Description
This International A Level Mathematics course provides the techniques in Algebra, Geometry, Trigonometry and Calculus that form the fundamental building blocks of further study in a variety of subjects including Science and Engineering. You will also find this course extremely valuable if you are looking for a progression route for further training whilst employed.
Difference between Cambridge & Edexcel Exam Boards
Cambridge and Edexcel A Levels are international qualifications. Cambridge A-Levels can be taken worldwide including the United Kingdom, whereas Edexcel A-Levels can only be taken outside of the United Kingdom. Both Cambridge and Edexcel courses are Full A Level qualifications allowing you to apply to universities internationally.
For Mathematics, Cambridge follows a more conventional route where the options available are more limited than what Edexcel have on offer. With Cambridge, you can choose to take the following routes during your study:
- Pure Mathematics, Mechanics and Probability & Statistics
- Pure Mathematics and Probability & Statistics
With Edexcel, there is a greater choice of routes available and if you feel one topic isn’t working well, you can switch a module in most cases. Here are the routes for Edexcel:
- Pure Mathematics, Mechanics and Statistics
- Pure Mathematics, Mechanics and Decision
- Pure Mathematics and Mechanics
- Pure Mathematics, Statistics and Decision
- Pure Mathematics and Statistics
- Pure Mathematics
You may wonder why there are so many choices with Edexcel, however some learners will want to specialise in certain degrees at University and these routes can help aid learning and show that you have knowledge within certain areas. For example, if you are planning a career in physics or engineering, you would find mechanics particularly useful.
It is also worth considering the pressure within the exams. For Cambridge, there is a total of four exam papers and with Edexcel, there are six papers.
Progression
The A Level in Mathematics course alone would help with immediate employment opportunities within banking, computing, financial services and retail.
If you decide to progress onto university and complete a degree, you could work towards one of the following careers:
Accountant, Scientist, Analyst, Engineer, Surveyor and many more.
Courses which compliment A Level Mathematics include Physics, Chemistry and Computer Science.
Cambridge Specification
Awarding Body: Cambridge
Course Code: 9709
Exams: June and November (March in India only)
Study Hours: 300 – 360 hours
Cambridge International Examinations (CIE)
This International A’ Level Mathematics Course with Cambridge develops a set of transferable skills. These include the skill of working with mathematical information, as well as the ability to think logically and independently, consider accuracy, model situations mathematically, analyse results and reflect on findings.
Learners can apply these skills across a wide range of subjects and these skills will equip you well for progression to higher education or directly into employment.
How will I benefit from the International A Level Mathematics Cambridge course?
The aims of this course are to enable learners to:
- develop their mathematical knowledge and skills in a way which encourages confidence and provides satisfaction and enjoyment
- develop an understanding of mathematical principles and an appreciation of mathematics as a logical and coherent subject
- acquire a range of mathematical skills, particularly those which will enable them to use applications of mathematics in the context of everyday situations and of other subjects they may be studying
- develop the ability to analyse problems logically
- recognise when and how a situation may be represented mathematically, identify and interpret relevant factors and select an appropriate mathematical method to solve the problem
- use mathematics as a means of communication with emphasis on the use of clear expression
- acquire the mathematical background necessary for further study in mathematics or related subjects.
Key Concepts
The key concepts for Cambridge International AS & A Level Mathematics are:
Problem solving
Mathematics is fundamentally problem solving and representing systems and models in different ways. These include:
- Algebra: this is an essential tool which supports and expresses mathematical reasoning and provides a means to generalise across a number of contexts.
- Geometrical techniques: algebraic representations also describe a spatial relationship, which gives us a new way to understand a situation.
- Calculus: this is a fundamental element which describes change in dynamic situations and underlines the links between functions and graphs.
- Mechanical models: these explain and predict how particles and objects move or remain stable under the influence of forces.
- Statistical methods: these are used to quantify and model aspects of the world around us. Probability theory predicts how chance events might proceed, and whether assumptions about chance are justified by evidence.
Communication
Mathematical proof and reasoning is expressed using algebra and notation so that others can follow each line of reasoning and confirm its completeness and accuracy. Mathematical notation is universal. Each solution is structured, but proof and problem solving also invite creative and original thinking.
Mathematical modelling
Mathematical modelling can be applied to many different situations and problems, leading to predictions and solutions. A variety of mathematical content areas and techniques may be required to create the model. Once the model has been created and applied, the results can be interpreted to give predictions and information about the real world.
Cambridge Mathematics Content Overview
The choice of modules are detailed below. Please see ‘Cambridge Assessment’ tab for the routes learners can take.
