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Leaving Cert Higher – Block 1

The Completion Level of Your Training.

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WEEK 1: Algebra

Review of All you know

Math Coaching Application

1 Name of student your are enquiring about Math Coaching?

2 Your e-mail

3 What Class in school is your teenager currently in?

4 What is their main problem area? (check all that apply)

5 What approach have you tried before now? (Check all that apply)

6 Why do you think this approach will be different for your teenager?

7 Any other information you wish to give.

Next

Factorising

Sum and difference of two cubes

Algebraic Fractions

Complex Fractions

Pascals Triangle

Binomial Expansion

Long Division in Algebra

Linear Equations

Simultaneous Linear Equations - two variables

Simultaneous Linear Equations - three variables

Quadratic Equations

Simultaneous Equations - One Linear, one non-linear

The Factor Theorem

Polynomials

Polynomial with the same roots

Unknown coefficients

Surd Equations

Linear Inequalities

Quadratic and Rational Inequalities

Absolute Value

Modulus Inequalities

Inequality Proofs

Discriminants

Week 2 - Length, Area and Volume

Two Dimensional Shapes

Circles

Sector of a Circle

Rectangular Solids

Rectangular Prisms

Cylinders, Cones, Spheres and hemispheres

Volume of a Cylinder

Right Circular Cones

Volume of a Cone

Volume of a Sphere

volume of a hemisphere

Surface Area of a Hemisphere

Trapezoidal Rule

Week 3 - Real Numbers

Natural Numbers

Prime Factors, Highest Common Factor, Lowest Common Multiple

Fundamental Theorem of Arithmetic

Integers

Rational Numbers

Irrational Numbers

Proof by Contradiction

Constructing root 2 and root 3

Rounding and Significant Figures

Orders of Magnitude and Scientific Notation

Week 4 - Functions

Introduction adn Important Terms

Inputs and Outputs

Functions as Mappings, Notation and Intervals

Composite Funtions

Linear and Quadratic Functions

Transformation of Linear Functions

Transformation of Quadratic Functions

Expressing functions in Vector Form

Cubic Functions

Exponential Functions

Logarithmic Functions

Injective, Surjective and Bijective

Inverse Functions

Graphs of Functions and their Inverses

Week 5 - Indices (Exponents) and Logarithms

Rules of Indices

Exponential Functions

Natural Exponential Function

Equations with x as an index

Surds

Laws of Logarithms

Week 6 - Number Patterns, Sequences & Series

Patterns

Arithmetic Sequence

General Term of an Arithmetic Sequence

Arithmetic Series

Gauss's Method

Quadratic Sequence

General Term of a Quadratic Sequence

Cubic Sequence

Geometric Sequence

General Term of a Geometric Sequence

Geometric Series

Limits of Sequences

Infinite Series

Infinite Geometric Series

Week 7 - Arithmetic

Approximation, Percentage Error and Tolerance

Estimates and Approximations of Calculations

Error

Percentage Error and Tolerance

Accumulated Error

Costing

Income Tax (PAYE)

Pay-related Social Insurance (PRSI)

Income Tax and Net Income

V.A.T.

Week 8 - Financial Mathematics

Present Value

Compound Interest

Annual Percentage Rate (APR) and Annual Equivalent Rate (AER)

Depreciation, Causes and Types

Problems involving Geometric Series

Amortisation

Derivation of the Amortisation Formula

Regular Payments at non annual intervals

Week 9 - Proof by Induction

Summations

Patahematical Induction

Proofs Involving Series

Proofs Involving Divisibility

Inequalities

Complex Numbers

The Argand Diagram

Modulus of a complex number

Addition and Subtraction

Multiplication of Complex number by real number

Transformations 1

Multiplication of Complex number by complex number

Transformations 2

Division of Complex Numbers and Complex Conjugates

Quadratic Equations with Complex Roots

Polynomials with Complex Roots - The Conjugate Root Theorem

Polar Form of Complex Numbers

Multiplying and Dividing in Polar Form

De Moivre's Theorem

Calculus - Differentiation

Limits and Continuity

Differentiation from first principles

Differentiating Polynomial Functions and Functions with Rational Powers

The Chain Rule

The Product and Quotient Rule

Trigonometric Functions

Differentiation of Invers Trigonometric Functions

Exponential Function

Natural Logarithm Function

Implicit Differentiation

Increasing and Decreasing Functions

Turning Points and Points of INflections

Local Maximum and Minimum Points

Classifying Turning Points

Maximum and Minimum Problems

Rates of Change

Calculus - Integration

Antiderivitieves and Indefinite Integral

Integrating Sums, Differences and Constant Multiples

Integrating Exponential Functions

Integrating Trigonometric Functions

Definite Integrals

Area under a graph

Intersecting Curves & the Trapezoidal Rule

Average Value of a Function