MAT111 Course Outline
Aims and learning objectives:
This pre-calculus course consolidates and builds upon school mathematics.
It will lead the student to a better understanding of algebraic concepts and
techniques.
Course synopsis:
Basic algebra
Introduction to functions and their graphs
Trigonometry
Complex numbers
MAIN REFERENCE:
INTRODUCTORY MATHEMATICS, University of Botswana, Customized
textbook based on Ron Larson, Pre-calculus.
Course content:
1. Number systems: Natural numbers, Integers, Real numbers, powers,
exponents.
2. Radicals (Surds)
3. algebraic and polynomials expressions. Polynomials & factoring, rational
expressions, multiplication and division of rational expressions,
simplification.
4. Domain, range, sketch and graph, max & min, linear functions, coordinate
plane, distance, midpoint, equation of circle, shifting, reflecting, graph
stretching, odd and even functions.
5. Algebra and composition of functions. Inverse functions, types of
functions: Injective (into=1-1), surjective (onto). Linear equations:
Simultaneous 2 equations in 2 unknowns. Roots=zeroes, double zero, up
and down, intersection of graphs.
6. Quadratic equations, equations that reduce to quadratics (equations
involving indices and logarithms), relation between roots and coefficients.
Aims and learning objectives:
This pre-calculus course consolidates and builds upon school mathematics.
It will lead the student to a better understanding of algebraic concepts and
techniques.
Course synopsis:
Basic algebra
Introduction to functions and their graphs
Trigonometry
Complex numbers
MAIN REFERENCE:
INTRODUCTORY MATHEMATICS, University of Botswana, Customized
textbook based on Ron Larson, Pre-calculus.
Course content:
1. Number systems: Natural numbers, Integers, Real numbers, powers,
exponents.
2. Radicals (Surds)
3. algebraic and polynomials expressions. Polynomials & factoring, rational
expressions, multiplication and division of rational expressions,
simplification.
4. Domain, range, sketch and graph, max & min, linear functions, coordinate
plane, distance, midpoint, equation of circle, shifting, reflecting, graph
stretching, odd and even functions.
5. Algebra and composition of functions. Inverse functions, types of
functions: Injective (into=1-1), surjective (onto). Linear equations:
Simultaneous 2 equations in 2 unknowns. Roots=zeroes, double zero, up
and down, intersection of graphs.
6. Quadratic equations, equations that reduce to quadratics (equations
involving indices and logarithms), relation between roots and coefficients.
