COURSE FACTSHEET
Advanced Level Foundation — Maths and Further Maths modules Who is this course for?
Recognised by widest choice of quality universities
The Kings Advanced Level Foundation is based on A-level syllabuses, taught by A-level teachers, assessed against A-levels and moderated by an independent Advisory Board of external examiners. As such, it is one of the most highly academic and successful pathways to leading UK universities.
Kings does not work with a narrow range of university partners. This is because our Advanced Level Foundation is based on, and linked to, A-levels. It is therefore automatically recognised and accepted by the widest choice of universities. Out of the Top 25 universities listed in the Times and Sunday Times 2019 rankings, 20 have accepted Kings Foundation students.
Pearson assured
Benchmarking against A-Level grades
Key Facts
The Kings Advanced Level Foundation has Pearson assured status, awarded after an annual Pearson audit of quality assurance.
Typical top 30 university offers to students following the Programme are based on their normal A-level offers. The Programme is benchmarked against A-level grades as follows:
Bournemouth Brighton
Level: Minimum IELTS 5.5 (standard version); IELTS 4.0 (extended version). Completed 11 – 12 years of schooling. Minimum age: 17 Length: 1 Academic Year (3 terms). Or Extended Advanced Level Foundation of 4 – 7 terms (including 3-term Advanced Level Foundation) Lessons: Average 21 hours per week (plus homework and private study) Class size: 8 – 12 Learning outcomes: à Raise academic qualifications to UK university entrance level à Raise English to university level à Develop learning and self study skills for degree level
Advisory Panel Standards for the Programme are set by an external and independent Advisory Board which meets three times each year to ensure best practice, moderate marks where required and hear appeals.
Assessment Paper
Weighting
Term 1 Assessment
30%
Term 2 Assessment
35%
Term 3 Assessment
35%
Jan
Sept
Jun
Apr
Jan
Sept
A*A*A*
80%
AAA
75%
AAB
70%
ABB
65%
BBB
60%
CCC
50%
Extended option Students with lower language levels can join an extended programme of 4 – 7 terms (including the 3-term Advanced Level Foundation), from IELTS 4.0. It offers practical content designed to provide a bridge into UK academic life. The main focus is developing suitable language proficiency for the Advanced level Foundation with concentrated IELTS lessons, but as the course is made up of English language classes and some 1:1 or small group study, it has the flexibility to also provide bespoke academic study skills and subject enrichment. The course can also include a Maths GCSE if required.
Pathways Jun
Typical Kings Foundation offer
Advanced Level Foundation
Sept
London
Typical A-level offer
Jun
Oxford
Apr
Start dates: 7 January, 8 April*, 1 July*, 9 September 2019; 6 January, 6 April*, 6 July*, 7 September 2020 (*Extended version) Locations offered:
Vacation
Advanced Level Foundation IELTS 4.0
Extended Foundation IELTS 5.0 IELTS 4.5
Extended Foundation
Top 20 university
Vacation
Advanced Level Foundation
Vacation
Top 20 university
Vacation
Advanced Level Foundation
Vacation
Top 20 university
Advanced Level Foundation
Vacation
Top 20 university
Advanced Level Foundation (Science and Engineering Pathway)
Vacation
Top 20 university
Advanced Level Foundation (Science and Engineering Pathway)
Vacation
Top 20 university
Extended Foundation IELTS 5.0 IELTS 4.5
Top 20 university
Ext. Found.
COURSE FACTSHEET
Course structure and content The programme is highly flexible, and able to adapt to the needs and academic aspirations of each student. It does this through a combination of core modules and a series of elective modules which can be combined in different ways to create main subject streams: Main subject streams à Business à Engineering à Life Sciences and Pharmacy à A rchitecture à Media and Communications à Humanities and Social Sciences à Mathematics, Computing and Science
Core modules are: à Communication and Study Skills à Data Handling and Information Technology Elective modules are: à A rt and Design à Biology à Business Studies à Chemistry
à Economics à History à Human Geography à Law à Mathematics à Media à Physics à Psychology à Politics and Government
2018 – 19 Sample academic timeline September
October
November
December
January
February
September starters
10 Sept: term starts Student induction
20 – 28 Oct: half term
University fairs/visits
14 Dec: term ends CSS Assessment 1 (Written) End of term exams
7 Jan: term starts
14 – 17 Feb: half term CSS Assessment 2 (Presentation) University fairs/visits
January starters
—
—
—
—
7 Jan: term starts Student induction
14 – 17 Feb: half term University fairs/visits
March
April
May
June
July
August
September starters
22 Mar: term ends Assignments* End of term exams
8 April: term starts Assignments*
Assignments*
14 June: term ends CSS Assessment 3 (Listening and Reading exam)
—
—
January starters
22 Mar: term ends Assignments* CSS Assessment 1 (Written) End of term exams
8 April: term starts Assignments*
Assignments*
17 – 18 June: 2 day break CSS Assessment 2 (Presentation)
CSS Assessment 3 (Listening and Reading exam)
2 Aug: term ends
*students spend two weeks on each assignment and do three in total — one for each of their ‘elective’ modules. Please note that specific dates are subject to change.
