# AS Further Mathematics

## Past mock examinations

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OCR AS Further Mathematics Formula Booklet
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L6 FM Mock Teacher X 18-19 L6 FM Mock Teacher X 18-19 SOLUTIONS
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L6 FM Mock Teacher Y 18-19 L6 FM Mock Teacher Y 18-19 SOLUTIONS
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L6 FM Mock Teacher X 19-20 L6 FM Mock Teacher X 19-20 SOLUTIONS
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L6 FM Mock Teacher Y 19-20 L6 FM Mock Teacher Y_19-20 SOLUTIONS

### Teacher X (4 periods)

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#### Topic X1: Matrices

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##### Lessons
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Matrix arithmetic
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Matrix multiplication
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Determinants of 2 by 2 matrices
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Inverse_of_2_by_2_matrices
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Determinant and inverse of 3 by 3 matrices
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Linear simultaneous equations
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Matrices as linear transformations
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Further transformations in 2-D
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Invariant points and invariant lines
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Transformations in 3-D
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##### Topic test preparation
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X1 (Pre-TT A) Matrices X1 (Pre-TT A) Matrices MS
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X1 (Pre-TT B) Matrices X1 (Pre-TT B) Matrices MS
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X1 (Post-TT A) Matrices X1 (Post-TT A) Matrices MS
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X1 (Post-TT B) Matrices X1 (Post-TT B) Matrices MS

#### Topic X2: Vectors and induction

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##### Lessons
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Vector equation of a line
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Cartesian equation of a line
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Intersection of two lines
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Scalar product and angles
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Vector product
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Induction and matrices
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Induction and divisibility
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Induction and inequalities
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##### Topic test preparation
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X2 (Pre-TT A) Vectors and induction
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X2 (Pre-TT A) Vectors and induction MS
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X2 (Pre-TT B) Vectors and induction
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X2 (Pre-TT B) Vectors and induction MS
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X2 (Post-TT A) Vectors and induction
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X2 (Post-TT A) Vectors and induction MS
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X2 (Post-TT B) Vectors and induction
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X2 (Post-TT B) Vectors and induction MS

#### Topic X3: Mechanics AS

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##### Lessons
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Work done by a force
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Kinetic energy and the work-energy principle
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PE, ME and the conservation of mechanical energy
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Work done by a force at an angle
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Power
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Defining and calculating dimensions
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Units and dimensions of sums and products
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Finding dimensions from units and derivatives
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Momentum and impulse
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Collisions and conservation of momentum
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Coefficient of restitution
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Impulsive tension in strings
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Linear speed vs. angular speed
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Acceleration in horizontal circular motion
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Conical pendulums
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Banked tracks
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Motion in a vertical circle
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Components of acceleration (general model) A2
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Problem solving with circular motion
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##### Topic test preparation
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X3 (Pre-TT A) Mechanics X3 (Pre-TT A) Mechanics MS
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X3 (Pre-TT B) Mechanics X3 (Pre-TT B) Mechanics MS
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X3 (Post-TT A) Mechanics X3 (Post-TT A) Mechanics MS
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X3 (Post-TT B) Mechanics X3 (Post-TT B) Mechanics MS

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### OCR Past_paper_MS

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#### Sample assessment material (SAM)

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OCR SAM Paper 1 (Pure) MS
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OCR SAM Paper 2 (Statistics) MS
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OCR SAM Paper 3 (Mechanics) MS

#### Practice papers Set 1

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PP Set 1 Paper 1 (Pure) MS
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PP Set 1 Paper 2 (Statistics) MS
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PP Set 1 Paper 3 (Mechanics) MS

#### Practice papers Set 2

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PP Set 2 Paper 1 (Pure) MS
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PP Set 2 Paper 2 (Statistics) MS
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PP Set 2 Paper 3 (Mechanics) MS

#### May 2018

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May 2018 Paper 1 (Pure) MS
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May 2018 Paper 2 (Statistics) MS
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May 2018 Paper 3 (Mechanics) MS
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### Teacher Y (3 periods)

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#### Topic Y1: Complex numbers and roots of polynomials

