## FOUNDATION MATHEMATICS

 SHE Level 1 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M1G112790 Module Leader Faridon Amdjadi School INTO Subject INTO Trimesters A (September start) B (January start)

### Pre-Requisite Knowledge

Foundation Programme Entry Requirements

### Summary of Content

This module provides a grounding in a range of mathematical topics at foundation level including algebraic manipulation, geometry, trigonometry, differential calculus and integral calculus.

### Syllabus

Arithmetic: The real number system. Basic arithmetic operations and their priority (BODMAS). Arithmetic involving fractions. Functions: Definition of a function. Linear, quadratic, exponential and logarithmic functions. Algebra: Manipulation of formulae. Solution of linear equations, simultaneous linear equations and quadratic equations. Laws of indices and logarithms. Solution of equations involving basic mathematical functions such as exponential and logarithmic. Co-ordinate Geometry: The Oxy-axes system. Graphs of functions. Equations and graphs of straight lines, parabolas and circles. Trigonometry: Angular measures. Definition of the trigonometric functions sine, cosine and tangent, and their inverses. Calculations involving right-angled triangles. Calculations involving scalene triangles (sine rule and cosine rule). Simple trigonometric identities. Graphs of the sine, cosine and tangent functions. Differential Calculus: Definition of the derivative of a function. Interpretation of the derivative of a function. Determination of the derivatives of x^n , n integer or fractional. Derivatives of simple functions reducible to sums and differences involving x^n . Integral Calculus: Indefinite integration of simple functions. Evaluation of simple definite integrals. Geometrical interpretation of definite integrals.

### Learning Outcomes

On completion of this module the student should be able to:- Algebraically manipulate basic mathematical expressions- Solve single and simultaneous linear equations, quadratic equations and basic nonlinear equations- Describe the Cartesian co-ordinate system, and use it to represent lines and curves- Sketch the graphs of basic algebraic equations including those of the straight line, parabola and circle- Determine the equations from the graphs of straight lines, parabolas and circles- Perform length and angle calculations involving triangles (right-angled and scalene)- Differentiate simple functions- Obtain indefinite and definite integrals of basic functions

### Teaching / Learning Strategy

This module will be based on lectures, tutorials and self learning. Lectures will demonstrate mathematical methods and indicate approaches to analytical problem solving. Techniques will be practiced under directed learning and tutorials. Formative assessments will be adminstered on a topic by topic basis to provide diagnostic feedback on progress.

Croft A and Davison R (2006) "Foundation Mathematics" (4th ed.) Prentice Hall "Mathcentre" web site: http://www.mathcentre.ac.uk/

### Transferrable Skills

Numeracy Skills Critical thinking and problem solving; I T Skills Cognitive/intellectual skills; Knowledge and understanding in the context of the subject; Independent working; Communication skills, written, oral and listening

### Module Structure

Activity Total Hours
Lectures (FT) 36.00
Tutorials (FT) 60.00
Independent Learning (FT) 84.00
Assessment (FT) 20.00

### Assessment Methods

Component Duration Weighting Threshold Description
Exam (School) n/a 50.00 35% exam by school
Exam (School) n/a 25.00 35% CLASS TEST
Exam (School) n/a 25.00 35% CLASS TEST