Pure Mathematics 1 (Paper 1)
- Quadratics
- Functions
- Coordinate geometry
- Circular measure
- Trigonometry
- Series
- Differentiation
- Integration
Pure Mathematics 2 (Paper 2)
- Algebra
- Logarithmic and exponential functions
- Trigonometry
- Differentiation
- Integration
- Numerical solution of equations
Pure Mathematics 3 (Paper 3)
- Algebra
- Logarithmic and exponential functions
- Trigonometry
- Differentiation
- Integration
- Numerical solution of equations
- Vectors
- Differential equations
- Complex numbers
Mechanics (Paper 4)
- Forces and equilibrium
- Kinematics of motion in a straight line
- Momentum
- Newton’s laws of motion
- Energy, work and power
Probability & Statistics 1 (Paper 5)
- Representation of data
- Permutations and combinations
- Probability
- Discrete random variables
- The normal distribution
Probability & Statistics 2 (Paper 6)
- The Poisson distribution
- Linear combinations of random variables
- Continuous random variables
- Sampling and estimation
- Hypothesis tests
Cambridge Assessment
YEAR 1 – IAS Level
All AS Level candidates take two written papers. All A Level candidates take four written papers.
The Cambridge International AS Level Mathematics qualification offers three different options:
- Pure Mathematics only (Paper 1 and Paper 2) or
- Pure Mathematics and Mechanics (Paper 1 and Paper 4) or
- Pure Mathematics and Probability & Statistics (Paper 1 and Paper 5)
Please note, the Pure-Mathematics-only option (Paper 1 and Paper 2) leads to an AS Level only and cannot be used as a staged route to a full A Level. Candidates who have taken Paper 1 and Paper 2 at AS Level and then wish to complete a full A Level would need to retake Paper 1 alongside three other components. These should be chosen from the specific combinations below.
YEAR 2 – Full A Level
The Cambridge International A Level Mathematics qualification offers two different options:
- Pure Mathematics, Mechanics and Probability & Statistics (Papers 1, 3, 4 and 5) or
- Pure Mathematics and Probability & Statistics (Papers 1, 3, 5 and 6).
Please note, it is not possible to combine Paper 4 and Paper 6. This is because Paper 6 depends on prior knowledge of the subject content for Paper 5.
Exam Papers
Paper 1: Pure Mathematics 1
Written Examination: 1 hour 50 minutes
Availability: June and November (March in India)
Assessment overview: 10 to 12 structured questions based on the Pure Mathematics 1 subject content
75 marks
Paper 2: Pure Mathematics 2
Time: 1 hour 15 minutes
Availability: June and November (March in India)
Assessment overview: 6 to 8 structured questions based on the Pure Mathematics 2 subject content
50 marks
Paper 3: Pure Mathematics 3
Written examination: 1 hour 50 minutes
Availability: June and November (March in India)
Assessment overview: 9 to 11 structured questions based on the Pure Mathematics 3 subject content
75 marks
Paper 4: Mechanics
Practical examination: 1 hour 15 minutes
Availability: June and November (March in India)
Assessment overview: 6 to 8 structured questions based on the Mechanics subject content.
50 marks
Paper 5: Probability and Statistics 1
Practical examination: 1 hour 15 minutes
Availability: June and November (March in India)
Assessment overview: 6 to 8 structured questions based on the Probability and Statistics 1 subject content.
50 marks
Paper 6: Probability and Statistics 2
Practical examination: 1 hour 15 minutes
Availability: June and November (March in India)
Assessment overview: 6 to 8 structured questions based on the Probability and Statistics 2 subject content.
50 marks
Edexcel Specification
Awarding Body: Edexcel
Specification Codes:
Edexcel International AS in Mathematics (XMA01)
Edexcel International A Level in Mathematics (YMA01)
Edexcel Exams: January & June (some exams in October too)
Edexcel Study Hours: 300 – 360 hours
Pearson Edexcel
Pearson Edexcel are the only board that offers dedicated IAS and IAL Pure Mathematics qualifications. They also enable learners to specialise purely in Mechanics or Statistics, for IAS and IAL. Also on offer is their Decision Mathematics Unit to enable progress for Computer Science Degrees.
Each paper has equal weightings and are the same length in time to help students prepare for a consistent exam experience.
How will I benefit from the International A Level Mathematics Edexcel course?
The aims and objectives of these qualifications are to enable students to:
- develop their understanding of mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment
- develop abilities to reason logically and recognise incorrect reasoning, to generalise and to construct mathematical proofs
- extend their range of mathematical skills and techniques and use them in more difficult, unstructured problems
- develop an understanding of coherence and progression in mathematics and of how different areas of mathematics can be connected
- recognise how a situation may be represented mathematically and understand the relationship between ‘real-world’ problems and standard and other mathematical models and how these can be refined and improved
- use mathematics as an effective means of communication
- read and comprehend mathematical arguments and articles concerning applications of mathematics
- acquire the skills needed to use technology such as calculators and computers effectively, recognise when such use may be inappropriate and be aware of limitations
- develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general
- take increasing responsibility for their own learning and the evaluation of their own mathematical development.
Key concepts
The key concepts for Edexcel International A Level in Mathematics are:
Structure
The Pearson Edexcel International Advanced Subsidiary in Mathematics, Further Mathematics and Pure Mathematics and the Pearson Edexcel International Advanced Level in Mathematics, Further Mathematics and Pure Mathematics are modular qualifications. The Advanced Subsidiary and Advanced Level qualifications can be claimed on completion of the required units, as detailed in the Qualification overview section.
