
Free Course

Advance Learning

1015 Hours

Assessment

Certification

Academic  Secondary  Level 2

50 Pts
Project Maths  Higher Level

Description

Outcome

Certification

This course is for students interested in studying the Project Maths Higher Level Course in its entirety. This course provides students with videos on all the Higher Level topics in one location listed by module and topic. In addition, a comprehensive assessment is provided which tests learners on the entire content of the Project Maths Higher Level Syllabus. These topics include Probability and Statistics, Geometry and Trigonometry, Numbers and Shapes, Algebra, Functions and Calculus.

Having completed this course students will be able to:
Describe the concepts of probability
Understand outcomes of random processes
Describe statistical reasoning with an aim to becoming a statistically aware consumer
Find, collect and organise data
Represent data graphically and numerically
Analyse, interpret and draw inferences from data
Develop synthesis and problemsolving skills
Determine the slope of a line given it’s equation
Find the equation of a line perpendicular to a given line and passing through a given point
Compute the angle between two given lines
Determine the equation of a circle having a given centre and radius
Find the equation of a tangent to a given circle at a specified point
Find distance and angle using Sine and Cosine Rules
Find length of an arc and area of a sector using circular measure
Solve the trigonometrical equations sin(x) = r and cos(x) = r in general form
Determine the sum of an arithmetic series
Determine the sum of a geometric series
Work out the repayment on a loan
Work out the future value of an investment
Represent a complex number in polar form
Use DeMoivres Theorem to simplify an expansion
Solve linear simultaneous equations with 3 unknowns
Factorise expressions of order 2 and 3
Search for roots of cubic equations and solve them
Solve one linear equation and one equation of order 2 with two unknowns
Solve basic inequalities
Solve inequalities involving fractions
Basic Differentiation of functions (including trig, exp and log)
The rules of differentiation (product rule, quotient rule, chain rule)
Determine the local maxima and local minima turning points of a curve
Understand rate of change of distance, area and volume
Understand the meaning of ‘antiderivative’ and Indefinite Integration
Basic Integration of algebraic functions
Basic Integration of Trigonometrical and Exponential functions
How to use integration to find an area and use of the Trapezoidal Rule 
All Alison courses are free to study. To successfully complete a course you must score 80% or higher in each course assessments. Upon successful completion of a course, you can choose to make your achievement formal by purchasing an official Alison Diploma, Certificate or PDF.
Having an official Alison document is a great way to celebrate and share your success. It is: Ideal to include with CVs, job applications and portfolios
 A way to show your ability to learn and achieve high results
Modules List( 16 )

PROJECT MATHS  HIGHER LEVEL

Module
1 Counting and Probability
Learn more about counting and probability.

Arrangements and selections
Start Topic

Expected value
Start Topic

Probability of simple events
Start Topic

Probability of compound events
Start Topic

Independent events
Start Topic

Probability using tree diagrams
Start Topic

Probability trees with and without replacement
Start Topic

Reverse probability  Bayes' theorem
Start Topic

Bayes' theorem and medical testing
Start Topic

Probability patterns of discrete variables
Start Topic

Comparing distributions
Start Topic

The binomial distribution
Start Topic

A problem using binomial distribution
Start Topic

Bernoulli trials and the binomial formula
Start Topic

The normal distribution
Start Topic

Using Excel to calculate binomial probabilities
Start Topic

Using Excel to find the mean of a binomial distribution
Start Topic


Module
2 Statistics
Learn more about statistics.

Cumulative frequency and the Ogive
Start Topic

Cumulative frequency, quartiles and the interquartile range
Start Topic

Mean of grouped frequency tables
Start Topic

Constructing a stem and leaf diagram
Start Topic

Comparative stem and leaf diagram
Start Topic

Histograms  Understanding that area gives frequency
Start Topic

Introduction to sampling techniques
Start Topic

Random stratified sampling
Start Topic

Statistical correlation
Start Topic

Measuring correlation  Pearson's Correlation Coefficient
Start Topic

Using Excel to calculate Pearson's Correlation Coefficient
Start Topic

Using Excel to find Pearson's Correlation Coefficient, using the inbuilt function
Start Topic

Regression lines and their equation
Start Topic

The meaning of the coefficients in the equation of the regression line
Start Topic

Using Excel to calculate the equation of the regression line
Start Topic

Using Excel to find the equation of the regression line, using inbuilt function
Start Topic


Module
3 Synthetic Geometry
Learn more about synthetic geometry.