Maths module structure and content à use calculating aids effectively and be aware of their limitations. Term 1 à Basic Algebra and Quadratic Functions Simplifying expressions; factorising quadratics; laws of indices; surds; rationalising denominators; completing the square; quadratic formula; sketching quadratics; modelling à Equations and Inequalities Simultaneous linear equations and inequalities, simultaneous quadratic and linear equations and inequalities à Coordinate Geometry Equation of a straight line; gradient; parallel and perpendicular lines à Curve Sketching Quadratic functions, cubic functions and reciprocal functions; graph intersections; transformations f(x ± a), f(x) ± a, f(ax), af(x)
à Binomial Theorem Pascal’s Triangle; combinations and factorial notation; expanding (a+bx)n à More Algebra and Functions Dividing a polynomial by x ± p; Factor and Remainder Theorems à Graphs of Trigonometric Functions Graphs of sin x, cos x, tan x; exact values of sin x, cos x, tan x for x = 30º, 45º, 60º etc. • Sequences and Series à Trigonometric Identities and Equations Solving trigonometric equations; sin/cos/tan (nx + c) = k; quadratic trigonometric equations à Vectors Add and subtract vectors; determine the magnitude of vectors; write a point as position vector; use vectors in modelling
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1233 07/15
Learning Outcomes On successful completion of the course, students should: à have a general understanding of mathematics and mathematical processes à have developed the ability to reason logically and to generalise à have extended their range of mathematical skills and techniques, and their ability to use them in increasingly difficult or unstructured problems à have an understanding of coherence and progression in mathematics à recognise how a situation may be modelled mathematically à use mathematics as an effective means of communication à be able to read and comprehend mathematical arguments and narrative concerning applications of mathematics
COURSE FACTSHEET
Maths module structure and content continued Term 2 à Differentiation 1 Meaning of derivative; differentiating powers of x; second order derivatives; rate of change at a point; tangents and normal; using differentiation for modelling à Integration 1 Integration as the reverse process to differentiation; integral notation; finding the constant of integration à Exponential and Logarithmic Functions Sketch Exponential and logarithmic functions; ax, ln x ; change bases of logarithms; laws of logarithms à Algebraic Functions and Partial Fractions Simplifying and manipulating expressions with algebraic fractions à Sequences and Series nth term of arithmetic series; sum of arithmetic series; nth term of geometric series; sum of geometric series; solving problems involving growth and decay; sum to infinity for convergent geometric series; use of sigma notation à Radian Measure Circles; arc length; area of sector and segment
Term 3 à Trigonometry Sec x, cosec x, cot x and their graphs; use in simple identities à Further Trigonometric Identities Addition Formulae; Double Angle Formulae; half-angle formula à Differentiation 2 Chain Rule; Product Rule; Quotient Rule; differentiating ex, ln x, and circular functions; second derivatives; implicit differentiation à Integration 2 Use with partial fractions; use of trigonometric identities; integration by substitution; integration by parts
Use differentiation for variable acceleration problems à Moments Turning effects; resultant moments à Forces and friction Components of forces; triangular law; friction as force; coefficient of friction à Application of forces Forces in equilibrium; tension and pulleys, Lami’s law
Mechanics in Term 3 à Modelling Vector and scalar quantities; SI units; limitations of modelling à Constant acceleration Distance-time graphs; velocity-time graphs; kinematics formulae; motion under gravity à Forces and Motion Newton’s three laws; force diagrams; forces on connected particles à Variable acceleration
Further Maths module structure and content Please note that this module is a half module, and will be studied in addition to the other 5 modules on the course by those students for whom it will help their progression onto a chosen degree, and whom the school feels will be able to succeed. Learning Outcomes On successful completion of the course, students should: à have a deeper understanding of the application of calculus methods to the solution of mechanical and other real-world problems à have acquired knowledge of and skills in a wider range of analytical techniques à have an understanding of mathematical methods relating to vectors and matrices, and their applications à be able to work confidently with complex numbers and be aware of their application to various systems
