A combination of different instructional methods will be used in order to balance instructional efficiency with individual student needs. Group instruction, individual assistance in lab tutorial or scheduled appointments and student-directed learning will be selected where appropriate and possible.
Trigonometry
- radian measure
- reciprocal trigonometric ratios
- graphs of sine, cosine, and tangent functions
- period, amplitude, domain, range
- graphing techniques applied to trigonometric functions
- trigonometric identities
- conditional trigonometric equations
Quadratic Relations
- absolute value equations and inequalities
- distance, midpoint formula
- geometric derivation of lines, circles and parabolas
- the hyperbola and its graph
- standard forms of all conic sections
- general form and standard form
- graphs of systems of equations and inequalities in two variables
- solving quadratic systems
- applications of quadratic relations and systems
Exponential and Logarithmic Functions
- inverse functions
- the exponential function
- the logarithmic function
- rules of operating with logarithms
- solving exponential and logarithmic equations
- applications of exponential and logarithmic functions
Polynomials
- polynomial functions and their graphs
- remainder and factor theorems
- solving polynomial equations and inequalities
- approximating real roots of polynomial equations
- applications of polynomial functions
Sequences and Series
- describing sequences algebraically
- arithmetic sequences and series
- geometric sequences and series
- infinite geometric series
- sigma notation
- applications of sequences and series
Introduction to Calculus
- limits and limit notation
- evaluating the limits of rational functions
- slope of a tangent line to a curve
- equation of a tangent line at a point
- definition of a derivative
- rules for finding derivatives
- instantaneous velocity
- use of the derivative to graph polynomial functions
- maximum and minimum values of quadratic functions
- applications of maximum and minimum values
Problem Solving
- emphasize reasoning skills
- require concepts from any strand or grade level
- involve several steps
- integrate the use of several strands of topics
The aims of the course are for students to:
- extend experience with algebra, geometry and trigonometry;
- extend ability to graph to include hyperbolas, conic sections and trigonometric functions;
- gain facility in solving exponential and logarithmic equations, solving quadratic systems, polynomial equations and inequalities and arithmetic and geometric sequences and series;
- gain experience with calculus through the use of derivatives, tangent lines, and maximum-minimum quadratic functions;
- increase reasoning skills by solving application problems of quadratic relations and systems, exponential and logarithmic functions, sequences and series, maximum and minimum values, and to integrate the use of several of the abovementioned topics.
Evaluation will be based on examinations and assignments in accordance with college policy. Details regarding the number and weighting of individual components will be announced in a “Course Information” handout at the beginning of the semester.
Textbooks and Materials to be Purchased by Students
Required Text: Kelly, Brendan et al. Mathematics 12: Student Text. Addison-Wesley or suitable alternative. (B.C. Edition)
MATU 0411 or permission of instructor