The Junior Cert
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:
• 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
Description:
• Types of Graphs : Not a function
• Distance Speed Time and Rate
• Comparing Visualisation methods for collected data
• Summarising and Displaying collected 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
• 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)
• 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
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
• Algebra: Substitution
• Shape and Space : Using Formulas
Description:
• Geometry: Co-ordinates
• Constructions : ASA Triangles
• Probability: Systematic counting
• 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