Module FOUN0481: CORE FOUNDATION MATHS FOR BUSINESS

Department: Foundation Year

FOUN0481: CORE FOUNDATION MATHS FOR BUSINESS

Prerequisites

• None.

Corequisites

• None.

Excluded Combination of Modules

• FOUD0041 Core Foundation Maths

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 extend knowledge of Cartesian coordinates in 2 dimensions to include equations of circles and lines.

Content

• Quadratic equations, factorisation, graphs, quadratic formula.
• Trigonometry, sine, cosine, tangent.
• 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)
• Minimum tour (Postman problem)
• Critical Path Analysis
• Cartesian equations in 2 and 3 dimensions of straight lines and perpendicular lines.

Learning Outcomes

• By the end of this module students will know how to:
• define sine, cosine and tangent (SK1)
• use logarithms to solve problems and to predict relationships from graphs (SK2)
• differentiate a number of different types of functions (SK3)
• give standard cartesian equations for lines (SK4)
• solve a range of predictable problems in Discreet Mathematics (SK5)

• By the end of this module the student will have acquired the skills to be able to:
• recall, select and use knowledge of appropriate differentiation techniques as needed in a variety of contexts (SS1)
• confidently manipulate a range of algebraic expressions and use a range of techniques as required in a variety of contexts and in problems appropriate to the syllabus (SS2).
• confidently manipulate a range of Cartesian equations in 2 dimensions (SS3)
• apply mathematics to a variety of problems (SS4)

• By the end of the module students will be able to:
• apply number both in the tackling of numerical problems (KS1)
• demonstrate problem solving skills (KS2)
• Portfolio with assess some of SK1-SK5, SS1-SS4, KS1-KS2
• Inclass tests will assess some of SK1-SK4, SS1-SS4, KS1-KS2
• Invigilated test will assess: SK1-SK5, SS1-SS4, 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 and seminars.
• Much of the learning, understanding and consolidation will take place through the use of structured exercise during seminar and tutorial sessions and students own time.
• Small coursework tasks testing, developing or consolidating the previous weeks work will be set usually on a weekly basis. These tutor marked tests 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 invigilated test. Additionally, they ensure that students master specific skills to an appropriate level prior to their requirement in more complex tasks. As an example, an earlier task on differentiation might require students to differentiate 4 functions. Tutor feedback from this task ensures that students are ready to build on these skills when moving onto integration.
• Ability to recall, select and use knowledge will be tested by 2 short in-class tests (which will be administered as 15 minute sub-tests) and an end of module test in addition to the portfolio of tasks. The 2 class tests will focus on selected sub-sets 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 test which will test a wider area of content.
• Logarithms and prediction of relationships from graphs will be consolidated and assessed within a coursework task.

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 a summative role (see section 14.). Students have access to 2 or more mock papers and answers to help prepare for the end of module test.

■ 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