Leaving Certificate Project Maths  Higher Level  Revised
This course is for students interested in studying the Project Maths Higher Level Course in its entirety.
Description
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.
Start Course NowModules
Counting and Probability Part 1

Counting and Probability Part 1  Learning Outcomes

Arrangements and Selections

Expected Value

Probability Of Simple Events

Probability Of Compound Events

Independent Events

Probability Using Tree Diagrams

Probability Trees With And Without Replacement

Reverse Probability  Bayes' Theorem

Bayes' Theorem And Medical Testing

Probability Patterns Of Discrete Variables

Counting and Probability Part 1  Lesson Summary
Counting and Probability Part 2

Counting and Probability Part 2  Learning Outcomes

Comparing Distributions

The Binomial Distribution

A Problem Using Binomial Distribution

Bernoulli Trials And The Binomial Formula

The Normal Distribution

Using Excel To Calculate Binomial Probabilities

Using Excel To Find The Mean Of A Binomial Distribution

Counting and Probability Part 2  Lesson Summary
Statistics Part 1

Statistics Part 1  Learning Outcomes

Cumulative Frequency and The Ogive

Cumulative Frequency, Quartiles And The InterQuartile Range

Mean Of Grouped Frequency Tables

Constructing A Stem And Leaf Diagram

Comparative Stem And Leaf Diagram

Histograms  Understanding That Area Gives Frequency

Introduction To Sampling Techniques

Random Stratified Sampling

Statistics Part 1  Lesson Summary
Statistics Part 2

Statistics Part 2  Learning Outcomes

Statistical Correlation

Measuring Correlation  Pearson's Correlation Coefficient

Using Excel To Calculate Pearson's Correlation Coefficient

Using Excel To Find Pearson's Correlation Coefficient, Using The Inbuilt Function

Regression Lines And Their Equation

The Mean Of The Coefficients In The Equation Of The Regression Line

Using Excel To Calculate The Equation Of The Regression Line

Using Excel To Find The Equation Of The Regression Line, Using Inbuilt Function

Statistics Part 2  Lesson Summary
Synthetic Geometry

Synthetic Geometry  Learning Outcomes

Properties of Shapes

Geometric Reasoning 1

Geometric Reasoning 2

Geometric Reasoning 3

Geometric Reasoning 4

Proof of Theorem 11

Proof of Theorem 12

Proof of Theorem 13

Synthetic Geometry  Lesson Summary
Coordinate Geometry

Coordinate Geometry  Learning Outcomes

Geometry with Coordinates

Equation of a Straight Line

Parallel Lines

Perpendicular Lines

The Graphs of y=kx^n

Translation of Functions

Reflection of Functions

Stretching Functions

General Transformation of Functions

Equation of a Circle 1  Centre (0,0)

Equation of a Circle 2  (Centre Not 0,0)

Equation of a Circle 3

Diameter of a Circle

Tangent and Normal to a Circle

Touching Circles

Prove that a Line is a Tangent to a Circle

Distance From a Point to a Line

Angle Between 2 Lines

Dividing a Line Segment in a Given Ratio

Coordinate Geometry  Lesson Summary
Trigonometry

Trigonometry  Learning Outcomes

Finding Angles with Sine Ratio

Finding Sides with the Sine Ratio

Finding Angles with the Cosine Ratio

Finding Sides with the Cosine Ratio

Finding Angles with the Tangent Ratio

Finding a Missing Side with the Sine Rule

Finding a Missing Angle with the Sine Rule

Problem Solving with the Cosine Rule

Trigonometry  Lesson Summary
Radians

Radians  Learning Outcomes

Introducing Radians

Using Radians to Find Area of Sector

Sketching and Matching Trigonometric Functions

Graphing Trig Functions. y = sinx  Calculator Work – in Degrees

Graphing Trig Functions. y = 3sin2x  Valculator Work – in Radians

Introducing the Unit Circle

The Unit Circle – Drawing Sine and Cosine

Comparing Degrees to Radians on the Unit Circle

Solving Trigonometric Equations

Proving The Sine Rule

Proving the Cosine Rule

Proving Trigonometric Identity  (Sin Squared + Cos Squared = 1)

Finding Areas with Trigonometry

3D Trigonometry  The Cuboid

3D Trigonometry  Rectangular Based Pyramid

Area of a Segment

Radians  Lesson Summary
Leaving Certificate Project Maths  Higher Level  First Assessment
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

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
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
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 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
Expressions and Formulae

Expressions and Formulae  Learning Outcomes

Factorising Quadratics

Factorising  Difference of Two Squares

Expanding Brackets (Grid Method)

Expanding Brackets (FOIL method)

