AS Level Mathematics Course

Open Learning College

A Level

Hard copy certificate - Included

Course Key Topics

the AS Level Mathematicscourse is divided into 4 modules.

Module 1: Pure Mathematics Part A

1. Proof :

• understanding the structure of mathematical proof
• proof by deduction,
• proof by exhaustion and disproof by deduction.

2. Algebra and functions:

• understanding the laws of indices for all rational exponents
• rationalising the denominator
• working with quadratic functions
• solving simultaneous equations and using graphical information to solve equations

3. Coordinate geometry in the (x, y) plane:

• understanding the equation of a straight line
• applying the use of coordinate geometry and understanding the use of parametric equations in modelling in a variety of contexts.

4. Sequences and series:

• understanding the use of Pascal’s triangle,
• working with sequences (including increasing, decreasing and periodic sequences)
• understanding sigma notation for sums of series.

5. Trigonometry:

• understanding the definitions of sine
• cosine and tangent
• solving trigonometric equations
• using trigonometric functions to solve problems in context

Module 2: Pure Mathematics Part B

1. Exponentials and logarithms:

• knowing and using functions and graphs that relate to exponentials and logarithms
• understanding the laws of logarithms and understanding exponential growth and decay
• consideration of limitations and refinements of exponential models

2. Differentiation

• understanding sketching the gradient function for a given curve
• second derivatives
• the use of second derivative as the rate of change of a gradient
• understanding how to apply differentiation to find gradients, tangents and normals

3. Integration

• knowing the Fundamental Theorem of Calculus
• understanding and evaluating definite integrals
• carrying out simple cases of integration by substitution and integration by parts and interpreting the solution of differential equation in the context of solving a problem

4. Vectors

• using vectors in two dimensions
• calculating the magnitude and direction of a vector
• adding vectors diagrammatically
• understanding and using position vectors
• using vectors to solve problems in pure mathematics and context

Module 3: Section A: Statistics

1. Statistical sampling:

• understanding and using the terms ‘population’ and ‘sample’
• understanding and using sampling techniques and applying sampling techniques in the context of solving a statistical problem

2. Data presentation and interpretation

• interpreting diagrams for single-variable data
• interpreting scatter diagrams and regression lines for bivariate data
• plus recognising and interpreting possible outliers in data sets and statistical diagrams

3. Probability

• understanding mutually exclusive and independent events when calculating probabilities
• understanding conditional probability and modelling with probability
• including critiquing assumptions made.

4. Statistical distributions

• understanding and using simple
• discrete probability distributions
• calculating probabilities using binomial distribution
• understanding the use of Normal distribution as a model and selecting an appropriate probability distribution for a context

5. Statistical hypothesis testing:

• understanding and applying the language of statistical hypothesis testing
• conducting statistical hypothesis test using binomial distribution and understanding a sample being used to make an inference about the population

Module 4: Section B: Mechanics

1. Quantities and units in mechanics:

• understanding and using fundamental quantities and units in the S.I. system
• understanding and using derived quantities and units.

2. Kinematics

• understanding and using the language of kinematics
• interpreting graphs in kinematics for motion in a straight line
• understanding how to derive the formulae for constant acceleration for motion in a straight line and using calculus in kinematics for motion in a straight line

3. Forces and Newton’s laws

• understanding the concept of a force
• applying and using Newton’s second law for motion in a straight line
• understanding using weight and motion in a straight line under gravity and applying Newton’s third law

What Will I Learn?

• In-depth understanding of AS Level Mathematics, covering advanced concepts and theories.
• Development of critical thinking and analytical skills through complex problem-solving.
• Preparation for higher education or entry into the workforce with specialised knowledge.
• Acquisition of practical skills and competencies relevant to chosen career paths or academic pursuits.

Targeted Audience

• High school students aiming to pursue further education at universities or colleges.
• Individuals seeking to fulfil academic requirements for specific career paths or professions.
• Mature students looking to enhance their qualifications for career advancement or personal development.
• Students interested in acquiring specialised knowledge and skills in particular subjects or disciplines.

The good news is that no prior learning knowledge or experience is essential to take this course. This course is openly available to anyone wishing to learn more about AS Level Mathematics and would like to take part in a highly rewarding distance learning study course.

We believe that everyone should have the opportunity to expand their knowledge and study further, so we try to keep our entry requirements to a minimum.

You have the freedom to start the course at any time and continue your studies at your own pace for a period of up to 12 months from initial registration with full tutor support.