### IA112-3-PS : Essential Mathematics

The module covers the mathematical skills needed to proceed to any degree course where knowledge of mathematics to A-level standard is required. The syllabus initially covers some basic mathematics of number work, Equations and Curve Sketching to ensure that all students have acquired basic skills before proceeding on to more advanced topics. The syllabus then expands to cover Trigonometry, Calculus, Ordinary Differential Equations, Further Algebra and Series, with lectures developing in range and content. The associated work in classes will help students develop Mathematical problem solving skills and be apply them to problems in other relevant subject areas such as economics, financial maths and engineering.

Aims

1. To provide students from a wide range of educational backgrounds with a broad understanding of basic and essential mathematical skills.
2. To demonstrate how Essential Mathematics knowledge can be applied in various practical applications, e.g. economics, finance and engineering contexts.
3. To give students the opportunity to engage actively with activities and class worksheets provided during lectures and classes.
4. To develop the ability to acquire knowledge and skills from lectures, from text books and class work exercises, and from the application of theory to a range of problems.
5. To enable students to develop their problem solving skills by using relevant and appropriate mathematical techniques.

Learning Outcomes

On successful completion of the module students are expected to be able to:

1. Use and understand basic arithmetic and algebra in problem-solving.
2. Solve linear single and simultaneous equations; linear inequality and regions; quadratic equations; functions.
3. Sketch linear and quadratic curves; formulas; rules of logarithm.
4. Understand and use differentiation; gradients of curves; equation of tangent and normal.
5. Solve and sketch cubic, log, exponential and trigonometric equations and functions; trigonometric identities.
6. Understand and use Integration; rules of integration; area under the curve.
7. Understand and solve basic ordinary differential equations; understand and solve quadratic simultaneous equations and higher-order inequalities.
8. Understand sequences and series; arithmetic and geometric series; solve and sketch Modulus equations and functions.

Syllabus

Essential arithmetic and number work
Algebra: algebraic expressions; solution of linear, simultaneous, quadratic and cubic equations; logarithms; inequalities; trigonometric ratios and functions for any angle
Graphical representation of functions and inequalities; curve sketching; graphical solution of equations; Tangents and Normals.
Calculus: differentiation and integration of linear, trigonometric, logarithmic and exponential functions, including function of a function, products and quotients; second derivative; turning points; applications of differentiation; methods of integration; definite integration; areas under curves.
Trigonometry and trigonometric identities.
Ordinary Differential equations and various methods of solving them.
Sequences and series: arithmetic and geometric progressions; summation and convergence of a series; binomial theorem

Assessment

A one-hour in-class test in week 22 (25% of coursework).
A two-hour in-class test in week 34 (62.5% of coursework).
Participation mark (12.5% of coursework) – Lab exercises throughout the terms.
A 2.5 hour-exam during summer examination period (60% of the module mark).

Non-assessed coursework

At the beginning of the Autumn Term students undergo a diagnostic test. Two weeks before each test there is a formative mock test followed by feedback.

40% coursework and 60% final exam
Pass mark: 40%