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##### Lessons
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Introduction to Complex Numbers
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Division and Complex Conjugates
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Argand Diagram
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Modulus of a Complex Number and Radians
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Modulus-Argument Form of a Complex Number
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Loci in the Argand Diagram
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Operations in Modulus-Argument Form
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Factorising Polynomials
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Complex Solutions to Polynomials
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Sum and Product of Roots (Quadratics)
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Cubic and Quartic Equations
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Finding an Equation with Given Roots
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Transforming Equations
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##### Topic test preparation
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Y1 (Pre-TT A) Complex numbers & roots of equations
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Y1 (Pre-TT A) Complex numbers & roots of equations MS
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Y1 (Pre-TT B) Complex numbers & roots of equations
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Y1 (Pre-TT B) Complex numbers & roots of equations MS
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Y1 (Post-TT A) Complex numbers & roots of equations
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Y1 (Post-TT A) Complex numbers & roots of equations MS
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Y1 (Post-TT B) Complex numbers & roots of equations
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Y1 (Post-TT B) Complex numbers & roots of equations MS

#### Topic Y2: Counting principals & probability distributions

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##### Lessons
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Permutations
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Permutations with Limited Places
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Combinations
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The Exclusion Principle
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Keeping Objects Together or Separated
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Permuting Objects with Repetitions
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Counting Principles and Probability
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Standard Deviation (AS Ma)
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Probability Distributions (AS Ma)
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Average and Spread of Discrete Random Variables
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Transformations of Discrete Random Variables
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Discrete Uniform Distributions
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Binomial Distribution (AS Ma)
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Mean and Variance of Binomial Distribution
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Geometric Distributions
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Introduction to the Poisson Distrubution
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Poission Distribution (worded questions)
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##### Topic test preparation
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Y2 (Pre-TT A) Counting principles & probability distributions
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Y2 (Pre-TT A) Counting principles & probability distributions MS
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Y2 (Pre-TT B) Counting principles & probability distributions
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Y2 (Pre-TT B) Counting principles & probability distributions MS
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Y2 (Post-TT A) Counting principles & probability distributions
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Y2 (Post-TT A) Counting principles & probability distributions MS
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Y2 (Post-TT B) Counting principles & probability distributions
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Y2 (Post-TT B) Counting principles & probability distributions MS

#### Topic Y3: Correlation, regression & chi-squared tests

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##### Lessons
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Pearson's Product Moment Correlation Coefficient
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Introduction to Hypothesis Testing
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PMCC and Hypothesis Testing
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Spearman's Rank Correlation Coefficient
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Linear Regression
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Contingency Tables
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Yates' Correction for 2 by 2 Tables
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Goodness-of-Fit Tests
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##### Topic test preparation
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Y3 (Pre-TT A) Correlation, regression & chi-squared tests
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Y3 (Pre-TT A) Correlation, regression & chi-squared tests MS
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Y3 (Pre-TT B) Correlation, regression & chi-squared tests
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Y3 (Pre-TT B) Correlation, regression & chi-squared tests MS
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Y3 (Post-TT A) Correlation, regression & chi-squared tests
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Y3 (Post-TT A) Correlation, regression & chi-squared tests MS
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Y3 (Post-TT B) Correlation, regression & chi-squared tests
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Y3 (Post-TT B) Correlation, regression & chi-squared tests MS

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### Edexcel Past_paper_MS

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#### Sample assessment material (SAM)

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Edexcel AS FM SAM QP and MS

#### Specimen papers

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Specimen Paper 1 (Pure) MS
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Specimen Paper 23 (Statistics) MS
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Specimen Paper 25 (Mechanics) MS

#### May 2018

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May 2018 Paper 1 (Pure) MS
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May 2018 Paper 23 (Statistics) MS
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May 2018 Paper 25 (Mechanics) MS
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### AQA Past_paper_MS

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#### Sample assessment material (SAM)

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AQA AS FM SAM Paper 1 (Pure) MS
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AQA AS FM SAM Paper 2S (Statistics) MS
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AQA AS FM SAM Paper 2M (Mechanics) MS

#### May 2018

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May 2018 Paper 1 (Pure) MS
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May 2018 Paper 2S (Statistics) MS
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May 2018 Paper 2M (Mechanics) MS
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