Further Maths – Notes

A1.1 Data Distributions
A1.1 Data Distributions
14 Topics
1.1.1 Overview of Data Types
1.1.2 Displaying Distributions of Categorical Data
1.1.3 Statistical Analysis of Categorical Distributions
1.1.4 Displaying Numerical Data
1.1.5 Mean, Median and Mode
1.1.6 Interquartile Range (IQR) and Upper/Lower Fence
1.1.7 Describing Numerical Distributions – Shape
1.1.8 Describing Numerical Distributions – Centre
1.1.9 Describing Numerical Distributions -Spread
1.1.10 Box Plots and the Five Number Summary
1.1.11 Statistical Analysis of Numerical Distributions
1.1.12 Normal Distribution and The 68-95-99.7% Rule
1.1.13 Normal Distribution – Standardised Values/z-scores
1.1.14 Further Statistical Concepts
A1.2 Associations between Two Variables
 8 Topics
1.2.1 Response and Explanatory Variables
1.2.2 Relationships between two Categorical Variables
1.2.3 Relationships between Numerical and Categorical Variables
1.2.4 Scatterplots and Association between Numerical Variables
1.2.5 Relationships between two Numerical Variables
1.2.6 Pearson’s Correlation Coefficient
1.2.7 Cause and Effect
1.2.8 Non-Causal Relationships
A1.3 Linear Associations and Modelling
 11 Topics
1.3.1 Least Squares Linear Regression
1.3.2 Least Squares Regression using Technology (Casio graphic calculator)
1.3.3 Modelling Linear Associations
1.3.4 Using the Formula for a Fitted Line
1.3.5 Coefficient of Determination and Measures of Strength
1.3.6 Residual Plots
1.3.7 Residual Analysis
1.3.8 Linearization and Square Transformatiuon
1.3.9 Log Transformation
1.3.10 Reciprocal Transformation
1.3.11 Least Squares Regression for Transformed Data
A1.4 Time Series Data and Modelling
 7 Topics
1.4.1 Introduction to Time Series Plots
1.4.2 Numerical Smoothing using Moving Mean Method
1.4.3 Numerical Smoothing using Centring
1.4.4 Numerical Smoothing using Moving Median Method
1.4.5 Seasonal Indices
1.4.6 De-Seasonalising Data
1.4.7 Analysis of De-seasonalised Data
A2 – Recursion and Financial Modelling
A2.1 Depreciation of Assets
 10 Topics
2.1.1 Sequence
2.1.2 Recurrence Relations, Appreciation and Depreciation
2.1.3 The First-order Recurrence Relation Formula
2.1.4 Rule for the ????th Term
2.1.5 Flat Rate Depreciation (Linear)
2.1.6 Unit Cost Depreciation (Linear)
2.1.7 Reducing Balance Depreciation (Non-Linear)
2.1.8 Predicting Future Values for Flat Rate Depreciation
2.1.9 Predicting Future Values for Unit Cost Depreciation
2.1.10 Predicting Future Values for Reducing Balance Depreciation
A2.2 Compound Interest Investment and Loans
 4 Topics
2.2.1 Simple and Compound Interest
2.2.2 Analysis of Compound Interest
2.2.3 Nominal and Effective Interests
2.2.4 Predicting Future Values for Compound Interest Loans and Investments
A2.3 Reducing Balance Loans
 3 Topics
2.3.1 Modelling Reducing Balance Systems with Regular Repayments
2.3.2 Modelling Reducing Balance Systems with Regular Repayments using Tables
2.3.3 Modelling Reducing Balance Systems with Regular Repayments using Technology
A2.4 Annuities and Perpetuities
 4 Topics
2.4.1 Modelling Compound Interest Systems with Regular Withdrawals
2.4.2 Modelling Compound Interest Systems with Regular Withdrawals using Tables