Expanding Any Two Brackets

Rearranging Simple Formulae

Rearranging Simple Formulae 2 Steps

Rearranging Formulae with Squares and Square Roots

Rearranging Formulae New Subject Appearing Twice

Simplifying Surds

Further Calculations with Surds

Completing The Square

General Completing The Square

Binomial Expansion

Expressions and Formulae  Lesson Summary
Solving Equations  Part 1

Solving Equations  Part 1  Learning Outcomes

Equations with Linear Functions in The Denominator

Quadratic Equations Using The Formula

Quadratic Equations Non Unitary x Squared

Quadratic Equations Both Brackets The Same Sign

Quadratic Equations Brackets With Different Signs

Quadratic Equations That Have to be Rearranged

Solving Simultaneous Equations Graphically

Simultaneous Equations Both Negative Signs

Simultaneous Equations Negative and Positive Signs

Simultaneous Equations Both Positive

Hidden Quadratics

Use of The Discriminant

Equations With Indices

Solving Equations  Part 1  Lesson Summary
Solving Equations  Part 2

Solving Equations  Part 2  Learning Outcomes

Logarithmic Equations

Solving Exponential Equations

From Roots to Functions

Non Linear Simultaneous Equations

Factor Theorem

The Remainder Theorem

General Remainder and Factor Theorem

Finding Roots of Cubic Equation

Modulus Equations

Using Graphs to Solve Modulus Equations

Solving Equations  Part 2  Lesson Summary
Inequalities

Inequalities  Learning Outcomes

Finding Inequalities from Shaded Regions

Solving Linear Inequalities with Fractions

Solving Quadratic Inequalities – Method 1

Solving Quadratic Inequalities – Method 2

Solving Quadratic Inequalities – Method 3

NonUnitary x^2  Trial and Error Method

NonUnitary x^2  Algebra Method

Nonunitary x^2  Graphical Method

Solving Quadratic Inequalities  Special Cases

Rational Inequalities

Modulus Equations

Using Graphs to Solve Modulus Equations

Modulus Inequalities

Modulus Function on a Graph

Graphical Solution of Modulus Inequalities

Inequalities  Lesson Summary
Leaving Certificate Project Maths  Higher Level  Second Assessment
Functions

Functions  Learning Outcomes

Plotting Quadratic Graphs from Table of Values

Plotting Cubic Graphs from Table of Values

Plotting Reciprocal Graphs from Table of Values

Plotting Exponential Graphs from Table of Values

Matching Equations and Sketches

Sketching Parabola Using Completing The Square

Completing the Square and Sketching the Full Method

Matching Functions and Graphs – Quadratic/Exponential

Translation of Functions Using f(xa)

Translating Functions Using f(x)+a

Stretching Functions in x Direction

Stretching Functions in the y Direction

The Discriminant

Inverse and Bijective Functions

Functions  Lesson Summary
Calculus  Differentiation  Part 1

Calculus  Differentiation  Part 1  Learning Outcomes

Basic Differentiation of y = x^n

Differentiation of Polynomials

Equation of a Tangent

Equation of a Normal

Harder Questions on Normals

General Differentiation of x^n

Second Derivative

Differentiation of Tangents

Using Different Variables

Differentiating Products and Quotients

The Chain Rule

The Product Rule

The Quotient Rule

Calculus  Differentiation  Part 1  Lesson Summary
Calculus  Differentiation  Part 2

Calculus  Differentiation  Part 2  Learning Outcomes

Differentiation of Logarithms

Differentiation of y = sinx

Differentiation of y = cosx

Differentiation and Rates of Change

Rate of Change Example 1

Rate of Change Example 2

Differentiation and Turning Points

Differentiation and Matching Graphs

Applications of Differentiation 1 (Displacement/Velocity/Acceleration)

Applications of Differentiation 2 (Voltage/Current)

Maximum Volume of Box

Exploring Relationships Between Graphs of Cubic Functions and Their Differentials

Exploring Relationships Between Graphs of Trigonometric Functions and Their Differentials

Exploring Relationships Between Graphs of Exponential Functions and Their Differentials

Inverse Functions Differentiated

Calculus  Differentiation  Part 2  Lesson Summary
Calculus  Integration

Calculus  Integration  Learning Outcomes

Basic Integration

The Integral Sign

Harder Integration

Definite Integration

Area Between Lines

Basic Differential Equations

Integration of Trig Functions (y=cos4x)

Integration of Exponentials

Introducing the Trapezoidal Rule

Trapezoidal Rule Into Integration

Finding the Area Between a Quadratic Function and a Straight Line

Calculus  Integration  Lesson Summary
Leaving Certificate Project Maths  Higher Level  Third Assessment
Course assessment
Learning Outcomes
Having completed this course students will be able to:
 Solve mathematical probability problems/questions
 Identify how to solve statistical questions/problem/equations
 Identify how to solve geometryrelated questions
 Recognise how to use trigonometry to find the area, sides and angles of shapes
 Discuss how to work with different number systems and series in mathematics
 Identify how to calculate percentages, profit and interest, including VAT and APR
 Recognise how to solve the length, area and volume of both 2D and 3D shapes
 Demonstrate how to solve quadratic equations and equations with indices, including simultaneous equations
 Solve basic inequalities and inequalities involving fractions
 Identify how to work with functions and solve calculusbased equations
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