26
Modules
318
Topics
1015
hours
Modules (26)
Resources ()

strand 1 higher level probability and statistics

Module 1
Counting and Probability Part 1
Resources availableLearn about counting and probability in this module.Counting and Probability Part 1  Learning Outcomes
Start TopicArrangements and Selections
Start TopicExpected Value
Start TopicProbability Of Simple Events
Start TopicProbability Of Compound Events
Start TopicIndependent Events
Start TopicProbability Using Tree Diagrams
Start TopicProbability Trees With And Without Replacement
Start TopicReverse Probability  Bayes' Theorem
Start TopicBayes' Theorem And Medical Testing
Start TopicProbability Patterns Of Discrete Variables
Start TopicCounting and Probability Part 1  Lesson Summary
Start Topic 
Module 2
Counting and Probability Part 2
Resources availableFurther you knowledge on counting and probability in this module.Counting and Probability Part 2  Learning Outcomes
Start TopicComparing Distributions
Start TopicThe Binomial Distribution
Start TopicA Problem Using Binomial Distribution
Start TopicBernoulli Trials And The Binomial Formula
Start TopicThe Normal Distribution
Start TopicUsing Excel To Calculate Binomial Probabilities
Start TopicUsing Excel To Find The Mean Of A Binomial Distribution
Start TopicCounting and Probability Part 2  Lesson Summary
Start Topic 
Module 3
Statistics Part 1
Resources availableLearn about statistics and its mathematical concepts and processes in this module.Statistics Part 1  Learning Outcomes
Start TopicCumulative Frequency and The Ogive
Start TopicCumulative Frequency, Quartiles And The InterQuartile Range
Start TopicMean Of Grouped Frequency Tables
Start TopicConstructing A Stem And Leaf Diagram
Start TopicComparative Stem And Leaf Diagram
Start TopicHistograms  Understanding That Area Gives Frequency
Start TopicIntroduction To Sampling Techniques
Start TopicRandom Stratified Sampling
Start TopicStatistics Part 1  Lesson Summary
Start Topic 
Module 4
Statistics Part 2
Resources availableLearn more about statistics and its mathematical concepts and processes in this module.Statistics Part 2  Learning Outcomes
Start TopicStatistical Correlation
Start TopicMeasuring Correlation  Pearson's Correlation Coefficient
Start TopicUsing Excel To Calculate Pearson's Correlation Coefficient
Start TopicUsing Excel To Find Pearson's Correlation Coefficient, Using The Inbuilt Function
Start TopicRegression Lines And Their Equation
Start TopicThe Mean Of The Coefficients In The Equation Of The Regression Line
Start TopicUsing Excel To Calculate The Equation Of The Regression Line
Start TopicUsing Excel To Find The Equation Of The Regression Line, Using Inbuilt Function
Start TopicStatistics Part 2  Lesson Summary
Start Topic 
Module 5
Synthetic Geometry
Resources availableIn this module you will learn about what geometry is and involves, along with gaining an understanding of Geometric reasoning and how to prove a theorem to be true.Synthetic Geometry  Learning Outcomes
Start TopicProperties of Shapes
Start TopicGeometric Reasoning 1
Start TopicGeometric Reasoning 2
Start TopicGeometric Reasoning 3
Start TopicGeometric Reasoning 4
Start TopicProof of Theorem 11
Start TopicProof of Theorem 12
Start TopicProof of Theorem 13
Start TopicSynthetic Geometry  Lesson Summary
Start Topic 
Module 6
Coordinate Geometry
Resources availableIn this module you will learn about geometry with using coordinates, including equation of a line, translation an reflection of functions, the equation of a circle, and more geometry involving circles.Coordinate Geometry  Learning Outcomes
Start TopicGeometry with Coordinates
Start TopicEquation of a Straight Line
Start TopicParallel Lines
Start TopicPerpendicular Lines
Start TopicThe Graphs of y=kx^n
Start TopicTranslation of Functions
Start TopicReflection of Functions
Start TopicStretching Functions
Start TopicGeneral Transformation of Functions
Start TopicEquation of a Circle 1  Centre (0,0)
Start TopicEquation of a Circle 2  (Centre Not 0,0)
