Math114 College Math & Statistics
Instructor: Dr. Carla C. Morris

TEXT: College Mathematics and Statistics:

               Custom Edition for University of Delaware

The following list of objectives is designed to give you some guidance at what topics are important from the various sections we will cover from the book.  These objectives are some of the key concepts that will be discussed for each section.  When you take exams in this course you must show me your work to earn full credit for a problem.  Correct answers with no work shown will be penalized. Partial credit will be given on problems; therefore showing your work is vital to your grade and it also allows me to better determine where your weakness may be if you need assistance with any of the material.

MATH114  OBJECTIVES

SECTION 1.1    LINEAR EQUATIONS

1)      Classify an equation as an identity, conditional equation, or inconsistent.
2)      Solve linear equations in one variable.
3)      Solve an equation involving fractional expressions. (You can multiply by LCD to eliminate the fractions if you do not feel comfortable working with fractions)
4)      Formulate and solve linear application problems.

SECTION 1.2    MATHEMATICAL MODELING

1)      Construct a mathematical model.
2)      Model and solve percent and distance problems.
3)      Model and solve mixture problems.
4)      Use common formulas to solve geometry problems.
5)      Solve for a particular variable of interest in common formulas.

REVIEW OF FACTORING (notes given in class)

1)      Determine the Greatest Common Factor (GCF) of an expression.
2)      Factor sums or differences of squares or cubes. (I will give you cube formulas)
3)      Factor simple trinomials of the form x2 + bx + c.
4)      Factor more complicated trinomials of the form ax2 + bx + c. (Trial and error)
5)      Factor four term expressions by using grouping.  

SECTION 1.3     QUADRATIC EQUATIONS

1)   Solve quadratic equations by factoring.
2)   Solve quadratic equations by applying the square root property.
3)   Construct and solve quadratic application problems.

SECTION 1.4     THE QUADRATIC FORMULA

1)   Understand the development of the quadratic formula by completing the square.
2)   Use the discriminant to determine the number and types of solutions to a quadratic equation.
3)   Use the quadratic formula to solve quadratic equations.
4)   Use the quadratic formula to solve application problems.

SECTION 1.6    LINEAR INEQUALITIES

1)   Be able to use interval notation.
2)   Recognize bounded and unbounded intervals.
3)   Show half-open, open, or closed intervals on a number line.
4)   Solve and graph linear inequalities.
5)   Solve absolute value inequalities.
6)   Construct and use linear inequalities to solve application problems.  

SECTION 2.2 LINES IN THE PLANE

  1) Find the slope of a line.

  2) Determine the x and y intercepts of linear functions.

  3) Find the equation of a line given certain information.

  4) Sketch graphs of lines.

  5) Understand the various forms of a line include standard, point slope, and slope intercept. 

      A vertical line takes the form x = a, while a horizontal line takes the form y = b

  6) Know the relationship that exists between parallel and perpendicular lines.

Graph a linear function

Your graphs should adhere to the following guidelines:

 

SECTION 2.3    LINEAR MODELING AND DIRECT VARIATION

1)      Use a mathematical model to approximate a set of data points (regression)
2)      Construct a linear model to relate quantities that vary directly.
3)      Construct and use a linear model with slope as the rate of change.
4)      Use a scatter plot to find a linear model that fits a set of data.

The regression here will be minimal as we will cover it more in depth in the statistics portion of the course.

SECTION 2.4 FUNCTIONS

1) Understand what a relation is.
2) Determine if a relation is a function.
3) Understand function notation and how to evaluate a function at a particular value of x.
4) Determine the domain or the range of a function.

SECTION 2.5 GRAPHS OF FUNCTIONS

1)      Determine the domain and range of a function from its graph.
2)      Determine if a graph is a function by using the vertical line test.
3)      Describe interval where a graph increases or decreases.
4)      Determine the local extrema of a function from its graph.
5)      Graph step functions.
6)      Understand the symmetry of graphs and if they are even or odd functions.
7)      Be able to recognize or graph lines, parabolas, absolute value, cubes, square root, and greatest integer functions.

SECTION 3.1 QUADRATIC FUNCTIONS AND MODELS

1)      Determine the maximum or minimum value of a quadratic function.
2)      Be able to graph a quadratic (parabola) by determining the axis of symmetry, vertex, y intercept, and x intercepts. (Quadratic of the form ax2 + bx + c)
3)      Be able to graph a quadratic in standard form a(x − h)2 + k.
4)      Construct and use a quadratic model to solve application problems.

         Your graph should have at least five points to help determine the shape of the graph and   

          as a check of your computations.

SECTION 5.1   SOLVING SYSTEMS USING SUBSTITUTION

1)   Solve a system of equations by the method of substitution.
2)   Solve a system of equations graphically.
3)   Construct and use a system of equations to solve an application problem.

SECTION 5.2    SOLVING SYSTEMS USING ELIMINATION

1)   Solve a system of equations by the method of elimination.
2)   Interpret the solution of a linear system graphically.
3)   Construct and use a linear system to solve an application problem.

Understand the three types of systems (consistent and independent, dependent, and inconsistent) Note: The solution if it exists should be in the form of an ordered pair (x, y)

SECTION 5.3       SYSTEMS OF INEQUALITIES

1)   Sketch the graph of an inequality in two variables.
2)   Solve a system of inequalities.
3)   Algebraically determine the corner points to the graph of a system of inequalities.
4)   Construct and use a system of inequalities to solve an application problem.

