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MAT108 - Survey of Mathematics
Catalog Description: A study of various topics including an introduction to estimation, algebra, geometry, consumer mathematics, probability and statistics, with an emphasis on critical thinking and interpreting results. Other topics may be covered at the discretion of the instructor. MAT108 is a common selection by Liberal Arts students with fewer than three years of high school mathematics. Either MAT108 or MAT092 can be used to satisfy the GCC math proficiency graduation requirement Either MAT108 or MAT092 can be used to satisfy the prerequisite for MAT129, Statistics. MAT108 does not satisfy the prerequisite for any other math course. Although this course can satisfy your mathematics requirement for some GCC programs and transfer to some baccalaureate institutions, speak with an academic advisor to ensure that this course meets your goals. Prerequisite: MAT091 with a grade of C or better, or by placement.
Lecture: 3 hrs.
Course Learning Outcomes (CLOs):
Upon successful completion of this course, the student will be able to:
1.1 Use estimation to approximate an answer to an applied problem.
1.2 Use estimation to determine whether a given answer to an applied problem is reasonable.
2.1 Add, subtract, multiply and divide fractions.
2.2 Use the correct order of operations to evaluate a numerical expression.
2.3 Evaluate formulas for specified values of the variables.
2.4 Solve first degree linear equations and inequalities containing one variable.
2.5 Translate verbal expressions into algebraic expressions.
2.6 Translate word problems into one-variable equations and solve.
3.1 Use the formula for the area of rectangles, squares, parallelograms, triangles and circles to solve applied problems.
3.2 Determine the perimeter of any given polygon and the circumference of any given circle, to solve applied problems.
3.3 Use the formula for the volume of rectangular solids, cylinders, cones and spheres to solve applied problems.
3.4 Determine the surface area of rectangular solids and cylinders.
3.5 Use the Pythagorean Theorem to solve applied problems.
3.6 Use unit conversions to solve applied problems.
4. Consumer Mathematics
4.1 Change a fraction to a percent, a decimal to a percent and a percent to a decimal, and be able to calculate a percentage change.
4.2 Solve applied problems by finding any of the variables in the following: n percent of a = b
4.3 In simple interest problems, solve for any variable in I = prt.
* 4.4 Solve applied problems by computing compound interest.
4.5 Compute effective annual yield [or effective annual interest rate], also known as annual percentage yield (APY).
4.6 Solve applied problems by computing present value.
4.7 Compute the monthly payment for a fixed installment loan.
4.8 Compute the annual percentage rate (APR) [or true annual interest rate] of a fixed installment loan.
4.9 Compute the minimum payment due on a credit card and the balance due the following month.
4.10 Compute finance charges using the average daily balance method or the unpaid balance method.
4.11 For a conventional mortgage loan compute the:
-monthly mortgage payment;
-the total amount of interest over the life of the mortgage.
5.1 Compute the empirical probability that event E will occur by means of the formula P(E) = the number of times event E has occurred / the total number of times the experiment has been performed.
5.2 Use the law of large numbers to explain the meaning of a probability. (e.g., A probability of 1/6 means that over the long run, on average, the event will occur one out of every 6 times.)
5.3 Compute the theoretical probability that event E will occur by means of the formula P(E) = the number of favorable outcomes / the total number of possible outcomes.
5.4 Write an explanation that probability must be a number between 0 and 1, inclusive.
5.5 In the context of a problem, explain that:
-an empirical probability of 0 means that the event never occurred, but could occur in the future
-an empirical probability of 1 means that the event always occurred, but may not occur in the future
-a theoretical probability of 0 means that the event will never happen
-a theoretical probability of 1 means that the event is certain to happen
5.6 Demonstrate an understanding that outcomes must be equally likely in order to calculate the probability of an event E using the formula P(E) = the number of favorable outcomes / the total number of possible outcomes. Students should be able to:
-articulate this assumption in an instance in which it is not stated (e.g., In order to calculate the probability of drawing a red ball from an urn containing 10 red and 5 green balls, you must assume that each ball is equally likely to be chosen.)
-write an explanation that there is insufficient information to calculate a probability in an instance in which it cannot be determined whether the outcomes are equally likely (e.g., In order to calculate the probability of drawing a red ball from an urn containing only red balls and purple balls, you must know how many there are of each color.)
5.7 Determine the odds in favor of or against event E occurring and determine the probability of an event given the odds.
5.8 Compute the expected value of an event E. Explain in the context of a problem that this is an average over the long run and cannot be used to predict the outcome the next time the event occurs.
5.9 Determine the fair price to play a "game".
5.10 Determine whether a "game" is fair or not.
5.11 Use sample spaces to show possible outcomes and calculate probabilities.
5.12 Determine whether two events, A and B, are mutually exclusive.
5.13 Determine whether two events, A and B, are dependent or independent.
5.14 Compute a compound probability, that is P(A and B) and P(A or B).
6.1 Define and recognize biased samples and random samples.
6.2 Explain how a graph or statement is a misinterpretation of statistics or is misleading.
6.3 Construct and interpret a frequency distribution table and a histogram from a given set of data.
6.4 Interpret a frequency polygon and a circle graph.
6.5 Distinguish among and compute the mean, median, mode and midrange for a given set of data.
6.6 Distinguish between and compute the range and standard deviation for a given set of data.
6.7 Identify rectangular distributions, J-shaped distributions, bi-modal distributions, skewed distributions and normal distributions from graphs.
6.8 Sketch and label a normal curve given the mean and standard deviation.
6.9 Determine what percentage of normally distributed data is within a given number of standard deviations from the mean, and explain your answer.
6.10 Write an explanation that a distribution must be normal in order to apply the empirical rule or use the z-score table to determine the percentage of data within a given number of standard deviations of the mean.
7. Metric System
7.1 Convert from one metric unit to another metric unit using liter, gram, and meter as basic units.
7.2 Use dimensional analysis (proportions) to convert units of measurements in the metric system to equivalent units in the U.S. Customary system and vice versa. (For example, convert liters to cups.)
* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.
Required Topics: Estimation, Algebra, Geometry, Consumer Mathematics, Probability, Statistics
Optional Topics: The instructor may choose additional topics such as: Topology, History of Mathematics,
Computer Applications, Numeration Systems, The Real Number System, Game Theory or Logic. Typically, an
additional topic would be made possible by "infusing" algebra throughout the topics rather than studying algebra as a separate topic.
I. Critical Thinking Skills
a. Inductive Reasoning
b. Estimation and Problem Solving
II. Number Theory and the Real Number System
a. Number Theory
b. The Integers
c. The Rational Numbers
d. Irrational Numbers and the Real Number System
e. Properties of Real Numbers
f. Rules of Exponents and Scientific Notation
a. Order of Operations
b. Linear Equations in One Variable
d. Applications of Linear Equations in One Variable
e. Linear Inequalities
IV. The Metric System
a. Basic Terms and Conversions Within the Metric System
b. Length, Area, and Volume
c. Mass and Temperature
d. Dimensional Analysis and Conversions to and from the Metric System
a. Points, Lines, Planes, and Angles
c. Perimeter and Area
d. Volume and Surface Area
a. The Nature of Probability
b. Theoretical Probability
d. Expected Value
e. Tree Diagrams
f. OR and AND Problems
a. Sampling Techniques
b. The Misuses of Statistics
c. Frequency Distributions and Statistical Graphs
d. Measures of Central Tendency
e. Measures of Dispersion
f. The Normal Curve
VIII. Consumer Mathematics
b. Personal Loans and Simple Interest
c. Compound Interest
d. Installment Buying
e. Buying a House with a Mortgage
Effective Term: Spring 2015