A certain background knowledge is strongly recommended for PUMP Level 1. In general terms, a student must have a working knowledge of basic high school algebra, linear and quadratic functions, and elementary analytic geometry. Students who do not have this background may still enrol and can do well if they work hard.
This course focuses on the mathematical background needed for entry-level university science and math courses, expanding and developing relevant skills and techniques of reasoning.
Topics to be covered include:
- Fundamental algebraic background: sets, operations and properties; Numbers, fractions, exponents and rational expressions; Factorization and reduction; Completing the square; Binomial expansion; Operations with general algebraic expressions.
- Equations, inequalities and systems: equations in quadratic form; Absolute value, rational and radical equations; General equation solving; Polynomial, rational and absolute value inequalities; General solving and graphing of algebraic inequalities; Systems of linear equations; Gaussian elimination; Non-linear systems and systems containing inequalities; General system solving; Setting up equations; inequalities and systems; Working with word problems; Applications.
- Basic trigonometry: The number p; Radians and degrees; Trigonometric functions and their graphs; Generalizations and inverse trigonometric functions; The algebra of trigonometric identities and equations; Right triangle trigonometry; The law of sines and the law of cosines; Applications.
- Exponential and logarithmic functions: the number e; Exponential functions and their graphs; The inverse of an exponential function; Logarithmic functions and their graphs; Properties of the logarithms; Exponential and logarithmic equations and inequalities; Exponential growth and decay.
- Analytic geometry and introductory calculus: rectangular co-ordinates; Basic formulas, equations and graphing; Lines, parabolas, and circles; The tangent line problem. Limits.
- Additional topics (if time permits): Sequences and series; Complex numbers and vectors; Mathematical induction; Matrices and determinants.