Mathematics 3C for Foundation Year, 10 fup

Aim

The aim of the course is to provide a basic training in mathematics and prepare students for university studies in mathematics. Completion of this course qualifies the corresponding Mathematics 3C. After the course students should be able to

• perform algebraic computations with real numbers
• solve equations, inequalities and systems of equations
• comprehend the concept of functions and conduct functional studies
• understand and apply the concept of derivative
• determine primitive functions and perform simple integral calculations with applications
• apply trigonometric relationships with the unit circle and use the theorems of triangle for an arbitrary triangle
• use programming as a tool for problem solving.

Content

Number systems, coordinate systems in the plane, algebraic expressions and operations, equations, systems of linear equations and inequalities, root equations, equations of straight lines, parabolas and circles, polynomial, polynomial equations and factor theorem, plane and solid geometry, the concept of functions, polynomial, power and exponential functions, exponentiation and logarithms, limits, rate of change and the derivative, differentiation of polynomial, power and exponential functions with applications, tangent and normal equations, analysis of the fundamental functions, determining the extreme values and sketching graph of a function, the unit circle, trigonometric concepts and angles in right triangles, theorems of triangle, primitive functions and integrals with applications.