16
Modules
275
Topics
1015
hours
Modules (16)
Resources ()

Module 1
Counting and Probability
Resources availableLearn more about counting and probability.Arrangements 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 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 Topic 
Module 2
Statistics
Resources availableLearn more about statistics.Cumulative 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 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 meaning 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 Topic 
Module 3
Synthetic Geometry
Resources availableLearn more about synthetic geometry.Properties of Shapes
Start TopicGeometric reasoning  Part 1
Start TopicGeometric reasoning  Part 2
Start TopicGeometric reasoning  Part 3
Start TopicGeometric reasoning  Part 4
Start TopicProof of Theorem 11
Start TopicProof of Theorem 12
Start TopicProof of Theorem 13
Start Topic 
Module 4
Coordinate Geometry
Resources availableLearn more about coordinate geometry.Geometry 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 two lines
Start TopicDividing a line segment in a given ratio
Start Topic 
Module 5
Trigonometry
Resources availableLearn more about trigonometry.Finding 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 sides 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 TopicIntroducing Radians
Start TopicUsing radians to find area of sector
Start TopicSketching and matching trigonometric functions
Start TopicGraphing trigonometric functions. y = sinx  calculator work – in degrees
Start TopicGraphing trigonometric functions. y = 3sin2x  calculator 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 Topic 
Module 6
Number Systems
Resources availableLearn more about number systems.Large numbers in standard form
Start TopicChanging decimals to standard fom
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 TopicManipulating complex numbers and the complex conjugate
Start TopicThe Argand Diagram and Modulus
Start TopicThe meaning of i
Start TopicPatterns with imaginary numbers
Start TopicRational or irrational
Start TopicRoot 2 is Irrational – Proof by contradiction
Start TopicFinding the cube roots of 8
Start TopicChanging the base of logarithms
Start TopicLogarithmic equations
Start TopicLimits 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 TopicThe sum of the first n natural numbers – Proof by induction
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 Topic 
Module 7
Arithmetic  Financial Maths
Resources availableLearn more about arithmetic using financial maths.Profit, markup and margin
Start TopicCalculating profit with special offers
Start TopicPercentage loss  Part 1
Start TopicPercentage loss  Part 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 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 – Harder example
Start TopicPresent value and amortisation problem
Start TopicCompleting an amortization schedule
Start TopicSavings and amortization
Start Topic 
Module 8
Length, Area and Volume
Resources availableLearn more about length, area and volume.Circumference 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 Topic 
Module 9
Complex Numbers
Resources availableLearn more about complex numbers.Manipulating 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 Topic 
Module 10
Expressions and Formulae
Resources availableLearn more about expressions and formulae.Factorising 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 Topic 
Module 11
Solving Equations
Resources availableLearn more about solving equations.Equations 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 TopicLogarithmic equations
Start TopicSolving exponential equations
Start TopicFrom roots to functions
Start TopicNonlinear simultaneous equations
Start TopicFactor Theorem  Part 1
Start TopicFactor Theorem  Part 2
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 Topic 
Module 12
Inequalities
Resources availableLearn more about inequalities.Finding 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 TopicSpecial Cases (use SQI DoTS)
Start TopicRational functions
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 Topic 
Module 13
Functions
Resources availableLearn more about functions.Plotting 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 of functions using f(x)+a
Start TopicSketching functions in x direction
Start TopicSketching functions in the y direction
Start TopicThe Discriminant
Start TopicInverse and bijective functions
Start Topic 
Module 14
Calculus  Differentiation
Resources availableLearn more about differentiation.Basic 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 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 Topic 
Module 15
Calculus  Integration
Resources availableLearn more about integration.Basic 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 Topic 
end of course assessment

Module 16
Project Maths Higher Level Assessment
Resources availableYou must score 80% or more to pass this assessment.Project Maths  Higher Level Assessment
Start Assessment