Start TopicEquation of a Circle 3
Start TopicDiameter of a Circle
Start TopicTangent and Normal to a Circle
Start TopicTouching Circles
Start TopicProve that a Line is a Tangent to a Circle
Start TopicDistance From a Point to a Line
Start TopicAngle Between 2 Lines
Start TopicDividing a Line Segment in a Given Ratio
Start TopicCoordinate Geometry  Lesson Summary
Start Topic 
Module 7
Trigonometry
Resources availableThis module will teach you about using trigonometric ratios to find out angles, and the sides of triangles.Trigonometry  Learning Outcomes
Start TopicFinding Angles with Sine Ratio
Start TopicFinding Sides with the Sine Ratio
Start TopicFinding Angles with the Cosine Ratio
Start TopicFinding Sides with the Cosine Ratio
Start TopicFinding Angles with the Tangent Ratio
Start TopicFinding a Missing Side with the Sine Rule
Start TopicFinding a Missing Angle with the Sine Rule
Start TopicProblem Solving with the Cosine Rule
Start TopicTrigonometry  Lesson Summary
Start Topic 
Module 8
Radians
Resources availableIn this module you will learn more about trigonometry, including Radians, the Unit circle, solving trigonometric equations, the area of a sector of a circle, and trigonometry with 3D geometric shapes.Radians  Learning Outcomes
Start TopicIntroducing Radians
Start TopicUsing Radians to Find Area of Sector
Start TopicSketching and Matching Trigonometric Functions
Start TopicGraphing Trig Functions. y = sinx  Calculator Work – in Degrees
Start TopicGraphing Trig Functions. y = 3sin2x  Valculator Work – in Radians
Start TopicIntroducing the Unit Circle
Start TopicThe Unit Circle – Drawing Sine and Cosine
Start TopicComparing Degrees to Radians on the Unit Circle
Start TopicSolving Trigonometric Equations
Start TopicProving The Sine Rule
Start TopicProving the Cosine Rule
Start TopicProving Trigonometric Identity  (Sin Squared + Cos Squared = 1)
Start TopicFinding Areas with Trigonometry
Start Topic3D Trigonometry  The Cuboid
Start Topic3D Trigonometry  Rectangular Based Pyramid
Start TopicArea of a Segment
Start TopicRadians  Lesson Summary
Start Topic 
Module 9
Leaving Certificate Project Maths  Higher Level  First Assessment
Resources availableThis module includes the First Assessment in the Leaving Certificate Project Maths  Higher Level course, which is based on Strand 1 and 2 of the Leaving Certificate syllabus.Leaving Certificate Project Maths  Higher Level  First Assessment
Start Assessment 
Module 10
Numbers Part 1
Resources availableIn this module you will learn how to work with and solve number systems including indices, converting decimal numbers to the standard form, multiplying indices, and Argand diagrams.Numbers Part 1  Learning Outcomes
Start TopicLarge Numbers in Standard Form
Start TopicChanging Decimals to Standard Form
Start TopicChanging Large Numbers from Standard Form
Start TopicChanging Small Numbers from Standard Form
Start TopicAdding and Multiplying Simple Powers
Start TopicWorking with Indices
Start TopicNegative Indices
Start TopicFractional Indices, Numerator of 1
Start TopicIndex Power Equal to 0
Start TopicPositive Fractional Indices All Types
Start TopicNegative Fractional Indices
Start TopicWriting Index Numbers as a Power of 2
Start TopicQuadratic Number Patterns
Start TopicThe Argand Diagram and Modulus
Start TopicThe Meaning of i
Start TopicNumbers Part 1  Lesson Summary
Start Topic 
Module 11
Numbers Part 2
Resources availableIn this module you will learn more on how to work with number including imaginary numbers, rational & irrational numbers, logarithms, sequences, Proof by induction, and finding cubed roots.Numbers Part 2  Learning Outcomes
Start TopicPatterns with Imaginary Numbers
Start TopicRational or Irrational
Start TopicProof by Contradiction – Root 2 is Irrational
Start TopicFinding the Cube Roots of 8
Start TopicChanging the Base of a Logarithm
Start TopicLogarithmic Equations
Start TopicLimit of Sequences
Start TopicArithmetic Series
Start TopicGeometric Series
Start TopicInfinite Geometric Series  Part 1
