The following is a list of Student Learning Outcomes for College Algebra:
Make sure you have accomplished all of these objectives for your final exam.
1. The student will review the rules of real and complex numbers; adding, subtracting, multiplying and dividing and factoring polynomials; review the laws of exponents; simplifying radicals; and simplify polynomials, solve linear, fractional, and quadratic equations; solve equations with variables under radicals by clearing exponents; use a "u" to help solve an equation; use factoring with fractional exponents to solve equations; and graph inequalities using intersections and unions, graph rational and quadratic inequalities, and be capable of using these concepts in conjunction with subsequent material.
2. The student will work on learning to solve word problems all semester.
3. The student will know and be able to find the x and y intercepts of a relation and graph it by plotting points and using symmetry. The student will be able to write the equation of a circle in standard form and be able to determine the center and the radius of the circle from this form. 4. The student will be able find and use the slope of a straight line, the slopes of parallel or perpendicular lines, and the point-slope, slope-intercept, and standard forms for the equation of a straight line.
5. Students should be able to determine the domain and the range of all graphs.
6. The student will be able to determine which relations are functions; graph functions including the use of translations and reflections; find the domain and range of all functions; evaluate functions at specified values, determine if a function is one-to-one.
7. The student will be able to graph a quadratic function, specifying the vertex, axis of symmetry, maximum and minimum values, and intercepts and write the equation for the parabola in standard form.
8. The student will be able to graph piecewise or step functions, absolute value functions and relations, and other graphs by making a "t" chart.
9. Students will be able to graph rational functions, determine asymptotes, x and y intercepts, domain and range for rational functions. Students will be able to determine if a rational function has a hole in it and name the point where that hole occurs.
10. Students will be able to combine functions by addition, subtraction, multiplication, division, and composition; and find the inverse of a function.
11. The student will be able to graph polynomial functions. The students will be able to divide a polynomial by a binomial using synthetic division and use the remainder and factor theorems and the fundamental theorem of algebra to find the roots of a polynomial or, given the roots, determine the polynomial.
12. The student will be able to manipulate and solve exponential and logarithmic functions, including common and natural logarithms, and related application problems and be able to graph these functions. The student will be able to use a calculator to evaluate logarithms.
13.. The student will be able to solve a system of equations by the use of matrices. The student will be able to perform algebraic operations on matrices. The student will be able to find determinants and use Cramer's Rule and Gaussian Elimination.
14. Students must be able to use a graphing calculator to graph functions, determine asympotes, turning points, name relative maxiums and minimums, zeros and holes in graphs. Students should know how to use the 2nd Calc menu and the table menu.