Module FOUN0738: Maths for Business

Department: Foundation Year

FOUN0738: Maths for Business

Prerequisites

• None

Corequisites

• None

Excluded Combination of Modules

• Core Foundation Maths for Scientists, Core Foundation Maths for Economics, Decision Maths, , Maths Applications for Scientists,

Aims

• To improve confidence in algebraic manipulation through the study of mathematical techniques and development of investigative skills.
• To introduce and develop a knowledge of logarithms and their uses.
• To introduce and develop a knowledge of trigonometry.
• To introduce and develop understanding of a range of standard techniques for differentiation and integration to include trigonometric and logarithmic functions.
• To provide the opportunity for students to engage in logical reasoning, algorithmic thinking and applications
• To introduce and develop a knowledge of matrices and their applications.
• To extend knowledge of Cartesian coordinates in two dimensions to include equations of circles and lines.
• To introduce complex numbers.
• To introduce the concept of linear programming

Content

• Quadratic equations, factorisation, graphs, quadratic formula.
• Trigonometry, sine, cosine, tangent.
• Sequences and Series , Arithmetic, geometric, use of sigma notation.
• Indices and Logarithms: laws, solution of equations.
• Reduction of a given relation to linear form, graphical determination of constants.
• Rate of change, increasing/decreasing functions, maxima and minima.
• Differentiation of: algebraic polynomials ,composite functions (chain rule), sum, product or quotient of two functions, trigonometric and exponential functions.
• Evaluation of integrals by using standard forms or partial fractions.
• Second derivatives of standard functions.
• Binomial expansion of (a+b)(to the power n) for positive integer n.
• Factor theorem.
• Percentage use, Simple and compound interest.
• Linear equations, Substitution and transposition of formulae
• Pythagoras' theorem
• Standard Index form
• Bipartate Graphs and matchings
• Shortest paths in networks (Dijkstra's algorithm)
• Spanning trees (Prim's and Kruska's algorithm and travelling salesperson problem)
• Minimum tour (postman problem)
• Critical Path Analysis
• Matrices (nxm): addition, subtraction, multiplication, determinant, transpose, inverse. Applications to simultaneous equations.
• Cartesian equations in two and three dimensions of straight lines and perpendicular lines.
• Complex numbers: +, -, x, /, complex conjugate, Argand diagrams,.
• Linear Programming

Learning Outcomes

• By the end of the module students will be know how to:
• Define sine, cosine and tangent (SSK 1)
• Use logarithms to solve problems and to predict relationships from graphs. (SSK2)
• Differentiate and integrate a number of different types of functions. (SSK3)
• State the rules for addition, subtraction and multiplication of matrices and for finding inverses. (SSK4)
• Give standard Cartesian equations for lines (SSK5)
• Solve a range of predictable problems in Discrete Mathematics. (SSK6) >

• By the end of the module the student will have acquired the skills to be able to:
• recall, select and use knowledge of appropriate integration and differentiation techniques as needed in a variety of contexts. (SSS1)
• confidently manipulate a range of algebraic expressions and use a range of techniques as required in problems appropriate to the syllabus. (SSS2)
• confidently manipulate a range of algebraic expressions as needed in a variety of contexts. (SSS3)
• confidently manipulate a range of Cartesian equations in two dimensions. (SSS4)
• understand and use complex numbers in a range of situations as appropriate to the syllabus. (SSS5)
• use matrices in a number of mathematical situations. (SSS6)
• reduce problems to a series of equations and inequalities and solve using linear programming techniques. (SSS7)
• apply mathematics to a variety of problems (SSS8)

• By the end of the module students will be able to:
• apply number in the tackling of numerical problems (KS1)
• demonstrate problem solving skills. (KS2)
• In class tests cover SSK1, SSK2, SSK3. SSK5, SSK6, SSS1-5, SSS8, KS1, KS2
• Invigilated test covers SSK 1-3, SSS 1-3, SSS8
• Examinations covers SSK4, SSK6, SSK5, SSS6, SSS7, SSS8 KS1, KS2
• Portfolio covers SSK1-6, SSS 1-8, KS1, KS2,

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Theory, initial concepts and techniques will be introduced during lectures.
• Much of the learning, understanding and consolidation will take place through the use of structured worksheets during seminars and students' own time.
• Small coursework tasks testing, developing or consolidating the previous week’s work will be set usually on a weekly basis. These tutor marked tasks allow rapid feedback and build confidence. Whilst the marks accumulate towards the overall portfolio mark, the tasks also perform a formative role enabling students to reflect on their own performance, identify areas of weakness, and practice some of the skills and techniques which will be required in the longer in-class tests and exam. Additionally, they ensure that students master specific skills to an appropriate level prior to their requirement in more complex tasks. As an example, an early task on differentiation might require students to differentiate four functions. Tutor feedback from this task ensures that students are ready to build on these skills when moving onto integration.
• Logarithms and prediction of relationships from graphs will be consolidated and assessed within a portfolio task.
• Ability to recall, select and use knowledge will be tested by four short class tests and an end of module invigilated exam in addition to the portfolio of tasks. The four class tests will focus on selected subsets of the content. In addition to their summative role, these tests also serve a formative function helping to prepare students for the end of module exam which will test a wider area of content

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Students will be given self-testing units on a weekly basis in the form of worksheets with answers and/or DUO quizzes. Portfolio tasks with a rapid marking turnaround fulfill a formative as well as summative role (See Section 14). Students have access to two or more mock papers and answers to help prepare for the class tests and the exam.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University