nature and scope of a problem, and can inform solutions. As they model with difference and differential equations students learn to abstract and apply techniques in a wide range of application areas. Students learn about Students should be able to Recurrence relations Real world phenomena involving incremental change such as Malthusian growth, Restricted growth Interest/loan payment Supply and demand Solving homogeneous and inhomogeneous difference equations numerically, graphically and with the aid of digital technology Analysing real word phenomena involving continuous change Predictive nature of differential equations Techniques for solving differential equations separation of variables reduction of order numerical solutions for digital implementation graphical methods that provide qualitative information compute the and higher differences of a given sequence of numbers identify real-world situations which can be suitably modelled by difference equations derive difference equations for real world phenomena involving incremental change analyse, interpret and solve difference equations in context Solve linear first order difference equations first-order non-linear difference equations identify situations which can be suitably modelled by differential equations derive and interpret in context differential equations for real world phenomena involving continuous change solve differential equations order separable second order which can be reduced to first order interpret the solution of differential equations in context
the student to display his/her skills of critical thinking, analysis, evaluation and his/her application of mathematical knowledge and understanding in real contexts. Written examination assessment criteria A high level of achievement in the written examination is characterised by a thorough knowledge and understanding of mathematical terms, concepts and theories from across the whole specification with few significant omissions. Students consistently apply their knowledge and understanding of mathematics from the three contextual strands to both familiar and new contexts, where appropriate. They accurately use mathematics to represent real world phenomena, analyse and evaluate information and data from different sources; manipulation of data, where appropriate, will be correct. Students present logical arguments and ideas which are clearly based on evidence. A moderate of achievement in the written examination is characterised by a good knowledge and understanding of mathematical terms, concepts and theories from many parts of the specification. Students apply their knowledge and understanding of mathematics from the three contextual strands to familiar contexts and in some new contexts, where appropriate. They adequately use mathematics to represent and analyse real world phenomena They carry out adequate levels of analysis and evaluation on information and data from different sources; much of their manipulation of data, where appropriate, will be correct. Students present arguments and ideas which, in the main, are based on evidence. A low level of achievement in the written examination is characterised by a limited knowledge and understanding of mathematical terms, concepts and theories. Students select appropriate facts, concepts and theories to apply to familiar contexts. They use basic mathematics to represent and analyse real world phenomena. They carry out basic levels of analysis and evaluation of information and data and carry out basic manipulation of data, where appropriate. Students present explanations which are referenced to some evidence. Modelling Project The modelling project assessment will require students to demonstrate proficiency in course content and skills that cannot be easily assessed by the written examination. The assessment will require students to present a solution to an authentic modelling problem, and to report on the work and process involved. Students must acknowledge (i.e. through citation, through attribution, by reference, and/or through acknowledgement in bibliographic entry) the source or author of all