Start TopicInfinite Geometric Series  Part 2
Start TopicDeriving Amortisation Formula from Geometric Series
Start TopicProof by Induction – The Sum of the First N Natural Numbers
Start TopicProof by Induction Applied to a Geometric Series
Start TopicFurther Proof by Induction – Multiples of 3
Start TopicFurther Proof by Induction – Factorials and Powers
Start TopicNumbers Part 2  Lesson Summary
Start Topic 
Module 12
Complex Numbers
Resources availableIn this module you will learn to work with complex numbers and what they are, including manipulating complex numbers, the complex conjugate, pattern with imaginary numbers, writing complex numbers in the polar form, De Moive's Theorem, solving quadratic equations, and cubic equations with complex numbers.Complex Numbers  Learning Outcomes
Start TopicManipulating Complex Numbers and The Complex Conjugate
Start TopicThe Argand Diagram and Modulus
Start TopicThe Meaning of i
Start TopicPatterns with Imaginary Numbers
Start TopicWriting Complex Numbers in Polar Form
Start TopicMultiplying and Dividing in Polar Form (Proof)
Start TopicMultiplying and Dividing in Polar Form (Example)
Start TopicProof of De Moivre’s Theorem
Start TopicComplex Numbers When Solving Quadratic Equations
Start TopicCubic Equations with Complex Roots
Start TopicFinding the Cube Roots of 8
Start TopicComplex Numbers  Lesson Summary
Start Topic 
Module 13
Arithmetic  Financial Maths  Part 1
Resources availableIn this module you will learn how to work with Arithmetic or financial maths, teaching you about percentage profit, percentage loss, calculating simple interest, using multipliers, compound interest and annual percentage rateArithmetic  Financial Maths  Part 1  Learning Outcomes
Start TopicPercentage Profit, Markup and Margin
Start TopicCalculating Profit with Special Offers
Start TopicPercentage Loss 1
Start TopicPercentage Loss 2
Start TopicSimple Interest – Calculating The Interest
Start TopicSimple Interest – Calculating The Rate
Start TopicSimple Interest – Calculating The Principal
Start TopicSimple Interest – Calculating The Period
Start TopicPercentage Changes Using Multipliers
Start TopicReverse Percentages and VAT
Start TopicIntroducing Compound Interest
Start TopicCompound Interest and Annual Equivalent Rate
Start TopicCompound Interest APR with Credit Cards
Start TopicArithmetic  Financial Maths  Part 1  Lesson Summary
Start Topic 
Module 14
Arithmetic  Financial Maths  Part 2
Resources availableIn this module you will learn more on how to work with arithmetic maths or financial maths, including calculating income tax, universal social charge, PRSI, net pay, the Present value formula and the amortisation problem.Arithmetic  Financial Maths  Part 2  Learning Outcomes
Start TopicDepreciation
Start TopicCalculating APR
Start TopicCalculating Monthly Interest From APR – 2 Methods
Start TopicIncome Tax, USC and PRSI
Start TopicNet Pay / Take Home Pay
Start TopicPresent Value – Working Out Future Value
Start TopicPresent Value  Working Out Present Value
Start TopicPresent Value and Amortisation Problem
Start TopicCompleting an Amortization Schedule
Start TopicSavings and Amortization
Start TopicArithmetic  Financial Maths  Part 2  Lesson Summary
Start Topic 
Module 15
Length, Area and Volume
Resources availableIn this module you will learn how to work out and calculate the area and volume of both 2 dimensional objects/shapes and 3 dimensional objects/shapes.Length, Area and Volume  Learning Outcomes
Start TopicCircumference of a Circle
Start TopicArea of a Circle
Start TopicFinding Radius and Diameter of a Circle From its Perimeter
Start TopicFinding Radius and Diameter From Area of Circle
Start TopicArea of Trapezium
Start TopicArea of Acute Angled Triangles
Start TopicArea of Obtuse Angled Triangles
Start TopicArea of Parallelogram
Start TopicArea of Rectangles
Start TopicArea Compound Shapes (Rectangles)
Start TopicArea of Compound Shapes
Start TopicArea of Compound Shapes (Triangles)
Start TopicVolume and Surface Area
