
Free Course

Advance Learning

34 Hours

Assessment

Certification

Academic  Secondary  Level 2

50 Pts
Strand 3 Higher Level Numbers and Shapes

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 hemispheres.

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 DeMoivres Theorem to simplify an expansion

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Modules List( 5 )

PROJECT MATHS STRAND 3 HIGHER LEVEL: NUMBERS AND ...

Module
1 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
2 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
3 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
4 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


END OF COURSE ASSESSMENT

Strand 3 Higher Level Numbers and Shapes Assessment

You must score 80% or more to pass this assessment.

Strand 3 Higher Level Numbers Assessment
Start Topic


RESOURCE

Resource: Examination Material Archive View Resource