Garth Hill College'A' Level Mathematics
For further information contact Mr N Sleeman n-sleeman@garthhillcollege.com
Exam Board and syllabus code:
- Year 12 - Students follow the AS syllabus (Edexcel 8MA0) but do not sit the external exam. Instead they take an internal exam at the end of the year to monitor progress.
- Year 13 – Advanced GCE in Mathematics (Edexcel 9MA0).
Year 12 & 13 Further Maths – Year 13 Advanced GCE in Mathematics (9MA0), Year 13 Advanced GCE in Further Mathematics (9FM0, option H0)
Content
AS/A Level Mathematics - Click to open
Pure Mathematics
- AS & A level: Pure mathematics includes proof, algebra, graphs, sequences, trigonometry, logarithms, calculus and vectors.
- A level only: Learners study these topics in more depth and also study functions, numerical methods and differential equations.
Year 12 Content:
● Topic 1 – Proof
● Topic 2 – Algebra and functions
● Topic 3 – Coordinate geometry in the (x, y) plane
● Topic 4 – Sequences and series
● Topic 5 – Trigonometry
● Topic 6 – Exponentials and logarithms
● Topic 7 – Differentiation
● Topic 8 – Integration
● Topic 9 – Vectors
Year 13 Content:
● Topic 1 – Proof
● Topic 2 – Algebra and functions
● Topic 3 – Coordinate geometry in the (x, y) plane
● Topic 4 – Sequences and series
● Topic 5 – Trigonometry
● Topic 6 – Exponentials and logarithms
● Topic 7 – Differentiation
● Topic 8 – Integration
● Topic 9 – Numerical methods
● Topic 10 – Vectors
Statistics
- AS & A level: Statistics includes working with data from a sample to make inferences about a population, probability calculations, using a binomial distribution as a model, and statistical hypothesis testing.
- A level only: Learners study these topics in more depth and also study the Normal distribution.
- There is a pre-release data set for both AS and A level. The purpose of the large data set is that learners experience working with real data in the classroom and explore this data using appropriate technology.
Year 12 Content:
● Topic 1 – Statistical sampling
● Topic 2 – Data presentation and interpretation
● Topic 3 – Probability
● Topic 4 – Statistical distributions
● Topic 5 – Statistical hypothesis testing
Year 13 Content:
● Topic 1 – Statistical sampling
● Topic 2 – Data presentation and interpretation
● Topic 3 – Probability
● Topic 4 – Statistical distributions
● Topic 5 – Statistical hypothesis testing
Mechanics
- AS & A level: Mechanics includes kinematics, working with forces and Newton’s laws.
- A level only: Learners study these topics in more depth and also study motion under gravity, friction and simple moments.
Year 12 Content:
● Topic 1 – Quantities and units in mechanics
● Topic 2 – Kinematics
● Topic 3 – Forces and Newton’s laws
Year 13 Content:
● Topic 1 – Quantities and units in mechanics
● Topic 2 – Kinematics
● Topic 3 – Forces and Newton’s laws
● Topic 4 – Moments
AS/A Level Further Mathematics - click to open
Core Pure Mathematics
- AS and A level: Some pure topics from AS level Mathematics are studied in greater depth, while some new topics are introduced. Algebraic work with series is extended. The powerful technique of proof by induction is used in various contexts. Complex numbers are introduced, including their geometrical representation. Matrices are used to solve systems of equations and to explore transformations. Scalar products of vectors are applied to problems involving planes.
- A level only: In addition to studying these topics in more depth, learners also applied vector methods to problems involving lines and planes and calculus techniques are extended, including the use of hyperbolic functions and polar coordinates, and culminate in the solution of differential equations.
- Year 13 – Further Mechanics: studies include Momentum and Impulse, Work, Energy and Power, Strings and springs.
- Year 13 – Decision Maths: Algorithms and graph theory, critical path analysis, linear programming.
