The Junior Cert
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Contents ******* Under Construction 2020 *******
Welcome to The Maths Guide.
Description:
  • An introduction to what The Maths Guide is all about and how the course works.
  • How to do an Exercise (or print a worksheet)
  • How to do revision
  • Start at the Beginning: Counting, Measuring, and Labelling
  • Operations like Adding, Subtracting, Multiplying and Dividing (and brackets)
  • Inverse Operations
Description:
  • Fractions Percents and Decimals
  • Using percentages
  • Reversing percentages
  • Percents and decimals
  • Cost Profit and Sale Prices
Description:
  • Which formula gives the better answer? All possible answers.
  • Sets of inputs to a formula
  • Sets of inputs with formula is a function
  • Function : Couples and Relationships
  • Plotting couples on a graph
Description:
  • Types of Graphs and Types of Data.
  • Discrete and Continuous Values. Nominal values
  • Bar Charts, Pie Charts, Histograms, Point plots, Line graphs
Description:
  • Types of Graphs : The line graph. The quadratic graph
  • Rounding values
  • Reversing Functions using graphs
  • Reversing Functions using equations
Description:
  • Types of Graphs : The line graph - Co-ordinate Geometry of the Line
  • Finding the Slope from Function
  • Finding the Intercept
  • Distance and mid-point between two points
Description:
  • Co-ordinate Geometry of the Line
  • Perpendicular and Parallel Lines
  • Finding the equation of the line
Description:
  • Patterns as a function
  • Continuing Patterns
  • General term of a Lnear pattern
  • Quadratic Patterns
Description:
  • Types of Graphs : Not a function
  • Reading and Understanding Graphs
  • Distance Speed Time and Rate
  • Comparing Visualisation methods for collected data
  • Summarising and Displaying collected data
  • Reading summarised data
Description:
  • Exam Type Questions on Material Covered
Description:
  • DATA: Collecting Displaying Summarising and Interpreting Information
  • What its purpose is and what its purpose is not
  • Display: Creating Pie Charts
  • Summarise: Finding and Using the Mean
  • The Mode and the Median
Description:
  • DATA: Usefulness of Summarised Data
  • Median, Lower Quartile, Upper Quartile
  • Median and Quartiles from summarised data values
Description:
  • Probability : The relationship with DATA
  • Counting : What probability is all about
  • Counting better
  • Counting methods
  • Counting carefully
Description:
  • Interesting Properties of Numbers
  • Prime Numbers, LCM, HCF
  • Powers
Description:
  • Interesting Properties of Shapes : Geometry
  • Discovery through Construction : This is an easy but work intensive week - be prepared
Description:
  • Expressions and Equations : An easier week than last one
  • Expanding brackets and Solving Equations
Description:
  • Shape and Space
  • Finding Missing Distances
  • Calculating Area with Positive and Negative Space : Using Brackets
  • Practise Expanding Brackets
  • Practise Equations
  • Practise Expression Substitution
Description:
  • Puzzles : Simultaneous Expressions
  • Simultaneous Equations : Basic
  • Simultaneous Equations : Multiples
  • Practise : Rearranging Equations
  • Simultaneous Equations : Rearranging
  • Simultaneous Equations : Rearranging with Multiples
Description:
  • Percentages, Fractions and Direct Decimals : Again (multiple methods)
  • Reversing Percentages using Equations
  • Reversing Percentages using The Unitary Method
  • Compound Interest : Step by Step
  • Compound Interest : Directly with Powers
  • Compound Interest : Multiple stage problems
Description:
  • Adding and Subtracting Sets and other operations
  • Union : Adding Sets
  • Set Difference : Subtracting Sets
  • Intersection : Where Sets Join
  • Complement : Where the Set is not
  • Brackets : Commutative and Associative with Sets
Description:
  • Exam Type Questions on Material Covered
Description:
  • Functions : Plotting Quadratic Functions
  • Finding crossing points from Quadratic Function
  • Finding the Function given crossing points (Reversing)
  • Form of the Function and Factorising
  • Factorising
Description:
  • Patterns - Non Maths puzzles
  • Quadratic Patterns : Continue the Pattern
  • General Term of a Quadratic Pattern
  • Applying to Questions
  • Linear or Quadratic or Something else?
