions

Example 2

Type 5  Linear Substitution
Antiderivatives of circular functions

Type 4  Inverse Circular Functions

Examples 1 and 2

Examples 3 and 4

Examples 5 and 6

Type 6  Odd and Even Powers

Odd Powers

Even Powers
Antiderivatives and their graphs

Relationships Between Graphs of Functions and their Antiderivatives

Original and Antiderivative Functions

Graphs of Antiderivatives

Examples 1 and 2

Examples 3 and 4

Examples 5 and 6
Conics (elipses and hyperbolae)

Graphs of Ellipses

Examples

Graphs of Hyperbolae

Example 1

Example 2

Example 3

Example 4

Transformations of hyperbolae

Translations
Degrees and radians
Inverse circular functions
Polynomial equations
Reciprocal function graphs
Vectors in 2 and 3 dimensions

Vector Definition

Symbols Used to Represent Vectors

Magnitude of a Vector

Zero Vector

Subtracting Vectors

Equal vectors

Parallel Vectors

Vectors in Cartesian Form

Position Vectors

The Cartesian Plane

Linear Dependence and Independence

Unit Vector

Multiplying by a Scalar

Linear Dependence and Independence Example
Scalar products of vectors

Scalar and vector resolutes

Scalar resolutes

Vector resolutes

Vector resolute examples

Scalar (or dot) Product

Using the Dot Product in Vector Proofs

Example 1

Finding the Angle Between Two Vectors

Example 2 (midpoints)

Perpendicular Vectors

Inclination to the x or y axis

Example 3 (midpoints)

Example 4 (Colinear points)
Symmetry and periodicity

Use of Symmetric, Periodic and Complementary Relationships of Circular Functions

Symmetry Example 1

Example 2

Example 3

Periodicity

Complementary Relationships

Complementary Relationship Examples
Trigonometric identities
Differential equations

Introduction

Order and degree of differential equations

Verifying solutions

Rates of change

Rates of change  chain rule

The rates of change example

First order differential equations  type 1

First order differential equations  type 2

Second order differential equations
Second derivatives
Kinematics

Introduction

Finding displacement from velocity

Solving differential equations (rectilinear motion) example

Finding acceleration or velocity from displacement

Constant acceleration  introduction

Constant acceleration  example 1

Velocity time graphs  introduction

Finding the acceleration from the velocity time graph

Finding the distance travelled from a velocity time graph

Velocity time graphs  example

Constant acceleration  example 2
Motion

Introduction

Newton's laws of motions

Forcesweight

Diagram of forces

Basic equation of motion

Resolution of forces

Horizontal and vertical

Equations of motion

Parallel and perpendicular to a plane

Equations of motion

Moving down the slope

Connected masses

Motion under a constant force

Motion under a constant force  example 1

Motion under a constant force  example 2

Motion under a variable force

Motion under a variable force  example 1

Motion under a variable force  example 2

Motion under a variable force  example 3

Momentum and impulse

Momentum and impulse example

Moving up the slope

Motion under a constant force  example 1 continued

Forcesnormal reaction

Forcesfriction

Forcestension
Resolution of forces
Vectors

Position vectors as functions of time (Parametric Equations)

Finding cartesian equations from parametric equations

Example 1

Example 2

Collision

Example 3

Using a graphic calculator with parametric equations

Using a graphic calculator with two parametric equations to show a collision

The closest distance to a path

Example 4
Vectors 2

The garden activity

Notation used in vector calculus

Differentiation and anti differentiation of vectors

Example 1

Example 2
Introduction to Algebra
Using Formulae 1

Using formulae

The XSIQ petrol pump

Petrol stations

Renting a car

Get real rentacar deal

Speed examples

Speed

Temperature

Temperature examples

Temperature converter
Using Formulae 2
Algebraic Expressions 1

Simplifying algebraic expressions without using algebra blocks

Verifying the simplified form of an algebraic expression

Verifying the simplification using substitution  examples

Verifying the simplification using a spreadsheet

Adding and subtracting terms  practice questions 1

Adding and subtracting terms  practice questions 2

Mulitplying terms  Commutative Law

Multiplying terms  rearranging 1

Multiplying terms  rearranging 2

Dividing terms  rearranging 1

Dividing terms  rearranging 2

Adding and subtracting like terms without using algebra blocks
Algebraic Expressions 2