Year 12 Content:
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Unit 1: Algebra and functions (part 1) |
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Unit 2: Further algebra |
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Unit 1: Data presentation and interpretation (part 1) |
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Unit 2: Statistical distributions |
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Unit 7: Quantities and units in mechanics |
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Unit 8a: Kinematics 1 (constant acceleration) |
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Unit 1: Complex numbers (part 1) |
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Unit 2a-b: Matrices |
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Unit 1: Momentum and impulse (part 1) |
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Unit 1: Algorithms and graph theory (part 1) |
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Unit 3: Differentiation |
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Unit 4: Integration |
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Unit 5a: Vectors (2D) |
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Unit 3: Probability |
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Unit 4: Statistical sampling |
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Unit 8b: Kinematics 1 (constant acceleration) |
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Unit 9a: Forces & Newton’s laws |
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Unit 2c-d: Matrices |
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Unit 3: Complex numbers (part 2) |
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Unit 2a-b: Work, energy and power |
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Unit 2: Algorithms on graphs I (part 1) |
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Unit 5b: Vectors (2D) |
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Unit 6a: Coordinate geometry in the (x, y) plane |
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Unit 6b: Coordinate geometry in the (x, y) plane |
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Unit 7a: Trigonometry |
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Unit 5: Statistical hypothesis testing |
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Unit 9b: Forces & Newton’s laws |
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Unit 4: Series |
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Unit 5: Algebra and functions |
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Unit 6: Proof |
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Unit 2c: Work, energy and power |
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Unit 3: Algorithms on graphs II (part 1) |
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Unit 4a: Linear programming (part 1) |
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Unit 7b: Trigonometry |
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Unit 8: Algebra and functions (part 2) |
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Unit 6: Data presentation and interpretation (part 2) |
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Unit 10: Kinematics 2 (variable acceleration) |
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Unit 7: Vectors |
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Unit 3a: Elastic collisions in one dimension |
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Unit 4b: Linear programming (part 1) |
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Unit 5a. Critical path analysis (part 1) |
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Unit 9: Exponentials and logarithms |
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Unit 8: Calculus |
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Unit 3b: Elastic collisions in one dimension |
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Unit 5b-c: Critical path analysis (part 1) |
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Unit 1: Algebraic and partial fractions |
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Unit 2a: Trigonometry |
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Unit 2b-c: Trigonometry |
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Unit 2d: Trigonometry |
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Unit 3: Differentiation |
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Unit 1a: The Normal distribution |
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Unit 4: Forces at any angle (part 1) |
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Unit 5: Further kinematics (part 1) |
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Unit 1: Complex numbers |
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Unit 4: Momentum and impulse (part 2) |
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Unit 6: Algorithms and graph theory (part 2) |
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Unit 7: Algorithms on graphs I (part 2) |
Year 13 Content:
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Unit 4: Integration |
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Unit 1b: The Normal distribution |
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Unit 6: Applications of kinematics |
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Unit 7: Forces at any angle (part 2) |
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Unit 2: Hyperbolic functions |
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Unit 3a: Polar coordinates |
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Unit 5a: Elastic strings and springs and elastic energy |
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Unit 8: Algorithms on graphs II (part 2) |
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Unit 5: Proof |
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Unit 6: Functions and modelling |
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Unit 7a: Series and sequences |
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Unit 7b: Series and sequences |
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Unit 7c: Series and sequences |