Start TopicSectors and Arcs
Start TopicArea of a Segment
Start TopicVolume of Compound Solid
Start TopicLength, Area and Volume  Lesson Summary
Start Topic 
Module 16
Expressions and Formulae
Resources availableLearn about expression and formulae used in the Irish Higher level leaving cert maths.Expressions and Formulae  Learning Outcomes
Start TopicFactorising Quadratics
Start TopicFactorising  Difference of Two Squares
Start TopicExpanding Brackets (Grid Method)
Start TopicExpanding Brackets (FOIL method)
Start TopicExpanding Any Two Brackets
Start TopicRearranging Simple Formulae
Start TopicRearranging Simple Formulae 2 Steps
Start TopicRearranging Formulae with Squares and Square Roots
Start TopicRearranging Formulae New Subject Appearing Twice
Start TopicSimplifying Surds
Start TopicFurther Calculations with Surds
Start TopicCompleting The Square
Start TopicGeneral Completing The Square
Start TopicBinomial Expansion
Start TopicExpressions and Formulae  Lesson Summary
Start Topic 
Module 17
Solving Equations  Part 1
Resources availableLearn about solving equations and types of equations you will be asked to solve during the Irish Leaving Cert Higher Level Maths exam.Solving Equations  Part 1  Learning Outcomes
Start TopicEquations with Linear Functions in The Denominator
Start TopicQuadratic Equations Using The Formula
Start TopicQuadratic Equations Non Unitary x Squared
Start TopicQuadratic Equations Both Brackets The Same Sign
Start TopicQuadratic Equations Brackets With Different Signs
Start TopicQuadratic Equations That Have to be Rearranged
Start TopicSolving Simultaneous Equations Graphically
Start TopicSimultaneous Equations Both Negative Signs
Start TopicSimultaneous Equations Negative and Positive Signs
Start TopicSimultaneous Equations Both Positive
Start TopicHidden Quadratics
Start TopicUse of The Discriminant
Start TopicEquations With Indices
Start TopicSolving Equations  Part 1  Lesson Summary
Start Topic 
Module 18
Solving Equations  Part 2
Resources availableLearn more about solving equations and types of equations you will be asked to solve during the Irish Leaving Cert Higher Level Maths exam.Solving Equations  Part 2  Learning Outcomes
Start TopicLogarithmic Equations
Start TopicSolving Exponential Equations
Start TopicFrom Roots to Functions
Start TopicNon Linear Simultaneous Equations
Start TopicFactor Theorem
Start TopicThe Remainder Theorem
Start TopicGeneral Remainder and Factor Theorem
Start TopicFinding Roots of Cubic Equation
Start TopicModulus Equations
Start TopicUsing Graphs to Solve Modulus Equations
Start TopicSolving Equations  Part 2  Lesson Summary
Start Topic 
Module 19
Inequalities
Resources availableLearn about solving and working out Inequalities in algebra for the Irish leaving cert higher level exam.Inequalities  Learning Outcomes
Start TopicFinding Inequalities from Shaded Regions
Start TopicSolving Linear Inequalities with Fractions
Start TopicSolving Quadratic Inequalities – Method 1
Start TopicSolving Quadratic Inequalities – Method 2
Start TopicSolving Quadratic Inequalities – Method 3
Start TopicNonUnitary x^2  Trial and Error Method
Start TopicNonUnitary x^2  Algebra Method
Start TopicNonunitary x^2  Graphical Method
Start TopicSolving Quadratic Inequalities  Special Cases
Start TopicRational Inequalities
Start TopicModulus Equations
Start TopicUsing Graphs to Solve Modulus Equations
Start TopicModulus Inequalities
Start TopicModulus Function on a Graph
Start TopicGraphical Solution of Modulus Inequalities
Start TopicInequalities  Lesson Summary
Start Topic 
Module 20
Leaving Certificate Project Maths  Higher Level  Second Assessment
Resources availableThis module includes the First Assessment in the Leaving Certificate Project Maths  Higher Level course, which is based on Strand 3 and 4 of the Leaving Certificate syllabus.Leaving Certificate Project Maths  Higher Level  Second Assessment
Start Assessment 
Module 21
Functions
Resources availableIn this module you will learn how to work with functions to plot graphs, including quadratic and cubic graphs with exponential graphs.Functions  Learning Outcomes
