# Mathematics

**Sixth Form**

Course title: AQA GCE A Level Mathematics, AQA-7357-SP-2017.PDF

**What are the knowledge and skills that students will gain over Key Stage 5?**

The study of AQA Mathematics develops: the skills of using and applying complex mathematical knowledge built on from GCSE; the ability to reason, interpret and communicate mathematically; as well as solve problems within mathematics and in other contexts. At John Colet School, we aim to provide a stepping stone for future study as well as to foster a passion for the subject.

The key mathematical skills that will be developed throughout Year 12 and Year 13 are:

Students will be able to select and correctly carry out routine procedures, accurately recall facts, terminology and definitions.

Students will be able to construct rigorous mathematical arguments (including proofs); make deductions and inferences; assess the validity of mathematical arguments; explain their reasoning and use mathematical language and notation correctly.

Students will be able to translate problems in mathematical and non-mathematical contexts into mathematical processes; interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations; translate situations in context into mathematical models; use mathematical models; evaluate the outcomes of modelling in context, recognise the limitations of models and - where appropriate - explain how to refine them.

Students will become familiar with a number of specific large data sets in advance of the final assessment. The use of real data will enable the concepts and skills of data presentation and interpretation in the specification to be explored. Students will use technology such as spreadsheets or specialist statistical packages to explore the data sets. Students will interpret real data presented in summary or graphical form as well as using the data to investigate questions arising in real contexts.

Use of technology is an intrinsic part of the course. Scientific calculators are used to promote efficiency and place an emphasis on interpretation rather than computation. Students will be fully aware of the functionality of the calculator and we will insist that all students purchase a Casio Classwiz. Online graphical calculators such as Desmos will offer students a graphical representation of a number of otherwise algebraic problems.

The study of mathematics at A Level is consistent across all examination bodies and the mathematical skills are taught through the following content:

Pure:

Proof

Algebra and functions

Coordinate geometry

Sequences and Series

Trigonometry

Exponentials and Logarithms

Differentiation

Integration

Numerical methods

Mechanics

Vectors

Quantities and units in mechanics

Kinematics

Forces and Newton’s laws

Moments

Statistics

Statistical sampling

Data presentation and interpretation

Probability

Statistical distributions

Statistical hypothesis testing

**Why is it delivered in this way?**

The AQA A Level in mathematics was selected at John Colet School due to the interesting large data set involving cars. We felt that the content would engage our students and offer a wide range of opportunities to compare different aspects of the data set using technology.

We feel that it is important that proof is taught in a scaffolded and interesting way at A Level to deepen our students' understanding of key mathematical concepts. We do not want them to appear complicated to the students but logical and satisfying. It forms an essential part of each topic area with students occasionally having to know specific mathematical proofs by recall.

The content is taught in a way that builds upon mathematical skills and content at GCSE as well as linking to previous content taught throughout the A Level course. For example, the equation of a circle is taught at GCSE, extended upon in Year 12 and then linked to parametric equations in Y13. The scheme of work provides opportunities for links between pure and mechanics as well as pure and statistics.

Problem solving and reasoning forms such an essential part of the A Level mathematician: the ability to tackle content in a range of contexts as well using their embedded mathematical skills not only will result in success in the examination but will provide them with the important attributes beyond A Level and improve their confidence.

It is also essential that students develop exam techniques to ensure that they are prepared for the requirements of the A Level exam. By regularly exposing students to exam style questions using scaffolded approaches and analysis of the mark scheme, students will ultimately improve their attainment in Mathematics.

**A Level Further Maths**

Course title: AQA GCE A Level Further Mathematics, AQA-7367-SP-2017.PDF

Proof

Complex numbers

Matrices

Further Algebra and Functions

Further Calculus

Further Vectors

Polar coordinates

H: Hyperbolic functions

I: Differential equations

J: Trigonometry

K: Numerical Methods

Choice: Students must study two of these options.

Optional application 1 – mechanics

Optional application 2 – statistics

Optional application 3 – discrete