# SFY0024 : Core Mathematics B

• 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 2 Credit Value: 30 ECTS Credits: 15.0 European Credit Transfer System

#### Aims

This module aims to cover the Pure Maths content of the A2 level Maths curriculum to prepare students for the rigor of stage 1 modules in Mathematics, Physics and Engineering.

Students will further develop skills in algebraic manipulation, be introduced to a wider range of functions and to further 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 methods (Algebraic fractions, partial fractions, algebraic division)
2.Functions and graphs (modulus function, composite functions, inverse functions, combining transformations)
3.Sequences and Series (Arithmetic/Geometric, Sum and sum to infinity, sigma notation, recurrence relations)
4.Binomial Expansion ((1+x)^n, (a+bx)^n, using partial fractions)
5.Radians (radian measure, arc length, area of sector/segment, solving trig equations, small angle approximation)
6.Trigonometric Functions (Sec, Cosec, Cot, Inverse trigonometric functions)
7.Trigonometry and modelling (Addition formulae, double angle formulae, Solving trig equations, simplifying acosx +/- bsinx, proving trig identities)
8.Parametric equations (Introduction, using trig identities, curve sketching, points of intersection)
9.Differentiation (Differentiating sin, cos, exp, log, product/quotient and chain rules, parametric and implicit differentiation, second derivatives, rates of change)
10.Numerical Methods (locating roots, iteration, Newton-Raphson)
11.Integration (Integrate f(ax+b), standard functions, reverse Chain rule, by substitution, by parts, using partial fractions, finding areas, solving differential equations, trapezium rule)
12.Vectors (3D cords, 3D vectors, solving geometric problems)

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion56:0030:005x In-course assessments each requiring 4 hours prep and 2 hours completion
Guided Independent StudyAssessment preparation and completion12:002:00Exam completion
Guided Independent StudyAssessment preparation and completion133:0033:00Exam Revision
Structured Guided LearningLecture materials331:0033:003 One hour lectures per week
Scheduled Learning And Teaching ActivitiesLecture130:0030:00Asynchronous material
Guided Independent StudyAssessment preparation and completion115:0015:00Final exam preparation
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 study169:0069:00Independent 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 Examination1202A70Final Exam
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M10Small in-course assessment. Contains 8-10 questions
Prob solv exercises2M10Small in-course assessment. Contains 8-10 questions
Prob solv exercises2M10Small 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 exercises2MSmall in-course assessment. Contains 8-10 questions
Prob solv exercises2MSmall 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.