Analysis and Approaches Higher Level

The Analysis and Approaches Higher Level (AAHL) course is aimed at those students who really enjoy Mathematics and wish to develop a deep appreciation and understanding of the subject. It is a challenging but thoroughly enjoyable course, that allows students to develop a full understanding of a wide range of mathematical topics.

Is AAHL right for me?

Students who choose to do the AAHL course:

need to have strong algebraic skills and the ability to understand mathematical proof;
will enjoy spending time working on problems and get pleasure and satisfaction from solving challenging problems;
may be considering studying a STEM subject at university, such as Mathematics, Physics or Engineering.

There are many prior knowledge topics in mathematics that AAHL students will need to be secure in, but the main ones include:

solving quadratic equations (by factorising, quadratic formula and completing the square);
manipulating and simplifying indices;
solving simultaneous equations, both with two linear equations and where one equation is non-linear;
manipulating surds, such as simplifying and rationalising the denominator;
probability, including working with tree diagrams;
statistical calculations, such as finding the mean, mode and median of sets of data;
trigonometry, including right-angled trigonometry and the sine and cosine rules;
volumes and surface areas of comon shapes, such as prisms, pyramids, cylinders, cones and spheres.

Students who have gaps in their knowledge and understanding of these topics often find the course more challenging as their algebra skills are not strong enough to cope with the more demanding parts of the course. These topics will be reviewed in the course, but are not normally explicitly taught, as it is assumed that students are capable in these topics.

What are the entry requirements for AAHL?

Whilst we take every case on an individual level, there are some general guidelines on prior qualifications for entry to the AAHL course. These are based on the fact that on average, those students who do not attain these grades do not do as well in the AAHL course.

GCSE - suggested minimum grade is 8, though we will accept those with a grade 7 if they show dedication to learning.

MYP Standard Level - suggested minimum grade is 7.

MYP Extended Level - suggested minimum grade is 6, though we will accept those with grade 5 if they show dedication to learning.

For external candidates we also require completion of a short test for use to see the level of your algebra skills in order to suggest the best course.

For internal candidates, your mathematics teacher will talk with you individually about your choices during S5.

How does AAHL compare to A-Level Mathematics

There is no direct comparison between IB DP Mathematics courses and A-Level mathematics. In general, AAHL is considered a little bit more challenging than A-Level mathematics, but not as challenging as A-Level Further Mathematics.

What Maths do we learn?

Over the course of two years, students will study a variety of mathematical ideas which are broadly grouped by the IB into 5 topics:

Number and Algebra
Functions
Geometry and Trigonometry
Statistics and Probability
Calculus

At Europa we split this into 10 units across the two years. Whist the more difficult topics do come towards the end of the course, it is worth noting that there is HL grade 7 content in the first few weeks of the course, to give students a taste of how challenging the course can be.

The ten units are:

Number and Algebra
Functions
Mensuration and Trigonometry
Differential Calculus
Integral Calculus
Statistics
Probability
Limits and Differential Equations
Vectors
Complex Numbers

Below you will find a copy of the overview of the two year AAHL course. Please note that the timeframe is given as an approximation, and we might not stick exactly to those topics in those weeks. There are many things that can affect this, and the teacher will use their professional judgement to adjust the curriculum as necessary based on the class.

How is the course taught?

The AAHL course is taught to develop both a conceptual and procedural understanding of the content. That is, students will be given explanations of how mathematical ideas work, where they come from and what their purpose is. But they will also be shown clear examples of how to solve problems, and given the opportunity to solve both similar and unfamiliar problems using this new knowledge.

This is in line with the research in how to teach mathematics, bearing in mind the ideas of cognitive load theory and also the expertise reversal effect.

Homework is set weekly and consists of 6 exam style questions on topics that have already been studied. This should take students approximately an hour to complete, and will give them an idea of the style of IB questions as well as help students to identify which topics they need to review.

The course is fast paced in order to cover the large amount of content in the syllabus. Students are expected to make use of their study periods to consolidate the work in class by making use of the textbook exercises and other materials provided by the teacher. It is an expectation that students are spending 1-2 hours a week on top of class and homework to work on developing their mathematical skills in topics they have identified as needing work.

How is the course assessed?

The AAHL course is assessed through a mixture of internal and external assessments. There are 3 exam papers which are sat in May of the second year of the IB, and an internal assessment.

There will also be various school assessments throughout the course, such as Winter Examinations, End of S6 Examninations and Mock Examinations, along with class tests at the end of most units. These do not count towards the final IB grade, but are used to help students and teachers identify areas that still need development. These inform the grades on reports throughout the course, and will help the teacher make a realistic prediction when the time comes in S7.

The AAHL Formula Booklet

You can find a clean copy of the AAHL formula booklet here.

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