2.4.3 Modelling Compound Interest Systems with Regular Withdrawals using Technology
2.4.4 Annuities and Perpetuities
A2.5 An Annuity Investment
 3 Topics
2.5.1 Modelling Annuity Investments
2.5.2 Modelling Annuity Investments using Tables
2.5.3 Modelling Annuity Investments using Technology
OA1 – Matrices
OA1.1 Matrices and Applications
 9 Topics
3.1.1 Matrices: Definition and Unique Cases
3.1.2 Elementary Matrix Operations
3.1.3 The Inverse of a Matrix
3.1.4 Basic Matrix Applications
3.1.5 Binary and Permutation Matrices
3.1.6 Matrix Applications: Communication Matrices
3.1.7 Matrix Applications: Dominance Matrices
3.1.8 Systems of Equations in Matrix Form
3.1.9 Dependant Systems and Inconsistent Systems
OA1.2 Transition Matrices
 5 Topics
3.2.1 Simple Matrix Recurrence Relations
3.2.2 Equilibrium of a Recurrence System
3.2.3 Transition Diagrams
3.2.4 Modelling Situations using Matrix Recurrence Relations
3.2.5 Extended Matrix Recurrence Relations
OA2 – Networks and Decision Mathematics
OA2.1 Graphs and Networks
 4 Topics
4.1.1 Basics of Network Graphs
4.1.2 Further Concepts for Network Graphs
4.1.3 Euler’s Rule
4.1.4 Introduction to Network Matrices
OA2.2 Exploring and Traveling Problems
 5 Topics
4.2.1 Introduction to Walks
4.2.2 Eulerian Trails and Circuits
4.2.3 Fleury’s Algorithm
4.2.4 Hierholzer’s Algorithm
4.2.5 Hamiltonian Paths and Cycles
OA2.3 Trees and Minimum Connector Problems
 3 Topics
4.3.1 Trees and Spanning Trees
4.3.2 Minimum Spanning Trees
4.3.3 Guide to Minimal Connector Problems
OA2.4 Flow Problems
 2 Topics
4.4.1 Introduction to Flow Problems
4.4.2 Methods for Solving Flow Problems
OA2.5 Shortest Path Problems
 2 Topics
4.5.1 Shortest Path by Inspection
4.5.2 Introduction to Dijkstra’s Algorithm
OA2.6 Matching Problems
 3 Topics
4.6.1 Matching Problem and Bipartite Graph
4.6.2 Optimum Assignment by Inspection
4.6.3 Optimum Assignment by Hungarian Algorithm
OA2.7 Scheduling Problem and Critical Path Analysis
 4 Topics
4.7.1 Activity Networks
4.7.2 Forward and Backward Scanning
4.7.3 Determine Critical Paths and Float Times
4.7.4 Using Crashing to Reduce Completion Time
OA3 – Geometry and Measurement
OA3.1 Measurement and Trigonometry
 7 Topics
5.1.1 Surface Area of Common Shapes
5.1.2 Volume of Common Shapes
5.1.3 Surface Area and Volume of Composite Shapes
5.1.4 Scaling Factor and its Applications
5.1.5 Methods for Solving Triangles
5.1.6 Solving Triangles in 2 and 3 dimensions
5.1.7 Three-Figure Bearings
OA3.2 Spherical Geometry
 13 Topics
5.2.1 Circles and Arcs
5.2.2 Area of Sectors and Segments
5.2.3 Solving Triangles using Trigonometry
5.2.4 Trigonometry in a Circle
5.2.5 The Unit Circle
5.2.6 Pythagoras’ Theorem
5.2.7 Pythagoras’ Theorem in a Circle
5.2.8 Trigonometry and Pythagoras’ Theorem in 3D
5.2.9 Distance Between Points on a Sphere
5.2.10 Modelling the World
5.2.11 Shortest Distance to the Poles or Equator
5.2.12 Shortest Distance between Points on a Parallel
5.2.13 Introduction to Time Zones
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A1.1 Data Distributions

Further Maths – Notes A1.1 Data Distributions
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