Math 1050 Objectives
- Be able to solve equations. The types of equations you should be prepared to solve are : rational equations, linear equations, quadratic equations, radical equations, absolute value equations.
- Be familiar with the following principles for solving equations : addition principle, multiplication principle, Zero-Product principle, Principle of Powers.
- Know how to solve equations that are reducible to a quadratic.
- Be able to solve inequalities.
- Be able to approximate solutions to equations and inequalities using a graphing calculator.
- Be able to represent solutions to inequalities using interval notation.
- Be able to find the zeros of a function algebraically and with a graphing calculator.
- Know what a complex number is.
- Know how to do complex number arithmetic. Be able to represent all complex numbers in the form i.
- Be familiar with all of the subsets of Real Numbers. Be able to determine if a given number is Real, Rational, Irrational, Integer, Whole, or Natural.
- Be able to convert a radical to an exponent and vice versa.
- Be able to simplify radical and exponential expressions. Be familiar with the properties of radicals and exponents.
- Be able to determine the distance between two points in a plane.
- Be able to find the equation of a circle given enough information to determine the center and the radius of the circle.
- Be able to find the center and the radius of a circle given an equation of a circle.
- Know the definition of a function
- Know how to represent a function graphically
- Be able to determine if a graph is a function.
- Know how to find the domain and range of a function.
- Be able to evaluate functions at both numbers and expressions.
- Be able to determine an interval for which a function is increasing or decreasing.
- Be able to graph a conditional function.
- Know the slope-intercept and point-slope forms for equations of lines.
- Know the relationship between perpendicular and parallel lines.
- Be able to graph a line with and without the help of a graphing calculator.
- Know how to find the exact distance between two points.
- Know how to algebraically and graphically determine if a function is even or odd or neither.
- Know the graphs for the functions
- Know how to use transformations to graph functions.
- Given the graph of a function, determine the expression for the function using transformations and the basic functions.
- Be able to combine functions using addition, subtraction, multiplication, division, and composition.
- Be able to find the domain and range of combined functions.
- Know the definition of an inverse function.
- Know how to determine if a given function has an inverse.
- Know how to find the inverse of a function.
- Know how to determine the following characteristics for the graph of a quadratic: Vertex, open up or open down, increasing, decreasing, -intercepts.
- Be able to determine end behaviors for a polynomial.
- Be able to draw a rough sketch of the graph of a polynomial written as a product of linear factors.
- Be able to use long division or synthetic division to divide a polynomial and write the polynomial as .
- Be able to determine if a given value is a zero of a polynomial.
- Know the relationship between the following: zero's, linear factors, roots, x-intercepts.
- Be able to use the fundamental theorem of algebra to know the number of complex zeros for a given polynomial.
- Be able to factor a polynomial into a product of linear factors.
- Know the theorems concerning complex zeros and irrational zeros.
- Know the rational zeros theorem.
- Be able to use a calculator along with the rational zeros theorem to determine all rational zeros of a polynomial.
- Be able to determine the following parts of the graph of a rational function: horizontal asymptotes, oblique asymptotes, vertical asymptotes, x-intercepts, y-intercepts.
- Be able to solve story problems related to rational and polynomial expressions.
- Know the seven properties of an exponential function, and be able to draw a rough sketch for the graph of an exponential function.
- Be able to draw the graph of an exponential function using transformations.
- Know what a logarithm is and be able to solve logarithms with and without a calculator.
- Be able to draw a rough sketch for the graph of a logarithmic function.
- Know how to use the change of base formula.
- Know the properties of logarithms.
- Remember that logarithms and exponents with the same base are inverses of each other.
- Know how to solve exponential equations.
- Know how to solve logarithmic equations.
- Know how to approximate solutions to exponential and logarithmic equations using a graphing calculator.
- Know how to solve applications involving exponential and logarithmic expressions.
- Know how to solve exponential growth and radioactive decay problems.
- Know what it means to be a solution to a system of equations, and know how many solutions are possible.
- Know how to solve linear systems of equations.
- Know how to create an augmented matrix for a given linear system of equations.
- Be able to interpret and use the RREF form of a matrix to find the solution to a given system
- Know how to use a calculator to solve a linear system of equations.
- If a system of linear equations has an infinite number of solutions, be able to represent the solutions using a free variable.
- Be able to define the augmented and coefficient matrix for a given system of linear equations.
- Be able to solve a system of linear equations using a matrix.
- Be able to solve a system of nonlinear equations both algebraically and graphically.
- Be able to graph the solution set for linear and non-linear inequalities.
- Be able to graph the solution set for a system of inequalities
- Given a region in a plane, be able to determine a system of inequalities whose solutions set is the given region.
- Be able to evaluate and simplify expressions that are defined using factorials.
- Be able to evaluate an expression defined using Sigma Notation.
- Be able to express a sum using Sigma Notation.