# SFY0023 : Core Mathematics A

• Offered for Year: 2024/25
• Module Leader(s): Dr Kate Henderson
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters

Your programme is made up of credits, the total differs on programme to programme.

 Semester 1 Credit Value: 30 ECTS Credits: 15.0 European Credit Transfer System

#### 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)

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion12:002:00Exam completion
Guided Independent StudyAssessment preparation and completion133:0033:00Exam revision
Scheduled Learning And Teaching ActivitiesLecture331:0033:003 One hour lectures per week
Structured Guided LearningLecture materials301:0030:00Asynchronous material
Guided Independent StudyAssessment preparation and completion115:0015:00Final exam preparation
Guided Independent StudyAssessment preparation and completion56:0030:005 x In-course Assessment each requiring 4 hours preparation 2 hours completion
Scheduled Learning And Teaching ActivitiesWorkshops221:0022:00Problem sessions/tutorials
Scheduled Learning And Teaching ActivitiesDrop-in/surgery111:0011:00Drop in/ Q&A sessions
Guided Independent StudyIndependent study331:0033:00Lecture follow-up
Guided Independent StudyIndependent study691:0069:00Independent study - Background reading, reviewing notes, re-enforcing knowledge.
Guided Independent StudyIndependent study221:0022:00Follow - up - Reviewing learning at workshops
Total300:00
##### 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 Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A70Final Exam
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10Small in-course assessment. Contains 8-10 questions
Prob solv exercises1M10Small in-course assessment. Contains 8-10 questions
Prob solv exercises1M10Small in-course assessment. Contains 8-10 questions
##### Formative Assessments

Formative Assessment is an assessment which develops your skills in being assessed, allows for you to receive feedback, and prepares you for being assessed. However, it does not count to your final mark.

Description Semester When Set Comment
Prob solv exercises1MSmall in-course assessment. Contains 8-10 questions
Prob solv exercises1MSmall in-course assessment. Contains 8-10 questions
##### 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.