Diploma in Mathematics

Modules

• Introduction to triangles

• Triangle letter names

• Equilateral triangles

• Isosceles triangles

• Scalene triangles

• Acute-angled triangles

• Right-angled triangles

• Obtuse-angled triangles

• Quiz on triangle names

• 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 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 - similarity and congruence

• Quiz on similar triangles

• Congruent triangles

• Corresponding angles

• Parallel lines

• Alternate and co-interior angles

• General angles quiz

• Quiz on angles and parallel lines

• 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 angle sum

• Quadrilaterals sum of exterior angles

• Quiz on angles in quadrilaterals

• Introduction to polygons

• What are polygons?

• Regular polygons

• Naming of polygon types

• Rotational symmetry in polygons

• Line symmetry in polygons

• Quiz on 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

• Prisms

• Prisms quiz

• Pyramids and cones

• Spheres, hemispheres and toruses

• Quiz on geometrical solids

• 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

• Introduction

• Types of data

• Types of univariate data

• Numerical data

• Displaying data

• Bar graphs

• Stem and leaf diagrams 1

• Stem and leaf diagrams 2

• Introduction

• Dependent and independent variables

• Percentaged tables

• Parallel boxplots

• Back-to-back stemplots

• Graphical display of bivariate data – in summary

• 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

• 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 and skew of a distribution

• Negative skew

• Positive skew

• Probability intervals

• Probability interval examples

• Comparing sample and population

• Calculating a seasonal index

• Interpreting seasonal indices

• Seasonal movements

• Deseasonalising the data

• Deseasonalising the data – example

• Scatterplots

• Scatterplots: using your calculator

• Pearson's product moment correlation coefficient, r

• Calculating r

• The coefficient of determination

• Practice question

• Strength of association

• Introduction

• Finding the equation of a regression line

• Interpretation of slope and intercept

• Practice question

• The three-median regression line

• Using your calculator

• The three-median regression example

• The three-median regression practice questions

• The least squares regression line

• Making predictions from a regression line

• Non-linear data

• Square transformation

• Log transformations

• Reciprocal transformation

• Example 1

• Example 2

• Introduction

• Residual analysis - part 1

• Plotting the residuals

• Residual analysis - part 2

• Residual analysis - part 3

• 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

• 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

• Finding the sum of an arithmetic series

• Finding the sum of an arithmetic sequence

• 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

• 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

• Applications of sequences and series

• Making rungs for a ladder

• Growing Town

• 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

• 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

• Intersection of half planes

• Finding maximum and minimum values

• Solving linear and programming problems

• Solving linear programming problems - example

• Example part (b)

• 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

• Interpreting graphs

• Step graphs

• Distance-time graphs

• Power graphs

• Linear representation of non-linear graphs

• Trigonometry introduction

• Right-angled triangles

• Solving non right-angled triangles

• The sine rule

• The cosine rule

• The area of a triangle

• Example

• Example 2

• Cosine rule – Example 1

• Cosine rule – Example 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

• 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

• 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

• The gears video

• Random variables

• Discrete probability distribution

• The mean and variance of a discrete random variable

• Standard deviation as a measure of spread

• 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 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

• 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

• Antidifferentiation

• Antiderivatives of basic functions

• Finding specific functions based on given information

• Indefinite integral

• Using related derivatives to find an integral

• Introduction

• Approximating an area

• Definite integrals

• Evaluating a definite integral

• 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

• Stationary Points

• Maximum or Minimum

• Maximum/Minimum Problems

• Equations of Tangents and Normals

• Examples

• 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

• 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

• 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 - many-to-one and one-to-many

• Inverse functions

• Further inverse functions

• Examples

• Indices and logarithms

• Solution of exponential and logarithmic equations

• Examples

• Binomial theorem – Pascal's triangle

• The binomial expansion

• The binomial expansion - examples

• 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

• Product Rule

• Example 1

• Example 2

• Example 3

• Review of Standard Antiderivatives

• Standard Antiderivative Types

• Type 2 - Hyperbolic Functions

• Type 3 - Partial Fractions

• Example 2

• Type 5 - Linear Substitution

• 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

• 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

• Graphs of Ellipses

• Examples

• Graphs of Hyperbolae

• Example 1

• Example 2

• Example 3

• Example 4

• Transformations of hyperbolae

• Translations

• Exact Values

• Conversions of Radian and Degree Measures

• Derivatives of Inverse Circular Functions

• Example 2

• Example 3

• Solution of Polynomial Equations

• Example

• The Fundamental Theroem of Algebra

• Equations

• Examples

• Graphs of Reciprocal Functions

• Example 1

• Example 2

• Example 3

• 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 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 (Co-linear points)

• Use of Symmetric, Periodic and Complementary Relationships of Circular Functions

• Symmetry Example 1

• Example 2

• Example 3

• Periodicity

• Complementary Relationships

• Complementary Relationship Examples

• Reciprocal Circular Functions

• Inverse Circular Functions

• Trigonometric Identities

• 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

• Introduction

• Use of the second derivative

• Examples

• Second derivatives

• 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

• Introduction

• Newton's laws of motions

• Forces-weight

• 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

• Forces-normal reaction

• Forces-friction

• Forces-tension

• Introduction

• Resolution of forces

• Three forces

• Static friction

• Angle of friction

• 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

• The garden activity

• Notation used in vector calculus

• Differentiation and anti differentiation of vectors

• Example 1

• Example 2

• Introduction to algebra

• The language of algebra

• Algebraic notation

• Using formulae

• The XSIQ petrol pump

• Petrol stations

• Renting a car

• Get real rent-a-car deal

• Speed examples

• Speed

• Temperature

• Temperature examples

• Temperature converter

• The using formulae speed video

• The using formulae temperature video

• 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

• Expanding and simplifying algebraic expressions

• Distributive Law - algebra blocks

• Distributive Law - expansion

• Expanding and collecting like terms

• Expanding and simplifying algebraic expressions

• 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

• Factorising algebraic expressions

• Factorising algebraic expressions

• Highest common factor

• More complex highest common factors

• Factorising algebraic expressions - practice questions

• Factorising algebraic expressions - grouping

• Grouping two and two

• Grouping three terms and one term

• Terminology for algebraic expressions

• 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 expansions with perfect and non-perfect squares

• Binomial expansions with non-perfect squares

• Expanding perfect squares - practice questions

• Binomial expansions with perfect squares

• Binomial expansions with perfect squares

• 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

• Factorising quadratic trinomials using the method of completing the square

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

• Using the difference of perfect squares 1

• Using the difference of perfect squares 2

• Factorising using the difference of perfect squares (DOPS) expressions

• 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

• Practice question - Sally's patio

• Practice question - in the swim with algebra

• Practice question - algebra can be fishy

• Summarising data - overview

• Mode

• Mean

• Median

• Mode, mean, median

• Comparing mode, mean, median

• Range of data

• Inter-quartile range

• Review - summarising 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

• 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

• Probability words

• Words describing chance

• Finding probabilities theoretically

• Probability with equally likely outcomes

• Odds and probability

• Odds

• Odds on

• Odds and probability

• Fair or unfair?

• Deciding fairness using probability

• Probability and relative frequency

• Short-run coin tossing

• Short-run dice rolling

• Predicting from past experience

• Towards probability with coins

• Towards probability with dice

• Probability as long-run relative frequency

• Diploma in Mathematics Assessment