Description:
  • Geometry
  • Angles : Vertically Opposite and in Isosceles Triangles
  • Pythagoras' Theorem
  • Angles : Parallel Lines
  • Angles : In combinations
Description:
  • Volume
  • Formulae : Find the Volume
  • Given Volume finding inputs (Reversing Formulae - Using Equations)
  • Multi Stage Volume questions
Description:
  • Visualizing Fractions and Percentages
  • Mental Arithemetic versus Calculator Arithmetic
  • Adding and Subtracting Fractional parts : What is left or what is taken away ?
Description:
  • Ratios Week
  • Ratios and Direct Proportion : Using Tables
  • Ratios and Currency Exchange
  • Currency Exchange : Buy versus Sell
  • Ratios and Complex Questions Using the LCM
  • Ratios : Application
Description:
  • Speed Distance and Time (and Timetables)
  • Reading Timetables
  • Calculating Time
  • Calculating Speed : Single Step and Multistep questions
Description:
  • Trigonometry Definitions of Sin Cos and Tan
  • Calculating Sin, Cos and Tan from Ratio
  • Evaluating Sin, Cos and Tan from Angle
  • Rearranging Equations
  • Pythagoras' Theorem
Description:
  • Trigonometry
  • Reversing Sin, Cos and Tan : Calculator
  • Reversing Sin, Cos and Tan : Which answer?
Description:
  • Some remaining things - To complete the course
  • Indices
  • Reversing Indices - Which answer ?
  • Creating Formulae and Functions
  • Consequences for Sets of Values : Solving Inequalities
Description:
  • Exam Type Questions on Material Covered
Description:
  • Choice to Follow the Spiral Path (Recommended) - Continue Below
  • Or to Review by Topic : Follow this link
Description:
  • An introduction to what The Maths Guide is all about and how the course works.
  • An introduction to the major topics that are on the course.
  • Exercises on Memory techniques and the first 5 topics.
Description:
  • Major Topics - Part 2.
  • An introduction to the remaining major topics that are on the course.
  • Introductory Exercises on the 6th to the 11th topics.
Description:
  • Number: Prime Factors and the HCF
  • Sets : Venn Diagrams, # (Cardinal Number), ∪ , ∩, The Universal Set
  • Functions: Using your calculator
  • Algebra: Substitution
  • Shape and Space : Using Formulas
Description:
  • Geometry: Co-ordinates
  • Constructions : ASA Triangles
  • Probability: Systematic counting
  • Statistics: Reading Frequency Tables
  • Arithmetic: More percentages revision
Description:
  • Number: Prime Factors and the LCM
  • Sets : Venn Diagrams, # (Cardinal Number), ∪ , ∩, U, ∖ : Counting elements
  • Functions: Plotting functions
  • Algebra: Terms
  • Algebra: Simplifying Terms
Description:
  • Co-Ordinate Geometry: Finding the halfway point between two points.
  • Constructions : Applying Memory techniques
  • Probability: Systematic Listing using Tree Diagrams
  • Statistics: Measures of Central Tendency (The Average)
  • Arithmetic: Adding VAT - New Method
Description:
  • Number: Rounding to the nearest...
  • Sets : Using Algebra to solve problems
  • Functions: Linear functions - Intercept and Slope
  • Algebra: Expanding and Simplifying
  • Equations: Introducting Equations
Description:
  • Co-Ordinate Geometry: Measuring distance between two points.
  • Constructions : Applying Memory techniques - Connecting images
  • Probability: The Fundamental Principle of Counting
  • Statistics: Measures of Central Tendency (The Average) Median of Frequency Tables
  • Arithmetic: Adding VAT (in reverse)
Description:
  • Number: Rounding to the 1st decimal place, 2dp...
  • Sets : Using Algebra to solve problems
  • Functions: Slope given two couples
  • Algebra: Substitution
  • Equations: Introducing Equations and Balancing
Description:
  • Co-Ordinate Geometry: Calculating distance between two points (Pythagoras).
  • Constructions : Applying Memory techniques - Connecting images 6 to 10
  • Probability: Probability of favourable outcome calculation
  • Statistics: Measures of Central Tendency : The Mean
  • Arithmetic: Percentage profit. Cost and Sale Price