# Strand 3 Higher Level Numbers and Shapes Free Course

• Description
• Outcome
• Certification
• The concepts of number and number patterns are the basic building blocks of arithmetic and algebra. Furthermore, we cannot escape the use of numbers in our everyday lives. We use clocks and watches to count through the hours and minutes of our day. We count out money to pay our bills and often take a flutter on the lottery by choosing six numbers. The application of Arithmetic and Geometric series in finance is investigated through loan repayments and investments. The use of AER (annual equivelant rate) and APR (annual percentage rate) when calculating repayments is investigated. Students are then introduced to the concept of a complex number and shown how to add, subtract, multiply and divide complex numbers. Complex numbers are used to represent the flow of current in a circuit and are also used in most areas of electronics. We use numbers to measure the perimeter and area of various shapes (triangles, rectangles, hexagons and circles) and we also use numbers to work out the volumes of solids such as cylinders, cones, spheres and hemi-spheres.

• Having completed this course students will be able to:

• 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 De-Moivres Theorem to simplify an expansion

• 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 share your success. Plus it’s:

• Ideal for including in CVs, job applications and portfolios
• An indication of your ability to learn and achieve high results
• An incentive to continue to empower yourself through learning
• A tangible way of supporting the Alison mission to empower people everywhere through education.

###### Modules List( 5 )
• PROJECT MATHS STRAND 3 HIGHER LEVEL: NUMBERS AND ...
• Module 1: Number Systems
• Large numbers in standard form
• Changing decimals to standard fom
• Changing large numbers from standard form
• Changing small numbers from standard form
• Adding and multiplying simple powers
• Working with indices
• Negative indices
• Fractional indices, numerator of 1
• Index power equal to 0
• Positive fractional indices all types
• Negative fractional indices
• Writing index numbers as a power of 2
• Manipulating complex numbers and the complex conjugate
• The Argand Diagram and Modulus
• The meaning of i
• Patterns with imaginary numbers
• Rational or irrational
• Root 2 is Irrational – Proof by contradiction
• Finding the cube roots of 8
• Changing the base of logarithms
• Logarithmic equations
• Limits of sequences
• Arithmetic series
• Geometric series
• Infinite geometric series - Part 1
• Infinite geometric series - Part 2
• Deriving Amortisation formula from geometric series
• The sum of the first n natural numbers – Proof by induction
• Proof by induction applied to a geometric series
• Further proof by induction – Multiples of 3
• Further proof by induction – Factorials and powers
• Module 2: Arithmetic - Financial Maths
• Profit, markup and margin
• Calculating profit with special offers
• Percentage loss - Part 1
• Percentage loss - Part 2
• Simple interest – Calculating the interest
• Simple interest – Calculating the rate
• Simple interest – Calculating the principal
• Simple interest – Calculating the period
• Percentage changes using multipliers
• Reverse percentages and VAT
• Introducing compound interest
• Compound interest and Annual Equivalent Rate
• Compound interest APR with credit cards
• Depreciation
• Calculating APR
• Calculating monthly interest from APR – 2 methods
• Income tax, USC and PRSI
• Net pay/Take home pay
• Present value – Working out future value
• Present value – Working out present value
• Present value – Harder example
• Present value and amortisation problem
• Completing an amortization schedule
• Savings and amortization
• Module 3: Length, Area and Volume
• Circumference of a circle
• Area of a circle
• Finding radius and diameter of a circle from its perimeter
• Finding radius and diameter from area of circle
• Area of trapezium
• Area of acute angled triangles
• Area of obtuse angled triangles
• Area of parallelogram
• Area of rectangles
• Area Compound Shapes (rectangles)
• Area of compound shapes
• Area of Compound shapes (Triangles)
• Volume and surface area
• Sectors and arcs
• Area of a segment
• Volume of compound solid
• Module 4: Complex Numbers
• Manipulating complex numbers and the complex conjugate
• The Argand Diagram and Modulus
• The meaning of i
• Patterns with imaginary numbers
• Writing complex numbers in polar form
• Multiplying and dividing in polar form (proof)
• Multiplying and dividing in polar form (example)
• Proof of De Moivre’s Theorem
• Complex numbers when solving quadratic equations
• Cubic equations with complex roots
• Finding the cube roots of 8
• END OF COURSE ASSESSMENT
• Strand 3 Higher Level Numbers and Shapes Assessment
• Strand 3 Higher Level Numbers Assessment
• RESOURCE
• Resource: Examination Material Archive
###### Topics List ( 32 )
Module 1: Number Systems
###### Topics List ( 24 )
Module 2: Arithmetic - Financial Maths
###### Topics List ( 16 )
Module 3: Length, Area and Volume
###### Topics List ( 11 )
Module 4: Complex Numbers
###### Topics List ( 1 )
Strand 3 Higher Level Numbers and Shapes Assessment
You must score 80% or more to pass this assessment.
##### Course Features
• Duration

3-4 Hours

• Publisher

• Video

Yes

• Audio

Yes

• Assessment

Yes

• Certification

Yes

• Price

Free

• Reward

50 Pts

• Responsive

No