Module Catalogue 2024/25

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

This module aims to cover the Pure Maths content of the AS level Maths curriculum to prepare students for the rigor of stage 1 modules in Mathematics, Physics and Engineering.

Students will develop skills in algebraic manipulation, be introduced to a wider range of functions and begin to explore elementary calculus and vectors. Students will develop skills and understanding commensurate with their eventual peers on their destination programme.

Outline Of Syllabus

1.Algebraic Expressions (index laws, surds)
2.Quadratics (complete the square, solve, graphs, discriminant)
3.Equations and Inequalities (simultaneous equations, solving, graphing inequalities including identifying regions)
4.Graphs and transforms (cubic, quartic, reciprocal graphs, all graph transformations)
5.Straight line graphs (y=mx+c, parallel and perpendicular lines)
6.Circles (bisectors, circle equation, intersection circle/line, tangent/chord properties, circles & triangles)
7.Algebraic methods (algebraic fractions, polynomial division, factor theorem, methods of proof)
8.Binomial Expansion (Pascal’s triangle, factorial notation, the binomial expansion, binomial estimation)
9.Trig (Sine/Cosine Rule, Area of triangle, graphs of sin, cos and tan)
10.Trigonometric Identities (CAST diagram, simple identities and solving equations with multiple solutions)
11.Vectors (Magnitude and direction, position vectors, modelling)
12.Differentiation (Gradients of curves, differentiating polynomials, tangents and normal, stationary points, sketching the gradient function)
13.Integration (Definite and indefinite integrals, area under the curve, area between curves – polynomials only)
14.Exponentials and Logs (Introduction to the functions, solving equations, laws of logs, natural logs)

Intended Knowledge Outcomes

At the end of this module students will be proficient in key algebraic skills and be able to use elementary calculus and understand its range of applications. They will know the derivatives and integrals of polynomial functions. Students will understand differentiation from first principals and the link between integration and area. They will also have understood exponentials and natural logs. Students will in addition have a strong foundation of trigonometry to build upon and will be familiar with a range of different functions. They will also understand the concept of a vector and being to perform basic calculations.

Intended Skill Outcomes

At the end of this module students should be confident differentiating simple functions from first principles and know some standard derivatives. They will be able to apply differentiation to curve-sketching. They should be able to calculate integrals of basic functions and understand how they relate to areas. They will be able to work with trigonometric, exponential and logarithmic functions.

Students will only consider calculus in terms of polynomial functions and other select simple functions.

Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Asynchronous lectures are used for the delivery of theory and explanation of methods, lectures broaden this understanding and provide illustrative examples, and can be used for giving general feedback on marked work.

Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity is vital to ensure students have the best chance of success in their destination programme.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

General Notes

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