Properties of Shapes
Start Topic

Geometric reasoning  Part 1
Start Topic

Geometric reasoning  Part 2
Start Topic

Geometric reasoning  Part 3
Start Topic

Geometric reasoning  Part 4
Start Topic

Proof of Theorem 11
Start Topic

Proof of Theorem 12
Start Topic

Proof of Theorem 13
Start Topic


Module
4 Coordinate Geometry
Learn more about coordinate geometry.

Geometry with coordinates
Start Topic

Equation of a straight line
Start Topic

Parallel lines
Start Topic

Perpendicular lines
Start Topic

The graphs of y=kx^n
Start Topic

Translation of functions
Start Topic

Reflection of functions
Start Topic

Stretching functions
Start Topic

General transformation of functions
Start Topic

Equation of a circle 1  Centre (0,0)
Start Topic

Equation of a circle 2  Centre not (0,0)
Start Topic

Equation of a circle 3
Start Topic

Diameter of a circle
Start Topic

Tangent and normal to a circle
Start Topic

Touching circles
Start Topic

Prove that a line is a tangent to a circle
Start Topic

Distance from a point to a line
Start Topic

Angle between two lines
Start Topic

Dividing a line segment in a given ratio
Start Topic


Module
5 Trigonometry
Learn more about trigonometry.

Finding angles with sine ratio
Start Topic

Finding sides with the sine ratio
Start Topic

Finding angles with the cosine ratio
Start Topic

Finding sides with the cosine ratio
Start Topic

Finding angles with the tangent ratio
Start Topic

Finding sides with the tangent ratio
Start Topic

Finding a missing side with the Sine Rule
Start Topic

Finding a missing angle with the Sine Rule
Start Topic

Problem solving with the Cosine Rule
Start Topic

Introducing Radians
Start Topic

Using radians to find area of sector
Start Topic

Sketching and matching trigonometric functions
Start Topic

Graphing trigonometric functions. y = sinx  calculator work – in degrees
Start Topic

Graphing trigonometric functions. y = 3sin2x  calculator work – in radians
Start Topic

Introducing the Unit Circle
Start Topic

The Unit Circle – drawing sine and cosine
Start Topic

Comparing degrees to radians on the Unit Circle
Start Topic

Solving trigonometric equations
Start Topic

Proving the Sine Rule
Start Topic

Proving the Cosine Rule
Start Topic

Proving Trigonometric Identity – (Sin squared + cos squared = 1)
Start Topic

Finding areas with trigonometry
Start Topic

3D trigonometry – The cuboid
Start Topic

3D trigonometry – Rectangular based pyramid
Start Topic

Area of a segment
Start Topic


Module
6 Number Systems
Learn more about number systems.

Large numbers in standard form
Start Topic

Changing decimals to standard fom
Start Topic

Changing large numbers from standard form
Start Topic

Changing small numbers from standard form
Start Topic

Adding and multiplying simple powers
Start Topic

Working with indices
Start Topic

Negative indices
Start Topic

Fractional indices, numerator of 1
Start Topic

Index power equal to 0
Start Topic

Positive fractional indices all types
Start Topic

Negative fractional indices
Start Topic

Writing index numbers as a power of 2
Start Topic

Quadratic number patterns
Start Topic

Manipulating complex numbers and the complex conjugate
Start Topic

The Argand Diagram and Modulus
Start Topic

The meaning of i
Start Topic

Patterns with imaginary numbers
Start Topic

Rational or irrational
Start Topic

Root 2 is Irrational – Proof by contradiction
Start Topic

Finding the cube roots of 8
Start Topic

Changing the base of logarithms
Start Topic

Logarithmic equations
Start Topic

Limits of sequences
Start Topic

Arithmetic series
Start Topic

Geometric series
Start Topic

Infinite geometric series  Part 1
Start Topic

Infinite geometric series  Part 2
Start Topic

Deriving Amortisation formula from geometric series
Start Topic

The sum of the first n natural numbers – Proof by induction
Start Topic

Proof by induction applied to a geometric series
Start Topic

Further proof by induction – Multiples of 3
Start Topic

Further proof by induction – Factorials and powers
Start Topic


Module
7 Arithmetic  Financial Maths
Learn more about arithmetic using financial maths.