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Unit 1c: The Normal distribution |
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Unit 8a: Applications of forces (part 1) |
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Unit 8b: Applications of forces (part 1) |
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Unit 3b: Polar coordinates |
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Unit 4: Further algebra and functions (series) |
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Unit 5b: Elastic strings and springs and elastic energy |
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Unit 9a-b: Linear programming (part 2) |
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Unit 8: The binomial theorem |
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Unit 9a: Trigonometry |
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Unit 9b: Trigonometry |
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Unit 9c-e: Trigonometry |
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Unit 2: Probability |
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Unit 9: Further kinematics (part 2) |
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Unit 10: Moments |
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Unit 5a-c: Further calculus |
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Unit 6a(i): Elastic collisions in two dimensions |
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Unit 9c: Linear programming (part 2) |
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Unit 10: Parametric equations |
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Unit 11: Numerical methods - see Integration (part 2) for the trapezium rule |
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Unit 3: Regression and correlation |
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Unit 11: Applications of forces (part 2) |
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Unit 5d-e: Further calculus |
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Unit 6a. Differential equations |
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Unit 6a(ii): Elastic collisions in two dimensions |
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Unit 6b(i): Elastic collisions in two dimensions |
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Unit 10a: Critical path analysis (part 2) |
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Unit 10: Parametric equations |
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Unit 11: Numerical methods - see Integration (part 2) for the trapezium rule |
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Unit 3: Regression and correlation |
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Unit 11: Applications of forces (part 2) |
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Unit 5d-e: Further calculus |
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Unit 6a. Differential equations |
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Unit 6a(ii): Elastic collisions in two dimensions |
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Unit 6b(i): Elastic collisions in two dimensions |
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Unit 10a: Critical path analysis (part 2) |
Assessment
Assessment A Level 9MA0
Students sit external exams at the end of Year 13 (an internal PPE in Year 12). The external exam consists of:
- Paper 1: 9MA0/01, 2 hour exam 33% of the qualification, 100 marks, based on any of the Pure maths topics.
- Paper 2: 9MA0/02, 2 hour exam 33% of the qualification, 100 marks, based on any of the Pure maths topics.
- Paper 3: 9MA0/03, 2 hour exam 33% of the qualification, 100 marks, based on any of the Statistics and Mechanics maths topics.
Assessment A Level Further Maths 9FM0
Students sit external exams at the end of Year 13. The external exam consists of:
For A2 maths:
- Paper 1: 9MA0/01, 2 hour exam, 33% of the qualification, 100 marks, based on any of the Pure maths topics.
- Paper 2: 9MA0/02, 2 hour exam, 33% of the qualification, 100 marks, based on any of the Pure maths topics.
- Paper 3: 9MA0/03, 2 hour exam, 33% of the qualification, 100 marks, based on any of the Statistics and Mechanics maths topics.
For Further maths:
- Paper 1: 9FM0/01, 90 minute exam, 25% of the qualification, 75 marks, based on any of the Pure maths topics.
- Paper 2: 9FM0/02, 90 minute exam, 25% of the qualification, 75 marks, based on any of the Pure maths topics.
- Paper 3: 9FM0/3C, 90 minute exam, 25% of the qualification, 75 marks, based on any Further Mechanics topics.
- Paper 4: 9FM0/4D, 90 minute exam, 25% of the qualification, 75 marks, based on any Decision Maths topics.
Skills/Aptitudes needed to succeed
Students wishing to start AS Mathematics will need a minimum of a grade 6 at GCSE, although a 7 is preferred. Further level 2 qualifications in Statistics and Additional Maths are welcomed and encouraged. Learners starting the Mathematical Studies MS will need at least a grade 4 at GSCE. In particular, students will need to be competent in dealing with the algebraic content of the higher tier of GCSE mathematics. The ability to work in organised fashion, think logically and to visualise mathematical concepts will be most beneficial.
Students wishing to start AS Further Mathematics will need a minimum of a grade 7 in GCSE Mathematics, although an 8 and/or a good pass in Additional Maths are preferred.
Benefits and Uses
Mathematics is used in many contexts to explain the world in which we live and to support endeavours in other disciplines. Mathematical knowledge and understanding is sought after by both employers and universities.
A level mathematics is a highly regarded qualification in the fields of business, technology, science and engineering. As well as preparing students to study Mathematics at undergraduate level, is also an essential qualification for entry to courses such as Accounting, Actuarial Studies, Aeronautics, Biomedical Sciences, Chemical Engineering, Computer Science, Economics, Electronic Engineering, Mechanical Engineering and Physics. It is often required or preferred for other courses from Management to Optometry, Dentistry to Computer Science, and from Architecture to Meteorology.