Start TopicPlotting Quadratic Graphs from Table of Values
Start TopicPlotting Cubic Graphs from Table of Values
Start TopicPlotting Reciprocal Graphs from Table of Values
Start TopicPlotting Exponential Graphs from Table of Values
Start TopicMatching Equations and Sketches
Start TopicSketching Parabola Using Completing The Square
Start TopicCompleting the Square and Sketching the Full Method
Start TopicMatching Functions and Graphs – Quadratic/Exponential
Start TopicTranslation of Functions Using f(xa)
Start TopicTranslating Functions Using f(x)+a
Start TopicStretching Functions in x Direction
Start TopicStretching Functions in the y Direction
Start TopicThe Discriminant
Start TopicInverse and Bijective Functions
Start TopicFunctions  Lesson Summary
Start Topic 
Module 22
Calculus  Differentiation  Part 1
Resources availableIn this module, you will learn to review differentiation in detail including the Product Rule, Chain Rule and Quotient Rule.Calculus  Differentiation  Part 1  Learning Outcomes
Start TopicBasic Differentiation of y = x^n
Start TopicDifferentiation of Polynomials
Start TopicEquation of a Tangent
Start TopicEquation of a Normal
Start TopicHarder Questions on Normals
Start TopicGeneral Differentiation of x^n
Start TopicSecond Derivative
Start TopicDifferentiation of Tangents
Start TopicUsing Different Variables
Start TopicDifferentiating Products and Quotients
Start TopicThe Chain Rule
Start TopicThe Product Rule
Start TopicThe Quotient Rule
Start TopicCalculus  Differentiation  Part 1  Lesson Summary
Start Topic 
Module 23
Calculus  Differentiation  Part 2
Resources availableThis module will further teach you about differentiation, including Differentiation of Logarithms, Turning Points, Rates of Change, and differentiating inverse functions.Calculus  Differentiation  Part 2  Learning Outcomes
Start TopicDifferentiation of Logarithms
Start TopicDifferentiation of y = sinx
Start TopicDifferentiation of y = cosx
Start TopicDifferentiation and Rates of Change
Start TopicRate of Change Example 1
Start TopicRate of Change Example 2
Start TopicDifferentiation and Turning Points
Start TopicDifferentiation and Matching Graphs
Start TopicApplications of Differentiation 1 (Displacement/Velocity/Acceleration)
Start TopicApplications of Differentiation 2 (Voltage/Current)
Start TopicMaximum Volume of Box
Start TopicExploring Relationships Between Graphs of Cubic Functions and Their Differentials
Start TopicExploring Relationships Between Graphs of Trigonometric Functions and Their Differentials
Start TopicExploring Relationships Between Graphs of Exponential Functions and Their Differentials
Start TopicInverse Functions Differentiated
Start TopicCalculus  Differentiation  Part 2  Lesson Summary
Start Topic 
Module 24
Calculus  Integration
Resources availableIn this module, you will learn about integration covering areas such as exponentials and trigonometric functions.Calculus  Integration  Learning Outcomes
Start TopicBasic Integration
Start TopicThe Integral Sign
Start TopicHarder Integration
Start TopicDefinite Integration
Start TopicArea Between Lines
Start TopicBasic Differential Equations
Start TopicIntegration of Trig Functions (y=cos4x)
Start TopicIntegration of Exponentials
Start TopicIntroducing the Trapezoidal Rule
Start TopicTrapezoidal Rule Into Integration
Start TopicFinding the Area Between a Quadratic Function and a Straight Line
Start TopicCalculus  Integration  Lesson Summary
Start Topic 
Module 25
Leaving Certificate Project Maths  Higher Level  Third Assessment
Resources availableThis module includes the First Assessment in the Leaving Certificate Project Maths  Higher Level course, which is based on Strand 5 of the Leaving Certificate syllabus.Leaving Certificate Project Maths  Higher Level  Third Assessment
Start Assessment 
course assessment: Leaving Certificate Project Maths  Higher Level  Revised

Module 26
Course assessment
Resources available