Profit, markup and margin
Start Topic

Calculating profit with special offers
Start Topic

Percentage loss  Part 1
Start Topic

Percentage loss  Part 2
Start Topic

Simple interest – Calculating the interest
Start Topic

Simple interest – Calculating the rate
Start Topic

Simple interest – Calculating the principal
Start Topic

Simple interest – Calculating the period
Start Topic

Percentage changes using multipliers
Start Topic

Reverse percentages and VAT
Start Topic

Introducing compound interest
Start Topic

Compound interest and Annual Equivalent Rate
Start Topic

Compound interest APR with credit cards
Start Topic

Depreciation
Start Topic

Calculating APR
Start Topic

Calculating monthly interest from APR – 2 methods
Start Topic

Income tax, USC and PRSI
Start Topic

Net pay/Take home pay
Start Topic

Present value – Working out future value
Start Topic

Present value – Working out present value
Start Topic

Present value – Harder example
Start Topic

Present value and amortisation problem
Start Topic

Completing an amortization schedule
Start Topic

Savings and amortization
Start Topic


Module
8 Length, Area and Volume
Learn more about length, area and volume.

Circumference of a circle
Start Topic

Area of a circle
Start Topic

Finding radius and diameter of a circle from its perimeter
Start Topic

Finding radius and diameter from area of circle
Start Topic

Area of trapezium
Start Topic

Area of acute angled triangles
Start Topic

Area of obtuse angled triangles
Start Topic

Area of parallelogram
Start Topic

Area of rectangles
Start Topic

Area Compound Shapes (rectangles)
Start Topic

Area of compound shapes
Start Topic

Area of Compound shapes (Triangles)
Start Topic

Volume and surface area
Start Topic

Sectors and arcs
Start Topic

Area of a segment
Start Topic

Volume of compound solid
Start Topic


Module
9 Complex Numbers
Learn more about complex numbers.

Manipulating complex numbers and the complex conjugate
Start Topic

The Argand Diagram and Modulus
Start Topic

The meaning of i
Start Topic

Patterns with imaginary numbers
Start Topic

Writing complex numbers in polar form
Start Topic

Multiplying and dividing in polar form (proof)
Start Topic

Multiplying and dividing in polar form (example)
Start Topic

Proof of De Moivre’s Theorem
Start Topic

Complex numbers when solving quadratic equations
Start Topic

Cubic equations with complex roots
Start Topic

Finding the cube roots of 8
Start Topic


Module
10 Expressions and Formulae
Learn more about expressions and formulae.

Factorising quadratics
Start Topic

Factorising – Difference of two squares
Start Topic

Expanding brackets (grid method)
Start Topic

Expanding brackets (FOIL method)
Start Topic

Expanding any two brackets
Start Topic

Rearranging simple formulae
Start Topic

Rearranging simple formulae  2 steps
Start Topic

Rearranging formulae with squares and square roots
Start Topic

Rearranging formulae new subject appearing twice
Start Topic

Simplifying Surds
Start Topic

Further Calculations with Surds
Start Topic

Completing the Square
Start Topic

General Completing the Square
Start Topic

Binomial expansion
Start Topic


Module
11 Solving Equations
Learn more about solving equations.

