From charlesreid1

See Math 102 Checklist

Outline

Chapter Outline

Chapter-by-chapter outline:

  • Module 1: Review
  • Module 2: Equations and Inequalities
  • Module 3: Graphs
  • Module 4: Functions and their Graphs
  • Module 5: Linear and Quadratic Functions
  • Module 6: Polynomial and Rational Functions
  • Module 7: Exponential/Log Functions
  • Module 8: Systems of Equations and Inequalities

Levitan Kolman Shapiro Outline

Midterm A

Module 1: Review (Levitan Chapter 1)

  • Real numbers
  • Algebra essentials
  • Geometry essentials
  • Polynomials
  • Factoring polynomials
  • Synthetic division
  • Rational Expressions
  • Radicals, nth roots, and Rational Exponents

Module 2: Equations and Inequalities (Levitan Chapter 2)

  • Linear equations
  • Quadratic equations
  • Radical equations and factorable equations
  • Solving inequalities
  • Equations and inequalities with absolute value
  • Applications (interest, rate, mixture)

Module 3: Functions (Levitan Chapter 3)

  • Rectangular coordinate system
  • Distance and midpoint formulas
  • Graphs of equations in 2 variables
  • Graphs of lines
  • Properties of functions
  • Graphing transformations
  • Inverse variation?
  • Modeling

Module 4: Linear and Quadratic Functions (Levitan Chapter 3 Linear functions/4 Quadratic functions)

  • Linear functions and properties
  • Linear models and functions from data
  • Quadratic functions and properties
  • Quadratic models and functions from data and descriptions
  • Inequalities with quadratics

Midterm B

Module 5: Polynomial and Rational Functions (Levitan Chapter 4 Polynomials/5 Rational functions)

  • Use my own notes:
  • Polynomial functions and properties
  • Polynomial models
  • Rational functions and properties
  • Graphs of polynomial and rational functions
  • Polynomial and rational inequalities

Module 6: Exponential/Log Functions (Levitan Chapter 6)

  • Composite functions, inverse functions
  • Exponential functions
  • Logarithmic functions
  • properties of logs and exponents
  • Exponential and log equations

Final Exam

Everything preceding, plus:

Module 7: SoE and Matrices (Levitan Chapter 7 SoE/8 Matrices)

  • Matrices and linear systems
  • Matrix operations and applications
  • Inverses of matrices
  • Determinants
  • Properties of determinants
  • Cramer's Rule

Sullivan Outline

Midterm A

Module 1: Review (Review Chapter) Math 102/Review

  • Real numbers
  • Algebra essentials
  • Geometry essentials
  • Polynomials
  • Factoring polynomials
  • Synthetic division
  • Rational Expressions
  • Radicals, nth roots, and Rational Exponents

Module 2: Equations and Inequalities (Chapter 1) Math 102/Chapter 1

  • Linear equations
  • Quadratic equations
  • Radical equations and factorable equations
  • Solving inequalities
  • Equations and inequalities with absolute value
  • Applications (interest, rate, mixture)

Module 3: Functions and their Graphs (Chapter 2, 3) Math 102/Chapter 2, Math 102/Chapter 3

  • Chapter 2 graphs
    • Distance/Midpoint formulas
    • Graphs of equations in 2 variables
    • Graphs and Lines
  • Chapter 3: Functions and their Graphs (Chapter 3) Math 102/Chapter 3
    • Functions
    • Graphs of functions (already covered in ch 2??)
    • Properties of functions
    • Library of functions, piecewise functions
    • Graphing transformations
    • Building functions (modeling)

Module 4: Linear and Quadratic Functions (Chapter 4) Math 102/Chapter 4

  • Linear functions and properties
  • Linear models and functions from data
  • Quadratic functions and properties
  • Quadratic models and functions from data and descriptions
  • Inequalities with quadratics

Midterm B

Module 5: Polynomial and Rational Functions (Chapter 5) Math 102/Chapter 5

  • Polynomial functions and models
  • Properties of rational functions
  • Graphs of rational functions
  • Polynomial and rational inequalities
  • Real zeros of polynomials

Module 6: Exponential/Log Functions (Chapter 6) Math 102/Chapter 6

  • Composition functions
  • One to one functions and inverse functions
  • Exponential functions
  • Logarithmic functions
  • Properties of logs
  • Log and exponential equations
  • Financial models
  • Exponential growth and decay
  • Logistic growth and decay
  • Building log/exp models


Module 7: Systems of Equations and Inequalities (Chapter 8) Math 102/Chapter 8

  • Systems of linear equations: substitution, elimination
  • Systems of linear equations: matrices
  • Systems of linear equations: determinants
  • Matrix algebra

Objective Outline

Chapter 1 Objectives

You should be able to do the following...

Section 1.1:

  • Solve a linear equation
  • Solve equations leading to linear equations
  • Solve problems modeled by linear equations

Section 1.2:

  • Solve quadratic equation by factoring
  • Solve quadratic equation by completing the square
  • Solve quadratic equation using quadratic formula
  • Solve problems modeled by quadratic equations

Section 1.4:

  • Solve radical equations
  • Solve equations quadratic in form
  • Solve equations by factoring

Section 1.5:

  • Use interval notation
  • Use properties of inequalities
  • Solve inequalities

Section 1.6:

  • Solve equations involving absolute value
  • Solve inequalities involving absolute value

Section 1.7:

  • Translate verbal descriptions into mathematical expressions
  • Solve interest problems
  • Solve mixture problems
  • Solve uniform motion problems

Chapter 2 Objectives

Section 2.1:

  • Use the distance formula
  • Use the midpoint formula

Section 2.2:

