A Level Further Mathematics (MEI) OCR
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50 topics in 9 modules
☑️ Core Pure 10 topics
- Proof
- Complex Numbers
- Matrices and Transformations
- Vectors and 3D Space
- Algebra
- Series
- Calculus
- Polar Coordinates
- Hyperbolic Functions
- Differential Equations
☑️ Mechanics Major 8 topics
- Dimensional Analysis
- Forces
- Work, Energy and Power
- Momentum and Impulse
- Circular Motion
- Hooke’s Law
- Centre of Mass
- Vectors and Variable Forces
☑️ Statistics Major 7 topics
- Sampling
- Discrete Random Variables
- Bivariate Data
- Chi-Squared Tests
- Continuous Random Variables
- Inference
- Simulation
☑️ Mechanics Minor 5 topics
- Dimensional Analysis
- Forces
- Work, Energy and Power
- Momentum and Impulse
- Centre of Mass
☑️ Statistics Minor 4 topics
- Sampling
- Discrete Random Variables
- Bivariate Data
- Chi-Squared Tests
☑️ Modelling with Algorithms 3 topics
- Algorithms
- Networks
- Linear Programming (LP)
☑️ Numerical Methods 6 topics
- Use of Technology
- Errors
- Solution of Equations
- Numerical Differentiation
- Numerical Integration
- Approximation to Functions
☑️ Extra Pure 4 topics
- Recurrence Relations
- Groups
- Matrices
- Multivariable Calculus
☑️ Further Pure with Technology 3 topics
- Investigation of Curves
- Exploring Differential Equations
- Number Theory
A Level Further Mathematics (MEI) OCR Revision Content
Take a look at the written content available for this course. Practice-question availability may vary.
A Level Further Mathematics (MEI) OCR - Core Pure - Proof Content Preview
Core Pure
Proof
Proof by Deduction
- Understand that proof by deduction involves starting from known truths and using logical reasoning to arrive at a new conclusion.
- Grasp the importance of clearly stating assumptions at the start.
- Appreciate that each step must follow logically from the previous one, with no gaps in reasoning.
Direct and Indirect Proof
- Recognise the difference between direct and indirect proofs.
- In direct proof, the result is proven by a sequence of logical steps.
- With indirect proof or proof by contradiction, an assumption is made that the opposite of what is to be proven is true. If this leads to a contradiction, then the original assertion must be true.
Disproof by Counterexample
- Understand the concept of disproof by counterexample.
- Identify that a single counterexample is enough to disprove a proposition.
- Practice constructing counterexamples to disprove given statements.
Proof by Exhaustion
- Know that proof by exhaustion involves testing all possible cases.
- Be aware this method can be laborious and so is often not the most efficient strategy.
Understanding of Terminology
- Be familiar with the term theorem for a proven mathematical statement of importance.
- Understand axioms, which are statements accepted as true without proof.
- Recognise the term corollary for a result that follows directly from a theorem.
Mathematical Language and Notation in Proofs
- Use precise mathematical language and notation in your proofs.
- Be comfortable with commonly used notation, such as "∀" for 'for all' and "∃" for 'there exists'.
- Use logical symbols like "∧" for 'and', "∨" for 'or', and "¬" for 'not'.
Question: Write a short indirect proof to demonstrate that if `n` is an even integer, then `n²` is also even.
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