Leaving Cert Mathematics - Notes & Exam Papers
Study for Leaving Cert Mathematics with teacher-written notes, past exam papers, marking scheme, quizzes, and flashcards. All study tools are aligned with the official Leaving Cert Mathematics syllabus to help students understand key topics, stay organised, and feel confident on exam day. Improve your Leaving Cert grades and maximise your CAO points with SimpleStudy Ireland.
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Leaving Cert Mathematics by Topics
Transformations
Introduction and Construction Equipment
Circles with Centre (0,0) and Radius Length r
Revision of Formulae
Right-Angled Triangles, Pythagoras' Theorem, and the Trigonometric Ratios
Proofs: An Introduction
Basic Concepts, Angles, and Axioms
Sequential Events, Independent Events, and Tree Diagrams
The Fundamental Principle of Counting
Sampling
Measures of Centre
Types of Data
Antiderivatives and the Indefinite Integral
The Second Derivative
Calculus, Limits, and Continuity
Introduction to Complex Numbers
Proof and Summations
Present Value
Approximation, Percentage Error, and Tolerance
Patterns
Indices and the Laws of Indices
Functions, Mapping, and Composite Functions
Factors, Multiples, and Prime Factors
Two-Dimensional Shapes
Surd Equations and Linear Inequalities
Solving Linear Equations
Expressions
Graphing Linear Functions
Fundamentals of Trigonometry
The Circle
Collecting Data and Sampling
Patterns and Sequences
Fundamentals of Probability
Enlargements and Constructions
Fundamentals of Geometry
Fundamentals of Functions
Fundamentals of Arithmetic
Fundamentals of Complex Numbers
The Line
Fundamentals of Calculus
Fundamentals of Area and Volume
Quadratic Equations
Fundamentals of Algebra
Properties of Enlargements
Constructions 16-22
Circles with Centre (h,k) and Radius Length r
Derivation of the Divisor of a Line Segment
Using Trigonometry to Solve Practical Problems
Congruent Triangles
Angles and Lines
Expected Value
Choosing and Combinations
Confidence Interval for a Mean
Deciding Which Average to Use
Sample Surveys
Integrating Sums, Differences, and Constant Multiples of Functions
Increasing and Decreasing Functions
Differentiation From First Principles
The Argand Diagram and the Modulus of a Complex Number
Proof by Induction
Compound Interest: Loans and Investments
Costing: Materials, Labour, and Wastage
Arithmetic Sequences
Equations with x as an Index
Linear and Quadratic Functions
Integers and Rational Numbers
Rectangular Solids and Prisms
Quadratic and Rational Inequalities
Solving Simultaneous Linear Equations in Two or Three Variables
Factorising
Graphs of Quadratic Functions
Measures of Location and Spread
Equations of a Certain Form
Finding the Equation of a Line
Degrees, Radians, and Angles of Different Sizes
Proofs
Triangles: Basic Properties
The Binomial Distribution: Bernoulli Trials
Probability, Relative Frequency, and Experimental Probability
Estimating a Population Proportion
Measures of Variation
Collecting Data and Tables
Integrating Exponential and Trigonometric Functions
Turning Points and Points of Inflection
Differentiating Polynomial Functions and Functions with Rational Powers
Addition and Subtraction of Complex Numbers and Multiplication by a Real Number
Proofs Involving Series
Depreciation: Reducing-Balance Method
Income Tax
Arithmetic Series
Surds
Expressing Quadratic Functions in Completed Square Form
Irrational Numbers
Cylinders, Cones, Spheres, and Hemispheres
Absolute Value: Modulus
Solving Quadratic Equations
Algebraic Fractions
Using and Interpreting Quadratic Graphs
Representing Data
Points Inside, Outside, or On a Circle
The Area of a Triangle
The Unit Circle and Trigonometric Ratios
Quadrilaterals
The Normal Distribution
Probability When All Outcomes Are Equally Likely
Hypothesis Testing
Measures of Relative Standing
Graphing Data
Definite Integrals
Maximum and Minimum Problems
The Chain Rule
Multiplication and Division of Complex Numbers
Proofs Involving Divisibility
Applications and Problems Involving Geometric Series
VAT: Value-Added Tax
Some Non-Linear Sequences
Logarithms
Cubic Functions
Rounding and Significant Figures
Trapezoidal Rule
Inequalities: Proofs
Simultaneous Equations: One Linear and One Non-Linear
Binomial Expansions
Quadratic Graphs and Real-Life Problems
Inferential Statistics
Intersection of a Line and a Circle
The Perpendicular Distance From a Point to a Line
Graphing Trigonometric Functions
Area of a Triangle and Area of a Parallelogram
Solving Problems Involving the Normal Distribution
Probability Theory
The Normal Distribution and the Empirical Rule
Scatter Graphs and Correlation
Area Under a Graph
Rates of Change
The Product Rule and Quotient Rule
Quadratic Equations and Polynomials with Complex Roots
Inequalities
Geometric Sequences and Series
Using Logarithms to Solve Practical Problems
Exponential Functions
Orders of Magnitude and Scientific Notation
Discriminants
The Factor Theorem
Long Division in Algebra
Cubic Functions
Tangents and Touching Circles
The Angle of Inclination and the Angle Between Two Lines
Graphing Functions of Certain Forms
Triangles: Further Properties
Conditional Probability
Linear Regression
Intersecting Curves and the Trapezoidal Rule
Trigonometric Functions
Polar Form of a Complex Number
Infinite Series
Graphing Logarithmic Functions
Manipulation of Formulae
Using Graphs of Cubic Functions
Problems in g, f, and c
Three Special Angles
Circles
Average Value of a Function
Differentiation of Inverse Trigonometric Functions
De Moivre's Theorem and Applications
Injective, Surjective, and Bijective Functions
Unknown Coefficients
Graphing Exponential Functions
Solving Trigonometric Equations
The Exponential Function and the Natural Logarithm Function
Inverse Functions
Problem Solving Using Algebra
Using the Sine Rule
Implicit Differentiation
Graphs of Functions and Their Inverses
Using the Cosine Rule
Area of a Triangle
Length of an Arc and Area of a Sector
Three-Dimensional Problems
Derivation of Trigonometric Formulae 1, 2, 3, 4, 5, 6, 7, and 9
Application of Formulae 1-24
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