 # Course Outline for College Algebra

 Dates Sections covered and topics 1 1 1 1 11 8/23 - 8/27 R.1 real numbers , interval notation, absolute value R.2 integers as exponents, scientific notation, order of operations R.3 polynomials, addition and subtraction , multiplication R.4 terms with common factors, special factorizations R.5 simplifying, multiplying, and dividing rational expressions, adding and subtracting rational expressions R.6 simplifying radical expressions , rationalizing denominators or numerator 2 2 2 2 8/30 - 9/3 R.7 linear and quadratic equations 1.1 definition of function, domain and range of function, vertical line test, finding domains of functions 1.2 equations of horizontal and vertical lines, slope intercept form, average rate of change, point slope form 1.3 using graphing calculator to fit data to a linear function, correlation coefficient 3 3 9/7 - 9/10 Labor Day on 9/6 1.4 finding relative maximum and relative minimum values of a function graphing piecewise functions, algebra with functions, finding the domain of sums, products and quotients 1.5 testing a graph for x-axis symmetry, y-axis symmetry and symmetry about the origin, testing if a function is even or odd or neither, vertical and horizontal translations of graphs, vertical stretching and shrinking of graphs, horizontal stretching and shrinking of graphs, reflections across the x-axis and across the y-axis 4 9/13 - 9/17 1.6 direct variation and finding the constant of proportionality , inverse variation and finding the constant of proportionality, combination of inverse and direct variation 1.7 distance formula for points in the plane, midpoint formula, equation of a circle in standard form 2.1 algebraically solving for zero of a linear function, solving equations on calculator by finding the zero of a function, by finding intersecting pt Exam 1 on 9/17 4 4 5 9/20 - 9/24 2.2 real and imaginary parts of complex numbers, addition, subtraction and multiplication of complex numbers, complex conjugation, dividing one complex number by another 2.3 using completing the square to solve quadratic equations, using the quadratic formula: discriminant determines types of answers, solving equations which are quadratic in form 2.4 graphing quadratic functions in vertex form , in standard form: finding the vertex, shape and line of symmetry, max-min word problems 5  5 6 9/27 – 10/1 2.6 solving rational equations, radical eqns and eqns with absolute value 2.7 multiplication principle for inequalities, solving linear inequalities, solving conjunction(and) and disjunction(or) type inequalities 3.1 degree and leading coefficient of a polynomial function, leading term test for general shape of the graph, maximum number of intercepts and turning points for a polynomial of degree n, using Intermediate Value Theorem to estimate the location of zero 6 6 77 10/4 - 10/810/11 -10/15 3.2 doing long division: identifying dividend, divisor, quotient and remainder and interpreting the result, the remainder theorem and factor theorem 3.3 multiplicity of zeros, finding real and complex zeros of polynomial functions by factoring, complex zeros of polynomials with real coefficients occur in conjugate pairs, rational zeros theorem 8 10/11 - 10/15 3.4 finding the domain of a rational function, finding equations of vertical asymptotes, finding equation of horizontal asymptote, oblique asymptote occurs when degree numerator is 1 more than degree of denominator 3.5 using sign charts and test points to solve polynomial and rational inequalities, using the graphing calculator to solve inequalities 8 9 10/18 - 10/22 4.1 finding the composition of functions, finding the domain of a composite function, writing a function as a composition, interchanging x and y coordinates to graph the inverse relation, using the horizontal line test to decide if a function is one to one, reflecting across line y=x to graph the inverse function, restricting the domain when the function is not one to one to define an inverse fn 4.2 graphs of exponential function Exam 2 on 10/22 9 10 10/25 - 10/29 4.3 definition of logarithmic function , converting a logarithmic to an exponential equation and vice versa, domain logarithm functions, natural logarithms, using the change of base formula to compute logarithms 4.4 using rules for logarithm of a product, quotient and power to other properties of logarithms 4.5 solving simple exponential equations, solving exponential equations by taking a logarithm on both sides, solving logarithmic equations 1010 11 1111 10/25 - 10/29 4.6 exponential growth and doubling time, exponential decay and half life 5.1 solving system of two equations and two unknowns: substitution and elimination methods 5.2 solving system of three equations 12 11/8- 11/12 5.3 augmented matrix for a system of linear equations, elementary row operations, recognizing row reduced echelon form, Gauss-Jordan method of solving systems of equations 5.4 addition, subtraction, and scalar multiplication of matrices, additive inverse of a matrix, the zero matrix, knowing when you can multiply matrices together, matrix multiplication 12 13 11/15-11/19 5.5 the identity matrix, definition of the multiplicative inverse of a square matrix, Gauss-Jordan method of finding an inverse (if it exists), using inverses to solve matrix equations 5.6 using geometric linear programming techniques to solve system of linear equations 13 14 11/22 - 11/23 Exam 3 on 11/22 Thanks giving this week 15 11/29- 12/3 5.7 decomposing rational expressions into partial fractions Review Dead Week Common Final Exam on December 4 at 2:00 PM
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