A level Further Mathematics
INTENT: Inspiration and excellence are at the heart of everything we do. Our main aim is to inspire confidence in our students and stimulate their interest in Mathematics, both within the curriculum and the wider world. We hope that this in turn will spark a love of learning and an improved ability to model and solve problems, applying the Mathematical knowledge gained in lessons to a variety of different circumstances. We believe that this will enable our students, irrespective of background, to flourish.
Students will be aiming to ‘draw together information from different areas of the specification’ and ‘apply their knowledge and understanding in practical and theoretical contexts’. Use of calculators in exams is more important now and students will learn to use the modes and abilities of their calculator efficiently.
The course consists of material that covers both Pure and Applied Mathematics. Two thirds of the course is focused on Pure Mathematics covering subjects such as complex numbers and matrices. One third is split evenly between further statistics and further mechanics.
TEACHER 1
Complex Numbers 1
●Arithmetic
●Conjugate
●Quadratics & Roots
●Argand diagram
●Modulus Argument form
●Loci
●Problem Solving
Maclaurin
Expansion
●Expansions
●Combining standard results
Matrices 1
● Introduction
● Arithmetic
● Determinate
● Inverses
● Singular
● Transformations
TEACHER 2
Summations
●Standard results
Proof
●Proof of differences
●Proof by induction summations, division, matrices and recurrance
TEACHER 1
Matrices 2
●Invariant Points
●Matrices PPQ
Complex Numbers 2
●Complex Polynomials
Roots of Polynomials
●Sum and product of roots of a quadratic
●Roots of a cubic
●Roots of a quartic
●Relationship between roots
Algebraic Inequalities
●Solving inequalities algebraically
Polar Coordinates
● Sketching polar graphs
● Polar to cartesian
● Intersecting lines
TEACHER 2
Graphs
●Linear rational equation & Inequalities
●Quadratic rational equations and inequalities
●Parabolas, ellipses and hyperbola
TEACHER 1
Momentum
● Conservation
● Experimental law
● Collisions
● Impulse
Dimension Analysis
● Analysis
● Consistency
Work, Energy & Power
● Work, energy and power
● Gravitational potential energy
● Kinetic energy
● Tension & EPE
TEACHER 1
Vectors
● Vector equation of a line
● Cartesian equation
● Intersection and Matrices
● Dot Product
● Angle between vectors
● Distances
Volume of Revolution
● Revolution around x axis
● Revolution around y axis
Mean Value
Theorem
● Finding mean value of a function using integration
Hyperbolic Functions
• Definitions and graph
• Inverse
• Identities and equations
FStats T2 FMech T2
Discrete Random Variables
● Expectation and variance
● Coding
● Sums and differences
● Functions
Chi Squared
● Hypothesis testing for independence on a contingency table
Continuous Random Variables
● Expectation and variance
● Mean and Quartiles
Circular Motion
● Angular Motion
● Constant speed
● Connected particles
Circular Motion (A level)
●Tangential acceleration
●Conical pendulum
FStats T2
Confidence Intervals
● Introduction to normal distribution
● Confidence interval for a mean
Poisson
• Definitions
• Sum of distributions
• Hypothesis Testing
Type I and Type II errors
CORE MATHS OT1: Mathematical argument, language and proof
Revision and Mock Exam TEACHER 1
Complex Numbers (A level)
• Exponential form
• Roots of complex numbers
• Euler’s form
Proof of Differences (A level)
• Proof of differences with partial fractions
OT1.1 Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction; precise statements involving correct use of symbols and connecting language, including: constant, coefficient, expression, equation, function, identity, index, term, variable.
OT1.2 Understand and use mathematical language and syntax as set out in the content
OT1.3 Understand and use language and symbols associated with set theory, as set out in the content.
OT1.4 Understand and use the definition of a function; domain and range of functions.
OT1.5 Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, including those relating to applications of mathematics
OT2: Mathematical problem solving
OT2.1 Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to be solved.
OT2.2 Construct extended arguments to solve problems presented in an unstructured form, including problems in context
OT2.3 Interpret and communicate solutions in the context of the original problem.
OT2.6 Understand the concept of a mathematical problem solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle.
OT2.7 Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics.
OT1: Mathematical Modelling
OT3.1 Translate a situation in context into a mathematical model, making simplifying assumptions.
OT3.2 Use a mathematical model with suitable inputs to engage with and explore situations (for a given model or a model constructed or selected by the student).
OT3.3 Interpret the outputs of a mathematical model in the context of the original situation (for a given model or a model constructed or selected by the student).
FStats T2
Yates Correction (A level)
Continuous Random Variables
OT3.4 Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate
OT3.5 Understand and use modelling assumptions.
Midterm Exam Year 12 Exam Week Further Statistics Assessment MOCK EXAMS Further Statistics and Further Mechanics Exam
TEACHER 1
Complex Numbers 1
●Nth roots of unity
Vectors
●Vector product
●Equation of line and area of triangle
●Planes, angles and intersections
●Distances
Matrices 1
●Determinate of 3x3
●Sim equations and geometric interpretation
●Factorising
●Eigen vectors and Eigen values
TEACHER 2
Graphs
●Modulus functions
●Rational with oblique asymptotes
●Composite transformations
Maclaurin & Limits
●Proving an expansion
●L’Hopitals rule
Matrices 2
●Diagonalisation
2nd Order
Differential Equations
●Solve homogenous
●Solve nonhomogenous
●Particular solutions
Continuous random variables
Rectangular distribution
T-Tests
● Hypothesis testing with t-tests
Continuous random variables
● Exponential distribution
Circular Motion
● Inclined planes
● Conical pendulum
● Vertical motion
TEACHER 1
Integration 1
● Improper integrals
● Integrating Partial fractions
● Polar integration
● Arc length
TEACHER 1
Integration 2
● Area of surface revolution
● Reduction formula Differential equations
● 1st order differential equations
● Simple harmonic motion
● Damped and forced motion
● Coupled equations
● Hyperbolic Functions
●Reciprocal hyperbolic functions
●Differentiating and integrating hyperbolic functions
● Osbourne’s rule
● Identities in proof
Revision
Centre of Mass
● Particles and rods
● Composite
● Volume of revolution
● Toppling or sliding
● Collisions
● Collisions with walls
● Impulse
OT1: Mathematical argument, language and proof
OT1.1 Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction; precise statements involving correct use of symbols and connecting language, including constant, coefficient, expression, equation, function, identity, index, term, variable.
OT1.2 Understand and use mathematical language and syntax as set out in the content
OT1.3 Understand and use language and symbols associated with set theory, as set out in the content.
OT1.4 Understand and use the definition of a function; domain and range of functions.
OT1.5 Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, including those relating to applications of mathematics
OT2: Mathematical problem solving
OT2.1 Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to be solved.
OT2.2 Construct extended arguments to solve problems presented in an unstructured form, including problems in context
OT2.3 Interpret and communicate solutions in the context of the original problem.
OT2.6 Understand the concept of a mathematical problem solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle.
OT2.7 Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics.
OT1: Mathematical Modelling
OT3.1 Translate a situation in context into a mathematical model, making simplifying assumptions.
OT3.2 Use a mathematical model with suitable inputs to engage with and explore situations (for a given model or a model constructed or selected by the student).
OT3.3 Interpret the outputs of a mathematical model in the context of the original situation (for a given model or a model constructed or selected by the student).
OT3.4 Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate
OT3.5 Understand and use modelling assumptions.