Strand 3 Higher Level Numbers and Shapes
Students are introduced to the concept of a complex number and how to add, subtract, multiply and divide complex numbers.
Description
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.
Start Course NowModules
Strand 3 Higher Level Numbers and Shapes Assessment
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

Quadratic number patterns

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
Learning Outcomes
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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