Learning Partnerships, Unit Catalogue 2009/10 |
AS00041: Mathematics 2 |
 Credits: |
12 |
| Level: |
Foundation |
| Period: | This unit is available in... |
| Semester 2 at City of Bath College | |
| Semester 2 at Wiltshire College |
| Assessment: |
CW 20%, EX 80% |
| Supplementary Assessment: | Like-for-like reassessment (where allowed by programme regulations) |
| Requisites: |
Before taking this unit you must take AS00040 |
| Description: | Aims: This unit aims to bring students up to a Year 1 entry standard of knowledge and skills in Mathematics. The unit will draw upon more advanced aspects of the 'A' level syllabus and will achieve an equivalent depth and standard in these aspects. The unit will offer opportunities for knowledge acquisition and practice of theoretical problem-solving. Learning Outcomes: On successful completion of the unit, students should be able to: (i) undertake more advanced algebraic processing including partial fractions. (ii) sketch curves. (iii) demonstrate competence in more advanced aspects of trigonometry, differentiation and integration and use vectors. Skills: Key transferable skills and theoretical problem solving. Content: Functions: concept of a function as a one-to-one or many-to one mapping. Domain and range. Composition of functions. Inverse functions. Graphical representation of a function and of its inverse to include quadratic functions. Modulus function. Equations of the form y=xn. Effect of simple transformations on the graph y=f(x) as represented by y = af(x), y=f(x)+a, y=f(x+a), y=f(ax). Sequences and series: recurrence relations, Binomial series and expressions. Algebraic Processing skills: Partial fractions. Remainder Theorem. Further Coordinate Geometry: The circle. Cartesian & parametric equations of curves. Further Trigonometry: Sec, cosec, cot. Trigonometric identities including compound angles, double angles. Further solution of trig equations including use of trig identities and equations of the form acosx + bsinx. Further Integration: Integration by substitution and parts. Integration using partial fractions. Volumes of revolution. Formation and solution of first order differential equations using integrating factors and separation of variables. Exponential growth and decay. Numerical methods: Solution of equations and numerical integration. Vectors: Definitions and operations of vectors (including components in two and three dimensions). Position vector. Scalar product. Methods of proof. Proof by induction, contradiction and counter example. |