The Junior Cert

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

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Contents ******* Under Construction 2020 *******

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

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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

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

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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