# Mathematics A-Level at Evelyn Grace Academy

## Course description

**Year 12**

Two units of Pure maths (“Core 1” & and “Core 2”), and one Applied unit (“Mechanics 1” or “Statistics 1”)

**Year 13**

Two units of Pure maths (“Core 3” & and “Core 4”), and one Applied unit (“Mechanics 2” or “Statistics 2”)

## Course content

**Core 1**

This is the foundations of the A-level course, and it links firmly with your favourite topics from the GCSE Higher Tier syllabus. The unit can be broken down into three sections :

- (a) Algebra . This involves mastering the algebraic skills necessary to solve problems involving linear functions, quadratic functions, and cubic functions (using the factor and remainder theorem). This includes a work-out on simultaneous equations, surds, and basic graph transformations.
- (b) Coordinate Geometry . This involves mastering the techniques required for sketching linear functions, quadratic functions and circles on a Cartesian coordinate grid. Problems involving gradients and intersections provide a probing test of this understanding
- (c) Calculus. An introduction to the main topic on the A-level course - which offers mathematicians a way to deal with the infinite (Mubarak get ready), wrapped up as it is in the analysis of smooth curves. This involves a grasp of the key principles of differentiation, and their application in finding maxima and minima(including second order derivatives); and the key principles of integration (as reverse differentiation), and their application for finding the area under a curve.

**Core 2**

This extends the knowledge base explored in Core 1. It can be broken down into five sections:

- (a) Algebra and Functions. A full understanding of graph transformations is achieved.
- (b) Sequences and Series. The sequences encountered at GCSE are understood according to the more abstract and rigorous classification of arithmetic and geometric sequences.This includes a study of the dark arts of Sigma notation, and analysis of the limits of infinite sequences. The Binomial expansion is introduced in its basic form.
- (c) Trigonometry. All those trigonometric skills from GCSE are dusted down and given a proper grounding. Radians are introduced as the measure of turn appropriate for calculus calculations. The first two trigonometric identities are introduced and a collection of trig equations are studied and mastered - this requires confidence in elucidating the multiple solutions that emerge from the cyclical trig graphs.
- (d) Exponentials and Logarithms. The laws of indices are turned on their heads, and your heads are expanded to cope with the counter-intuitive laws of logarithms. This enables us to study exponential functions and graphs, and to appreciate their total fundamental pre-eminence amen. Simple equations involving exponentials are encountered.
- (e) Calculus. The basic skills encountered in Core 1 are given a work-out, involving strange new breeds of function, and their application in more warped geometric problems. This boils down to differentiating and integrating functions involving fractional and negative indices. The trapezium rule is introduced to approximate anything that is not integratable.

**Mechanics 1**

This module illuminates one of the most powerful applications and motivations for the Differential Calculus : the study of particles according to Newton's laws of motions. This looks like Physics, but it just involves wielding the mathematical tools of Core
1&2 (and some GCSE vectors) in a controlled one-dimensional environment of sustained acceleration. Master this and you master the world.

**Statistics 1**

This module builds the foundations for an understanding of hypothesis testing, and significance, which are achieved in Statistics 2. These are the nuclear weapons of modern medicine, allowing a laser-like precision of judgement to be applied to the most disordered
of data sets. The working tools of this are the laws of probability, which can be abstracted and refined into the Binomial distribution, and then further expanded into a study of the mother of probability distributions, the Normal Distribution.

## How to apply

If you want to apply for this course, you will need to contact Evelyn Grace Academy directly.