Learning Partnerships, Unit Catalogue 2008/09 |
AS00040 Mathematics 1 |
| Credits: 12 |
| Level: Foundation |
| Semester: 1 at City of Bath College |
| Semester: 1 at Wiltshire College |
| Assessment: CW 20%, EX 80% |
| Requisites: |
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Aims: This unit aims to ensure that students have a foundation of underpinning knowledge and skills in Mathematics. The unit will draw upon core 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) use indices and surds, solve linear, simultaneous, and quadratic equations; (ii) demonstrate algebraic processing skills; and (iii) demonstrate competence in basic concepts of trigonometry, co-ordinate geometry, integration and differentiation. Skills: Key transferable skills and theoretical problem solving. Content: Laws of indices including negative and rational exponents. Using and manipulating surds. Algebra: Addition, subtraction, multiplication and factorisation of polynomials. Factor Theorem. Quadratic Functions. simultaneous equations in two unknowns (2 linear and 1 linear with 1 quadratic), quadratic equations (factorisation, completing the square and formula). Solutions of linear and quadratic inequalities in one variable. Simplifying simple algebraic expressions. Equations involving fractions. Trigonometry: Radians, area of sector, arc lengths. 3 trig ratios for angles greater than 90 degrees, simple trigonometric equations (using Pythagoras identities) within given range, graphs of sin, cos and tan, sine and cosine rule and applications. Coordinate Geometry: Rectangular cartesian coordinates in two dimensions including the equation of a straight line, gradient of a line joining two points and distance between two points. Parallel & perpendicular lines. Mid-points. Series: Arithmetic and Geometric series including infinite GP's. Exponents & logs. Functions. Laws of logs. Equations ax=b. Differentiation: Differentiation of xn, logs and exponentials, Increasing & decreasing functions. Second derivatives. Tangents and normals. Integration: Integration as the inverse of differentiation including xn, exponentials, logs. Definite integration, areas and volumes. |