Strand 3 Leaving Certificate Higher Level Numbers and Shapes  Revised
This free online maths course looks at Numbers and Shapes, a central topic in the Leaving Certificate Paper.
Description
The concepts of number patterns are the basic building blocks that make up arithmetic and algebra. We cannot escape the use of numbers in our day to day lives. We use watches and clocks to count through the hours and minutes. We count out money for our bills and play the lottery by choosing six numbers.
The application of Geometric and Arithmetic series in finance is looked at through loan repayments and investments. The use of APR (annual percentage rate) and AER (annual equivelant rate) when calculating repayments is looked at. Students are then introduced to complex numbers and shown how to subtract, add, divide and multiply complex numbers.
Complex numbers represent the flow of current in circuits and they are also used in many other areas of electronics. We use numbers to measure the area and perimeter of various shapes (triangles, circles, hexagons and rectangles) and we also use them to work out the volumes of solids like cylinders, spheres, cones and hemispheres.
Start Course NowModules
Numbers Part 1

Numbers Part 1  Learning Outcomes

Large Numbers in Standard Form

Changing Decimals to Standard Form

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

Quadratic Number Patterns

Manipulating Complex Numbers and The Complex Conjugate

The Argand Diagram and Modulus

The Meaning of i

Numbers Part 1  Lesson Summary
Numbers Part 2

Numbers Part 2  Learning Outcomes

Patterns with Imaginary Numbers

Rational or Irrational

Proof by Contradiction – Root 2 is Irrational

Finding the Cube Roots of 8

Changing the Base of a Logarithm

Logarithmic Equations

Limit of Sequences

Arithmetic Series

Geometric Series

Infinite Geometric Series  Part 1

Infinite Geometric Series  Part 2

Deriving Amortisation Formula from Geometric Series

Proof by Induction – The Sum of the First N Natural Numbers

Proof by Induction Applied to a Geometric Series

Further Proof by Induction – Multiples of 3

Further Proof by Induction – Factorials and Powers

Numbers Part 2  Lesson Summary
Arithmetic  Financial Maths  Part 1

Arithmetic  Financial Maths  Part 1  Learning Outcomes

Percentage Profit, Markup and Margin

Calculating Profit with Special Offers

Percentage Loss 1

Percentage Loss 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

Arithmetic  Financial Maths  Part 1  Lesson Summary
Arithmetic  Financial Maths  Part 2

Arithmetic  Financial Maths  Part 2  Learning Outcomes

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

Arithmetic  Financial Maths  Part 2  Lesson Summary
Length, Area and Volume

Length, Area and Volume  Learning Outcomes

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

Length, Area and Volume  Lesson Summary
Complex Numbers

Complex Numbers  Learning Outcomes

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

Complex Numbers  Lesson Summary
Course assessment
Learning Outcomes
Having completed this course you will be able to:
 Identify how to write numbers in the standard form or scientific notation
 Discuss how to work with indices
 Calculate the equation for a quadratic number pattern
 Define the meaning of i and what imaginary number are
 Identify how to change the base of a logarithm
 Define what both an Arithmetic series and a Geometric series are
 Identify how to apply and use proof by Induction and proof by contradiction
 Discuss what percentage profit is and the differences between markup and margin profit
 Calculate the interest on a loan or investment
 Calculate the depreciation of value on items
 Identify the two methods for calculate the annual percentage rate
 Calculate the income tax, universal social charge, and PRSI on your paycheck
 Discuss working out the present value formula both for future values and present values
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