Content
A variety of 14 equally weighted units allowing many different combinations, resulting in flexible options.
Core mathematics content separated into four Pure Mathematics units.
Approach
Students will be encouraged to take responsibility for their own learning and mathematical development. They will use their knowledge and skills to apply mathematics to real-life situations, solve unstructured problems and use mathematics as an effective means of communication.
Edexcel Mathematics Content Overview
Modules are outlined below and to see the routes you can take, please see ‘Edexcel Assessment’ tab.
Pure Mathematics 1
- Algebra and functions
- Coordinate geometry in the (x, y)
- Trigonometry
- Differentiation
- Integration
Pure Mathematics 2
- Proof
- Algebra and functions
- Coordinate geometry in the (x, y) plane
- Sequences and series
- Exponentials and logarithms
- Trigonometry
- Differentiation
- Integration
Pure Mathematics 3
- Algebra and functions
- Trigonometry
- Exponentials and logarithms
- Differentiation Integration
- Numerical methods
Pure Mathematics 4
- Proof
- Algebra and functions
- Coordinate geometry in the (x, y) plane
- Binomial expansion
- Differentiation
- Integration
- Vectors
Further Pure Mathematics 1
- Complex numbers
- Roots of quadratic equations
- Numerical solution of equations
- Coordinate systems
- Matrix algebra integration
- Transformations using matrices
- Series
- Proof
Further Pure Mathematics 2
- Inequalities
- Series
- Further complex numbers
- First order differential equations
- Second order differential equations
- Maclaurin and Taylor series
- Polar coordinates
Further Pure Mathematics 3
- Hyperbolic functions
- Further coordinate systems
- Differentiation
- Integration
- Vectors
- Further matrix algebra
Mechanics 1
- Mathematical models in mechanics
- Vectors in mechanics
- Kinematics of a particle moving in a straight line
- Dynamics of a particle moving in a straight line or plane
- Statics of a particle
- Moments
Mechanics 2
- Kinematics of a particle moving in a straight line or plane
- Centres of mass
- Work and energy
- Collisions
- Statics of rigid bodies
Statistics 1
- Mathematical models in probability and statistics
- Representation and summary of data
- Probability; correlation and regression
- Discrete random variables
- Discrete distributions
- The Normal distribution
Statistics 2
- The Binomial and Poisson distributions
- Continuous random variables
- Continuous distributions
- Samples
- Hypothesis tests
Decision Mathematics 1
- Algorithms
- Algorithms on graphs
- Algorithms on graphs II
- Critical path analysis
- Linear programming
Edexcel Assessment
International AS Level
All AS Level learners take three written papers. The Unit options are as follows:
- Pure Mathematics (P1 and P2) and Statistics (S1)
- Pure Mathematics (P1 and P2) and Mechanics (M1)
- Pure Mathematics (P1 and P2) and Decision (D1)
- Pure Mathematics (P1 and P2) and Further Pure (FP1)
Full A Level
All A Level learners take six written papers. The Unit options are as follows:
- Pure Mathematics (P1, P2, P3 and P4), Mechanics and Statistics (M1 and S1)
- Pure Mathematics (P1, P2, P3 and P4), Mechanics and Decision (M1 and D1)
- Pure Mathematics (P1, P2, P3 and P4), and Mechanics (M1 and M2)
- Pure Mathematics (P1, P2, P3 and P4), Statistics and Decision (S1 and D1)
- Pure Mathematics (P1, P2, P3 and P4), and Statistics (S1 and S2)
- Pure Mathematics (P1, P2, P3, P4 and FP1), and Further Pure (FP2 or FP3)
Exam Papers
P1: Pure Mathematics 1
Written Examination: 1 hour 30 minutes
Availability: January, June and October
75 marks
P2: Pure Mathematics 2
Written Examination: 1 hour 30 minutes
Availability: January, June and October
75 marks
P3: Pure Mathematics 3
Written Examination: 1 hour 30 minutes
Availability: January, June and October
75 marks
P4: Pure Mathematics 4
Written Examination: 1 hour 30 minutes
Availability: January, June and October
75 marks
FP1: Further Pure 1
Written Examination: 1 hour 30 minutes
Availability: January and June
75 marks
FP2: Further Pure 2
Written Examination: 1 hour 30 minutes
Availability: January and June
75 marks
FP3: Further Pure 3
Written Examination: 1 hour 30 minutes
Availability: January and June
75 marks
M1: Mechanics 1
Written Examination: 1 hour 30 minutes
Availability: January, June and October
75 marks
M2: Mechanics 2
Written Examination:
Availability: January, June and October
75 marks
S1: Statistics 1
Written Examination:
Availability: January, June and October
75 marks
S2: Statistics 2
Written Examination:
Availability: January, June and October
75 marks
D1: Decision 1
Written Examination:
Availability: January and June
75 marks