Algebra & Trigonometry

At the end of the course, the successful student should be able to:

• solve word problems involving linear and quadratic equations (applications will include:  geometry problems, work problems, motion problems, mixture problems)
• graph relations and functions on the Cartesian coordinate system (including linear, quadratic, polynomial, y=1/x, logarithmic, exponential, trigonometric, absolute value, radical and piecewise functions)
• define a function
• determine domains and ranges of functions and represent them using interval notation
• use the vertical line test to determine whether a relation is a function
• classify functions as periodic, one-to-one, piece-wise, or continuous
• identify maxima, minima, and intervals of increase/decrease by looking at the graph of a function
• apply function transformations (translations, dilations and reflections)
• find and/or graph the inverse of a function
• evaluate composite functions
• use linear functions which model real-life situations to solve problems
• find the vertex of a parabola by completing the square
• use quadratic functions which model real-life situations to solve problems including optimization problems
• solve quadratic inequalities both analytically and graphically, and express the solution in interval notation
• graph polynomial functions
• demonstrate an understanding of the Remainder and Factor Theorems
• divide polynomials using long division and synthetic division
• solve factorable polynomial equations
• graph exponential and logarithmic functions with any base and be able to identify axis-intercepts, asymptotes, domain and range
• understand the inverse relationship between exponential and logarithmic functions
• convert between logarithmic and exponential forms
• evaluate simple logarithms without using a calculator
• change logarithms from one base to another
• use the properties of logarithms to simplify expressions
• solve logarithmic and exponential equations with any base
• define sine, cosine, tangent, secant, cosecant and cotangent in terms of:  right triangles, points-in-the-plane and unit circles
• use a calculator to find the trig values for any acute angle, and given the function value for an acute angle, find the angle
• solve right-triangles and word problems involving right-triangles using trigonometry
• convert from degree measure to radian measure and vice versa
• identify special angles on a unit circle
• use reciprocal and Pythagorean identities to simplify trigonometric expressions
• solve simple trigonometric equations giving only the acute angle solution
• graph the sine and cosine functions
• from the graph of a trig function determine the period, amplitude, domain, range and phase-shift
• solve systems of equations in two variables using substitution or elimination methods
• solve systems of equations in three variables using the substitution method
• distinguish between sequences and series, arithmetic sequences, arithmetic series, geometric sequences, geometric series, infinite geometric sequences, recursively defined sequences
• describe a given sequence algebraically
• use formulas to find terms,  positions of terms in sequences or series, arithmetic or geometric means, sums of series and sums of infinite series
• use sigma notation to describe series
• evaluate series designated in sigma notation