Expanding and simplifying algebraic expressions

Distributive Law  algebra blocks

Distributive Law  expansion

Expanding and collecting like terms

Expanding and simplifying algebraic expressions
Algebraic Fractions 1

Introduction to algebraic fractions

Adding simple algebraic fractions

Subtracting algebraic fractions

Fractions with letters in the denominators

Binomials in denominator

Speed and algebraic fractions

The faster car takes less time

Calculating the time difference

Adding and subtracting algebraic fractions  practice questions
Algebraic Fractions 2

Factorising algebraic expressions

Factorising algebraic expressions

Highest common factor

More complex highest common factors

Factorising algebraic expressions  practice questions
Algebraic Fractions 3
Terminology for Algebraic Expressions
Binomial Expressions 1

Binomial expressions

Binomial expansions with like and unlike terms

Binomial expansions

Binomial expansions and areas

Using binomial expansions for problem solving

Binomial expansions  reminder

Binomial expansion with two variables

Binomial expansions  practice questions
Binomial Expressions 2

Binomial expansions with perfect and nonperfect squares

Binomial expansions with nonperfect squares

Expanding perfect squares  practice questions

Binomial expansions with perfect squares

Binomial expansions with perfect squares
Binomial Expressions 3

Binomial expansions  Difference of perfect squares

Difference of perfect squares (DOPS)

Expanding and simplifying algebraic expressions  practice questions

Expanding using the difference of perfect squares rule

Difference of perfect squares rule

Difference of perfect squares
Completing the Square

Completing the square

Factorising quadratic trinomials using the method of completing the square

Process to factorise a quadratic trinomial by the method of completing the square
Perfect Squares

Using the difference of perfect squares 1

Using the difference of perfect squares 2

Factorising using the difference of perfect squares (DOPS) expressions
Quadratic Trinomials

What are quadratic trinomials?

Factorising the general form by inspection

Factorising quadratic trinomials

Factorising algebraic expressions  quadratic trinomials

Factorising quadratic trinomials

Factorising quadratic trinomials

Factorisation of quadratic trinomials
Substitution into Algebraic Expressions
Summary of Factorisation

Summary of factorisation

Practice question  Sally's patio

Practice question  in the swim with algebra

Practice question  algebra can be fishy
Summarising data

Summarising data  overview

Mode

Mean

Median

Mode, mean, median

Comparing mode, mean, median

Range of data

Interquartile range

Review  summarising data
Frequency and graphs

Frequency and graphs  overview

Nominal data

Discrete data

Continuous data

Frequency tables with nominal data

Frequency tables with discrete data

Frequency tables  discrete data and summary statistics

Mean from frequency tables  discrete data

Interpreting column graphs

Family size cumulative frequency
Graphs of all kinds

Graphs of all kinds

Ice cream pictograph

Column and bar graphs

Examples of column graphs

Pie charts

Examples of pie charts

Line graphs

Temperature line graphs

Types of graphs

Interpreting column graphs

Manchester flights bar graph

Movie line graph

Interpretation of a sports pie graph

Review  graphs
Introduction to probability

Introduction to probability

Probability words

Words describing chance

Finding probabilities theoretically

Probability with equally likely outcomes
Odds and probability

Odds and probability

Odds

Odds on

Odds and probability

Fair or unfair?

Deciding fairness using probability
Probability and relative frequency

Probability and relative frequency

Shortrun coin tossing

Shortrun dice rolling

Predicting from past experience

Towards probability with coins

Towards probability with dice

Probability as longrun relative frequency
Assessment
Learning Outcomes
Alison's math course will greatly enhance your skills, giving you a greater understanding of core mathematics components such as geometry, trigonometry, calculus and more as well as expanding your knowledge base in areas such as chance, data distributions, statistics, probability, correlations and regression.
You will learn about using binomial expansions for problem solving and will understand the relationship between the graphs of functions and their antiderivatives. You will be able to confidently create graphs and make advanced calculations such as straightline calculations, kinematics, motion, vectors, algebra, binomial expressions, and quadratic functions.
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Diploma course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Diploma course, you have the option to acquire an official Diploma, which is a great way to share your achievement with the world. Your Alison Diploma is:
Ideal for sharing with potential employers  include it in your CV, professional social media profiles and job applications
An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning
Alison offers 3 types of Diplomas for completed Diploma courses:
Digital Diploma  a downloadable Diploma in PDF format, immediately available to you when you complete your purchase
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