The Junior Cert

... your guide to excellence from day one to your exam

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Contents

The Spiral Method of Learning involves working on a topic and then coming back later to look at it in more detail.

Gradually you build up more and more information about everything and how it all fits together.

This way, you don't feel overwhelemed at the beginnning. You return to all the topics again and again ( in a spiral).

Do your best each step of the way.

AND

While the ideas might be new and challenging, as you practise everything makes more and more sense.

So Enjoy. Start with Week01 below

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- Welcome to The Maths Guide.
- Your Weekly Schedule : Day 0 to Day 6
- How to do an Exercise (or print a worksheet)
- How to do revision
- Start at the Beginning: Measures - Adding and Subtracting

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- Fractions Percents and Decimals
- Using percentages
- Reversing percentages
- Percents and decimals
- Cost Profit and Sale Prices

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- 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

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- Types of Graphs and Types of Data.
- Discrete and Continuous Values. Nominal values
- Bar Charts, Pie Charts, Histograms, Point plots, Line graphs

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- Types of Graphs : The line graph. The quadratic graph
- Rounding values
- Reversing Functions using graphs
- Reversing Functions using equations

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- 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

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- Co-ordinate Geometry of the Line
- Perpendicular and Parallel Lines
- Finding the equation of the line

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- Patterns as a function
- Continuing Patterns
- General term of a Lnear pattern
- Quadratic Patterns

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- 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

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- Exam Type Questions on Material Covered

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- 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

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- DATA: Usefulness of Summarised Data
- Median, Lower Quartile, Upper Quartile
- Median and Quartiles from summarised data values

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- Probability : The relationship with DATA
- Counting : What probability is all about
- Counting better
- Counting methods
- Counting carefully

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- Interesting Properties of Numbers
- Prime Numbers, LCM, HCF
- Powers

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- Interesting Properties of Shapes : Geometry
- Discovery through Construction : This is an easy but work intensive week - be prepared

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- Expressions and Equations : An easier week than last one
- Expanding brackets and Solving Equations

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- Shape and Space
- Finding Missing Distances
- Calculating Area with Positive and Negative Space : Using Brackets
- Practise Expanding Brackets
- Practise Equations
- Practise Expression Substitution

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- Puzzles : Simultaneous Expressions
- Simultaneous Equations : Basic
- Simultaneous Equations : Multiples
- Practise : Rearranging Equations
- Simultaneous Equations : Rearranging
- Simultaneous Equations : Rearranging with Multiples

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- 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

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- 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

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- Exam Type Questions on Material Covered

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- Functions : Plotting Quadratic Functions
- Finding crossing points from Quadratic Function
- Finding the Function given crossing points (Reversing)
- Form of the Function and Factorising
- Factorising

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- Patterns - Non Maths puzzles
- Quadratic Patterns : Continue the Pattern
- General Term of a Quadratic Pattern
- Applying to Questions
- Linear or Quadratic or Something else?

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- Geometry
- Angles : Vertically Opposite and in Isosceles Triangles
- Pythagoras' Theorem
- Angles : Parallel Lines
- Angles : In combinations

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- Volume
- Formulae : Find the Volume
- Given Volume finding inputs (Reversing Formulae - Using Equations)
- Multi Stage Volume questions

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- Visualizing Fractions and Percentages
- Mental Arithemetic versus Calculator Arithmetic
- Adding and Subtracting Fractional parts : What is left or what is taken away ?

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- 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

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- Speed Distance and Time (and Timetables)
- Reading Timetables
- Calculating Time
- Calculating Speed : Single Step and Multistep questions

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- 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

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- Trigonometry
- Reversing Sin, Cos and Tan : Calculator
- Reversing Sin, Cos and Tan : Which answer?

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- Some remaining things - To complete the course
- Indices
- Reversing Indices - Which answer ?
- Creating Formulae and Functions
- Consequences for Sets of Values : Solving Inequalities

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- Exam Type Questions on Material Covered

Off the path

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- Choice to Follow the Spiral Path (Recommended) - Continue Below
- Or to Review by Topic : Follow this link

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- 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.

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- 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.

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- 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

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- Geometry: Co-ordinates
- Constructions : ASA Triangles
- Probability: Systematic counting
- Statistics: Reading Frequency Tables
- Arithmetic: More percentages revision

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- Number: Prime Factors and the LCM
- Sets : Venn Diagrams, # (Cardinal Number), ∪ , ∩, U, ∖ : Counting elements
- Functions: Plotting functions
- Algebra: Terms
- Algebra: Simplifying Terms

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- 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

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- Number: Rounding to the nearest...
- Sets : Using Algebra to solve problems
- Functions: Linear functions - Intercept and Slope
- Algebra: Expanding and Simplifying
- Equations: Introducting Equations

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- 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)

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- 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

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- 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