AS Further Mathematics

Teacher X (4 periods)

Topic X1: Matrices

Lessons

Matrix arithmetic

Matrix multiplication

Determinants of 2 by 2 matrices

Inverse_of_2_by_2_matrices

Determinant and inverse of 3 by 3 matrices

Linear simultaneous equations

Matrices as linear transformations

Further transformations in 2-D

Invariant points and invariant lines

Transformations in 3-D

Topic test preparation

X1 (Pre-TT A) Matrices X1 (Pre-TT A) Matrices MS

X1 (Pre-TT B) Matrices X1 (Pre-TT B) Matrices MS

X1 (Post-TT A) Matrices X1 (Post-TT A) Matrices MS

X1 (Post-TT B) Matrices X1 (Post-TT B) Matrices MS

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Topic X2: Vectors and induction

Lessons

Vector equation of a line

Cartesian equation of a line

Intersection of two lines

Scalar product and angles

Vector product

Induction and matrices

Induction and divisibility

Induction and inequalities

Topic test preparation

X2 (Pre-TT A) Vectors and induction

X2 (Pre-TT A) Vectors and induction MS

X2 (Pre-TT B) Vectors and induction

X2 (Pre-TT B) Vectors and induction MS

X2 (Post-TT A) Vectors and induction

X2 (Post-TT A) Vectors and induction MS

X2 (Post-TT B) Vectors and induction

X2 (Post-TT B) Vectors and induction MS

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Topic X3: Mechanics AS

Lessons

Work done by a force

Kinetic energy and the work-energy principle

PE, ME and the conservation of mechanical energy

Work done by a force at an angle

Power

Defining and calculating dimensions

Units and dimensions of sums and products

Finding dimensions from units and derivatives

Momentum and impulse

Collisions and conservation of momentum

Coefficient of restitution

Impulsive tension in strings

Linear speed vs. angular speed

Acceleration in horizontal circular motion

Conical pendulums

Banked tracks

Motion in a vertical circle

Components of acceleration (general model) A2

Problem solving with circular motion

Topic test preparation

X3 (Pre-TT A) Mechanics X3 (Pre-TT A) Mechanics MS

X3 (Pre-TT B) Mechanics X3 (Pre-TT B) Mechanics MS

X3 (Post-TT A) Mechanics X3 (Post-TT A) Mechanics MS

X3 (Post-TT B) Mechanics X3 (Post-TT B) Mechanics MS

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Revision

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Teacher Y (3 periods)

Topic Y1: Complex numbers and
roots of polynomials

Lessons

Introduction to Complex Numbers

Division and Complex Conjugates

Argand Diagram

Modulus of a Complex Number and Radians

Modulus-Argument Form of a Complex Number

Loci in the Argand Diagram

Operations in Modulus-Argument Form

Factorising Polynomials

Complex Solutions to Polynomials

Sum and Product of Roots (Quadratics)

Cubic and Quartic Equations

Finding an Equation with Given Roots

Transforming Equations

Topic test preparation

Y1 (Pre-TT A) Complex numbers & roots of equations

Y1 (Pre-TT A) Complex numbers & roots of equations MS

Y1 (Pre-TT B) Complex numbers & roots of equations

Y1 (Pre-TT B) Complex numbers & roots of equations MS

Y1 (Post-TT A) Complex numbers & roots of equations

Y1 (Post-TT A) Complex numbers & roots of equations MS

Y1 (Post-TT B) Complex numbers & roots of equations

Y1 (Post-TT B) Complex numbers & roots of equations MS

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Topic Y2: Counting principals &
probability distributions

Lessons

Product and Addition Principles

Permutations

Permutations with Limited Places

Combinations

The Exclusion Principle

Keeping Objects Together or Separated

Permuting Objects with Repetitions

Counting Principles and Probability

Standard Deviation (AS Ma)

Probability Distributions (AS Ma)

Average and Spread of Discrete Random Variables

Transformations of Discrete Random Variables

Discrete Uniform Distributions

Binomial Distribution (AS Ma)

Mean and Variance of Binomial Distribution

Geometric Distributions

Introduction to the Poisson Distrubution

Poission Distribution (worded questions)

Topic test preparation

Y2 (Pre-TT A) Counting principles & probability distributions

Y2 (Pre-TT A) Counting principles & probability distributions MS

Y2 (Pre-TT B) Counting principles & probability distributions

Y2 (Pre-TT B) Counting principles & probability distributions MS

Y2 (Post-TT A) Counting principles & probability distributions

Y2 (Post-TT A) Counting principles & probability distributions MS

Y2 (Post-TT B) Counting principles & probability distributions

Y2 (Post-TT B) Counting principles & probability distributions MS

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Topic Y3: Correlation, regression &
chi-squared tests

Lessons

Pearson's Product Moment Correlation Coefficient

Introduction to Hypothesis Testing

PMCC and Hypothesis Testing

Spearman's Rank Correlation Coefficient

Linear Regression

Contingency Tables

Yates' Correction for 2 by 2 Tables

Goodness-of-Fit Tests

Topic test preparation

Y3 (Pre-TT A) Correlation, regression & chi-squared tests

Y3 (Pre-TT A) Correlation, regression & chi-squared tests MS

Y3 (Pre-TT B) Correlation, regression & chi-squared tests

Y3 (Pre-TT B) Correlation, regression & chi-squared tests MS

Y3 (Post-TT A) Correlation, regression & chi-squared tests

Y3 (Post-TT A) Correlation, regression & chi-squared tests MS

Y3 (Post-TT B) Correlation, regression & chi-squared tests

Y3 (Post-TT B) Correlation, regression & chi-squared tests MS

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Revision

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