  • Graph equations by plotting points
  • Find intercepts from a graph
  • Find intercepts from an equation
  • Test an equation for symmetry with respect to the x-axis, the y-axis, and the origin
  • Know how to graph key equations

Section 2.3:

  • Calculate and interpret the slope of a line
  • Graph lines given a point and a slope
  • Find the equation of a vertical line
  • Use the point-slope form of a line
  • Write equation of a line given two points, identify horizontal lines
  • Write equation of a line in slope-intercept form
  • Identify slope and y-intercept of line from its equation
  • Graph lines written in general form using intercepts
  • Find equations of parallel lines
  • Write equations of perpendicular lines

Chapter 3 Objectives

Section 3.1:

  • Determine whether a relation represents a function
  • Find the value of a function
  • Find the domain of a function defined by an equation
  • Form the sum, difference, product, and quotient of two functions

Section 3.2:

  • IDentify the grpah of a function
  • Obtain information from or about the graph of a fucntion

Section 3.3

  • Determine even and odd functions from a graph
  • Identify even and odd functions from the equation
  • Use a graph to determine where a function is increasing or decrasing
  • Use graph to locate local min max
  • USE grpah to locate abs min miax
  • Use graphing utility to locate approx local min max
  • Find average rate of change of function

Section 3.4:

  • Graph functions listed in library of functions
  • Graph piecewise defined functions
  • Graph functions using vertical and horizontal shifts
  • Graph functions using compressions and stretches
  • Graph functions using reflection about x-axis or y-axis
  • Build and analyze functions

Chapter 4 Objectives

Section 4.1:

  • Graph linear functions
  • Use average rate of change to identify linear functions
  • Determine whether linear function is increasing, decreasing, or constant
  • Build linear models from verbal descriptions

Section 4.2:

  • Draw and interpret scatter diagrams
  • Distinguish between linear and nonlinear relations
  • Use graphing utility to find line of best fit

Section 4.3:

  • Graph a quadratic function using transformations
  • Identify the vertex and axis of symmetry of quad functions
  • Graph quadratic functions using vertex, axis, and intercepts
  • Find quadratic function given its vertex and one other point
  • Find the max or min value of a quadratic function

Section 4.4:

  • Build quadratic models from verbal descriptions
  • Build quadratic models from data

Section 4.5:

  • Solve inequalities involving a quadratic function

Chapter 5 Objectives

Section 5.1:

  • Identify polynomial functions and their degree
  • Graph polynomial functions using transformations
  • Identify the real zeros of a polynomial function and their multiplicity
  • Analyze the graph of a polynomial function
  • Build cubic models from data

Section 5.2:

  • Find the domain of a rational function
  • Find the vertical asymptotes of a rational function
  • Find the horizontal or oblique asymptote of a rational function

Section 5.3:

  • Analyze the graph of a rational function
  • Solve applied prob.ems involving rational functions

Section 5.4:

  • Solve polynomial inequalities
  • Solve rational inequalities

Section 5.5:

  • Use the remainder and factor theorems
  • Use the rational zeros theorem to list the potential rational zeros of a polynomial function
  • Find the real zeros of a polynomial funciton
  • Solve opoynoial equations
  • Use the Theorem for Bounds on Zeros
  • Use intermediate value theorem

Section 5.6:

  • Use the conjugate pairs theorem
  • Find a polynomial function with specified zeros
  • Find the complex zeros of a polynomial

Chapter 6 Objectives

Section 6.1:

  • Form a composite function
  • Form the domain of a composite function

Section 6.2:

  • Determine whether a function is one-to-one
  • Determine the inverse of a ffunction defined yb a map or a set of ordered pairs
  • Obtain the graph of the inverse funciton from the graph of the funcitno
  • Find the inverse of a funciton defined by an equation

Section 6.3

  • Evaluate exponential functions
  • Grha exp functions
  • Define e

8 Solve exponential equations

Section 6.4

  • Change exp statements to log statements and log statements to exp statements
  • Evaluate log expressions
  • Determine domain of log function
  • Graph log functions
  • Solve log equations

Section 6.5:

  • Work with the properties of logs
  • Write a log expression as a sum or difference of logs
  • Write a log expression as a single log
  • Evaluate logs whose base is neither 10 nor e

Section 6.6:

  • Solve log equations
  • Solve exponential equations
  • Solve log and exponential equations using a graphing utility

Section 6.7:

  • Determine the future value of a lump sum of money
  • Calculate effective rates of return
  • Determine the present value of a lump sum of money
  • Determine the rate of interest or time required to double a lump sum of money

Section 6.8:

  • Find equations of populations obeying law of uninhibited growth
  • Find equations of populations obeying law of decay
  • Use Newton's Law of Cooling
  • Use logistic models

Section 6.9:

  • Build exp model from data
  • Build log model from data
  • build logistic model from data

Chapter 8 Objectives

Section 8.1:

  • Solve systems of equations by substitution
  • Solve systems of equations by elimination
  • Identify inconsistent/impossible linear systems
  • Express solution of system of dependent equations containing two variables
  • Solve systems of three equations containing three variables
  • Identify incosnistent ssytems of equations with 3 variables
  • Express solution of system of dependent equations containing three variables

Section 8.2:

  • Write augmented matrix of system of linear equations
  • Write the system of equations from augmented matrix
  • Perform row operations on matrix
  • Solve system of linear equations using matrix

Section 8.3

  • Evaluate 2x2 determinant
  • Use Cramer's rule to solve system of equations with two vars
  • Evaluate 3x3 determinant
  • Use Cramer's rule to solve a 3x3 system
  • Know the properties of determinants

Section 8.4

  • Find sum and diff of two matrices
  • Find scalar multiples of a matrix
  • Find product of 2 matrices
  • Find inverse of a matrix
  • Solve system of linear equations using an inverse matrix

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