Equations with linear functions in the denominator
Start Topic

Quadratic equations using the formula
Start Topic

Quadratic equations non unitary x squared
Start Topic

Quadratic equations both brackets the same sign
Start Topic

Quadratic equations brackets with different signs
Start Topic

Quadratic equations that have to be rearranged
Start Topic

Solving simultaneous equations graphically
Start Topic

Simultaneous equations both negative signs
Start Topic

Simultaneous equations negative and positive signs
Start Topic

Simultaneous equations both positive
Start Topic

Hidden quadratics
Start Topic

Use of the discriminant
Start Topic

Equations with indices
Start Topic

Logarithmic equations
Start Topic

Solving exponential equations
Start Topic

From roots to functions
Start Topic

Nonlinear simultaneous equations
Start Topic

Factor Theorem  Part 1
Start Topic

Factor Theorem  Part 2
Start Topic

The Remainder Theorem
Start Topic

General Remainder and Factor Theorem
Start Topic

Finding roots of cubic equation
Start Topic

Modulus equations
Start Topic

Using graphs to solve modulus equations
Start Topic


Module
12 Inequalities
Learn more about inequalities.

Finding inequalities from shaded regions
Start Topic

Solving linear inequalities with fractions
Start Topic

Solving quadratic inequalities – Method 1
Start Topic

Solving quadratic inequalities – Method 2
Start Topic

Solving quadratic inequalities – Method 3
Start Topic

Nonunitary x^2  Trial and error method
Start Topic

Nonunitary x^2  Algebra method
Start Topic

Nonunitary x^2  Graphical method
Start Topic

Special Cases (use SQI DoTS)
Start Topic

Rational functions
Start Topic

Modulus equations
Start Topic

Using graphs to solve modulus equations
Start Topic

Modulus inequalities
Start Topic

Modulus function on a graph
Start Topic

Graphical solution of modulus inequalities
Start Topic


Module
13 Functions
Learn more about functions.

Plotting quadratic graphs from table of values
Start Topic

Plotting cubic graphs from table of values
Start Topic

Plotting reciprocal graphs from table of values
Start Topic

Plotting exponential graphs from table of values
Start Topic

Matching equations and sketches
Start Topic

Sketching parabola using completing the square
Start Topic

Completing the square and sketching the full method
Start Topic

Matching functions and graphs – quadratic / exponential
Start Topic

Translation of functions using f(xa)
Start Topic

Translating of functions using f(x)+a
Start Topic

Sketching functions in x direction
Start Topic

Sketching functions in the y direction
Start Topic

The Discriminant
Start Topic

Inverse and bijective functions
Start Topic


Module
14 Calculus  Differentiation
Learn more about differentiation.

Basic differentiation of y = x^n
Start Topic

Differentiation of polynomials
Start Topic

Equation of a tangent
Start Topic

Equation of a normal
Start Topic

Harder questions on normals
Start Topic

General differentiation of x^n
Start Topic

Second derivative
Start Topic

Differentiation of tangents
Start Topic

Using different variables
Start Topic

Differentiating products and quotients
Start Topic

The Chain Rule
Start Topic

The Product Rule
Start Topic

The Quotient Rule
Start Topic

Differentiation of logarithms
Start Topic

Differentiation of y = sinx
Start Topic

Differentiation of y = cosx
Start Topic

Differentiation and rates of change
Start Topic

Rate of change  Example 1
Start Topic

Rate of change  Example 2
Start Topic

Differentiation and turning points
Start Topic

Differentiation and matching graphs
Start Topic

Applications of differentiation 1 (displacement / velocity / acceleration)
Start Topic

Applications of differentiation 2 (voltage / current)
Start Topic

Maximum volume of box
Start Topic

Exploring relationships between graphs of cubic functions and their differentials
Start Topic

Exploring relationships between graphs of trigonometric functions and their differentials
Start Topic

Exploring relationships between graphs of exponential functions and their differentials
Start Topic

Inverse functions differentiated
Start Topic


Module
15 Calculus  Integration
Learn more about integration.

Basic integration
Start Topic

The integral sign
Start Topic

Harder integration
Start Topic

Definite integration
Start Topic

Area between lines
Start Topic

Basic differential equations
Start Topic

Integration of Trig functions (y=cos4x)
Start Topic

Integration of exponentials
Start Topic

Introducing the Trapezoidal Rule
Start Topic

Trapezoidal Rule into integration
Start Topic

Finding the area between a quadratic function and a straight line
Start Topic


END OF COURSE ASSESSMENT

Module
16 Project Maths Higher Level Assessment
You must score 80% or more to pass this assessment.

Project Maths  Higher Level Assessment
Start Topic