à be able to use approximation and powerseries methods in the solution of suitable problems Term 1 Hyperbolic Functions: à Definitions à Basic identities à Use in integration Differential Equations: à 1st order variables separable à 1st order linear à 2nd order linear with constant coefficients Term 2 Numerical Methods à Decimal search à Newton-Raphson method
Vectors à Basic algebra of vectors à Scalar product à Vector product Term 3 Matrices à Basic concepts à Transformations in 2 and 3 dimensions à Eigenvectors and eigenvalues Complex Numbers à Basic algebra à Solution of quadratic equations à Modulus and argument; the form reiθ à Transformations of the complex plane
Power Series à Taylor and Mclaurin series à Use in solving differential equations
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COURSE FACTSHEET
Recommended reading Below is a list of text books normally used on this course, as well as books which may help you prepare for your studies prior to arrival. In many cases the textbooks will be supplied by the school, and you may borrow them for the duration of your time at school. However, if you already know what three subjects you want to choose you may prefer to purchase one before you arrive. àE dexcel AS and A level Mathematics Pure Mathematics Year 1/AS Textbook + e-book àE dexcel AS and A level Mathematics Statistics & Mechanics Year 1/AS Textbook + e-book àE dexcel A level Mathematics Pure Mathematics Year 2 Textbook + e-book àE dexcel A level Mathematics Statistics &
Sample enrichment activities Mechanics Year 2 Textbook + e-book à Edexcel AS and A level Further Mathematics, Core Pure Mathematics AS Book 1* à Edexcel A level Further Mathematics, Core Pure Mathematics Book 2* à Edexcel AS and A level Further Mathematics, Further Pure Mathematics 1* à GCSE Maths Edexcel Revision Guide: Foundation - for the Grade 9-1 Course à GCSE Maths AQA Revision Guide: Foundation - for the Grade 9-1 Course All published by Pearson *Further Maths only
à Bletchley Park visit à The Big Bang fair, NEC Birmingham à U K Maths Challenge à Science Club à Astronomy Club à Science in the News Club
Alumni who took the Maths module Below is a selection of degree courses some of our most recent alumni have gone on to study: Student name
Advanced Level Foundation Modules
University
Course name
Ademike Olufunmilayo Abimbola
Mathematics/Geography/Physics/CSS/Data
University of Leeds
Geological Science
Abdulrahman Elgalassi
Mathematics/Chemistry/Physics/CSS/Data
Aston University
Chemical Engineering
Amr Faour
Mathematics/Chemistry/Physics/CSS/Data
University of Nottingham
Pharmacy
Ana Sofia da Silva Ferraz
Mathematics/Business/Art & Design/CSS/Data
Oxford Brookes University
Architecture
Thibault Fievez
Mathematics/Chemistry/Physics/CSS/Data
University of Bath
Civil Engineering
Fisnik Fsahzi
Mathematics/Physics/Economics/CSS/Data
University of Bath
Civil Engineering with Architectural Studies
Nina Hasebe
Mathematics/Physics/Government and Law/CSS/Data
King’s College London
Robotics and Intelligent Systems
Chian Kiat Lai
Mathematics/Chemistry/Physics/CSS/Data
University of Surrey
Civil Engineering
Yong Ren Leu
Mathematics/Economics/Geography/ CSS/Data
University of Leicester
Law
Baoqiao Liao
Mathematics/Business/Economics/CSS/Data
Lancaster University
Marketing
Sungmin Lim
Mathematics/Geography/Economics/CSS/Data
University of Loughborough
International Business
Gia Bach Pham
Mathematics/Biology/Chemistry/CSS/Data
University of Glasgow
Psychology
Arsalan Samedi
Mathematics/Business/Physics/CSS/Data
University of Sussex
Automotive Engineering
Kristina Urosova
Mathematics/Economics/Government and Politics/ CSS/Data
King’s College London
Computer Science
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Nina Hasebe
1800 08/18
Being at Kings also gave me a better understanding of the subject matter. I like the fact — especially with physics and maths — that I actually didn’t do very well in Japan, but after coming here I really improved my understanding of these two subjects. I think it’s partly because of the small classes, but also the way it’s taught. I noticed the difference especially with maths because here we do a lot of proving formulas, and understanding how to apply mathematical concepts to real life, for example in engineering. In Japan we don’t do that, it’s all theoretical and more remembering formulas and applying them to equations — it didn’t feel very interesting for me, and was a bit harder.