SECTION 5.4       LINEAR PROGRAMMING

1)   Use Linear Programming to minimize or maximize an objective function.
2)   Understand the feasible region and consequences when it is unbounded.
3)   Use linear programming to optimize an application.
4)   Recognize the constraints in applications often place feasible region in quadrant I.

SECTION 4.1   INVERSE FUNCTIONS

1)   Determine whether a function has an inverse function. (Horizontal line test)
2)    Find the inverse of a function.
3)   Graph a function and its inverse function.

SECTION 4.2   EXPONENTIAL FUNCTIONS

1)   Evaluate an exponential function.
2)   Sketch the graph of an exponential function.
3)   Evaluate and sketch the graph of the natural exponential function.
4)   Use the common compound interest formulas.
5)   Use an exponential model to solve an application problem.

 

 SECTION 4.3   LOGARITHMIC FUNCTIONS

1)   Recognize and evaluate a logarithmic function with base a
2)   Sketch the graph of a logarithmic function.
3)   Recognize and evaluate the natural logarithmic function.
4)   Use a logarithmic model to solve an application problem.

SECTION 4.4 PROPERTIES OF LOGARITHMS

1)   Evaluate a logarithm using the change of base formula.
2)   Use properties of logarithms to evaluate and rewrite a logarithmic expression.
3)   Use properties of logarithms to expand or condense a logarithmic expression.
4)   Use logarithmic functions to model and solve application problems.

SECTION 4.5 SOLVING EXPONENTIAL AND LOGARITHMIC EQUATIONS

1)   Understand the strategies for solving exponential and logarithmic equations.
2)   Solve an exponential equation.
3)   Solve a logarithmic equation.
4)   Use an exponential or logarithmic model to solve application problems.

SECTION 4.6   EXPONENTIAL AND LOGARITHMIC MODELS

1) Use a model for exponential growth or decay.

RIGHT TRIANGLE TRIGONOMETRY HANDOUT

1)   Use the Pythagorean Theorem to determine a missing side of a triangle.
2)   Use the six definitions of the trigonometric functions (SOH CAH TOA).
3)   Be able to solve application problems such as angle of elevation.

UNIT CIRCLE TRIGONOMETRY HANDOUT

1)   Convert between degree and radian measure.
2)   Use the definition of the six trig functions, reference angles, and the quadrant location to determine trig values.
 

 
 MATH114 STATISTICS OBJECTIVES

 SECTION 1.1    WHAT IS STATISTICS?

1)      Identify variables in a statistical study.
2)      Distinguish between qualitative and quantitative variables.
3)      Identify variables measured on nominal, ordinal, ratio, or interval scales.
4)      Understand the concepts of populations, samples, parameters, and statistics.
5)      Understand the difference in descriptive and inferential statistics.

SECTION 1.2    RANDOM SAMPLES

1)      Understand what a simple random sample is.
2)       Understand the basics of different types of sampling techniques.

SECTION 2.1    FREQUENCY DISTRIBUTIONS, HISTOGRAMS, AND RELATED TOPICS

1)    Organize raw data
2)    Construct histograms, relative frequency histograms and ogives.
3)    Interpret graphs and understand distribution shapes.

SECTION 2.2   BAR GRAPHS, CIRCLE GRAPHS, AND TIME-SERIES GRAPHS

1)       Determine the types of graphs that are appropriate for different types of data.
2)      Construct bar graphs and pie charts.
3)      Interpret information displayed in various types of graphs.

SECTION 2.3    STEM-AND-LEAF DISPLAYS

1)   Understand how to construct a stem-and-leaf display.

SECTION 3.1    MEASURES OF CENTRAL TENDENCY:

                            MODE, MEDIAL, AND MEAN

1)   Compute the mean, median, and mode from raw data.
2)   Explain how the measures of central tendency are affected by extreme values.
3)   Compute a weighted average.

 
SECTION 3.2   MEASURES OF VARIATION

1)   Find the range, variance, and standard deviation.
2)   Understand the difference in the standard deviation of a sample and a population.

SECTION 3.3    PERCENTILES AND BOX-AND-WHISKER PLOTS

1)   Understand percentiles and quartiles
2)   Understand the basics of a box-and-whisker plot.

SECTION 4.1   SCATTER DIAGRAMS AND LINEAR CORRELATION

1)      Make a scatter diagram.
2)      Understand the basics of correlation.

SECTION 5.1     WHAT IS PROBABILITY?

1)   Assign probabilities to events
2)   Apply basic rules of probability.
3)   Understand the complement of an event.

SECTION 7.1   GRAPHS OF NORMAL PROBABILITY DISTRIBUTIONS

1)   Understand the properties of a Normal Curve.
2)   Understand the Empirical Rule and how to apply it.

SECTION 7.2   STANDARD UNITS AND AREAS UNDER THE STANDARD NORMAL DISTRIBUTION

1)      Understand z-scores
2)      Be able to convert raw data to z-scores
3)      Determine areas under the Standard Normal Curve.

SECTION 7.3   AREAS UNDER ANY NORMAL CURVE

1)   Compute probabilities of “standardized events”.
2)   Find a z-score from a given Normal Probability.

MATH 114 REGRESSION HANDOUT


1) Determine the least squares regression line given a set of ordered pairs (You will be given the formulas to find slope and intercept here.
It is up to you to be able to understand the various summation operators that will be used.