MATH 100 College
Algebra: A Modeling Approach
Course Objectives for Fall 2008
1.1.1
Given
calculations like those in exercises 1-20 on p. 17, calculate the results of those
calculations without using a calculator.
1.1.2
Given a data
table like #37 on p. 19, draw an appropriate graph for that data.
1.2.1
Solve
proportional equations like those in exercises 1-31 on p. 31.
1.2.2
Write an
equation that corresponds to a proportional relationship between
variables. Be sure to identify the
meanings of all variables you introduce. (See exercises 45-48 on pp. 32-33.)
1.2.3
Solve
problems involving proportional relationships.
Be sure to identify all variables you introduce and clearly state your
conclusion using a complete sentence.
(See exercises 38-44 on p. 32)
1.2.4
Given a
proportional relationship, specify the constant of proportionality. (See exercises 32-37 on p. 31)
1.2.5
Without use
of a calculator, sketch the graph of proportionality relationships like those
in exercises 10-21 on p. 31.
1.3.1
Solve linear
equations like those in exercises 1-14 and 25-30 on pp. 45-46.
1.3.2
Simplify
expression like those in the “Basic
Skills Assessment” and the “Algebra
Review Exercises.”
1.3.3
Given a
situation that can be modeled by a linear equation, write and solve a linear
equation that represents the situation.
Be sure to identify all variables you introduce and clearly state your
conclusion. (See exercises 31-41 on pp.
46-47.
2.1.1
Demonstrate
the ability to work with the slope-intercept form for the equation of a
line. (See exercises 1-21 odd on pp.
70-71)
2.1.2
Given the
equation for a linear relationship, express the relationship in slope-intercept
form. (See exercises 15-27 odd on p.
84.)
2.1.3
Given a
verbal description of a linear relationship, express the relationship with an
equation in slope-intercept form.
(See exercises 31-39 odd on pp. 71-72.)
2.2.1
Given
geometric features of a line, write an equation for the line. (See exercise 1-13 odd on pp. 83-84.)
2.2.2
Given the
graph of a line, write an equation for the line. (See exercises 29-33 odd on pp.85-86.)
2.3.1
Given descriptions
of some real world applications, formulate and solve linear equations that
represent the situations described.
Interpret your results in terms of the application. (See exercises 25-37 odd on pp. 113-116.)
2.3.2
Given a
verbal description of a “realistic” situation where two quantities are linearly
related and questions about the relationship formulate and solve appropriate
linear equations. Identify any variables
you introduce and carefully state your conclusions using complete sentences.
(See exercises 25-39 odd on pp. 113-116.)
2.4.1
Given a
linear relation described in slope-intercept form, invert the equation. (See exercises 13-23 odd on p. 128.)
2.4.2
Given
descriptions of some real world linear relations formulate, solve, and interpret
linear equations designed to answer questions about the relations. (See exercises 35-43 on pp. 128-129)
3.1.1
Given a
system of two linear equations in two variables, graph the equations and
estimate the solution by looking for the point of intersection if one
exists. (See exercises 1-11 odd on pp.
163-164.)
3.1.2
Given a
system of two linear equations in two variables, solve the system algebraically.
(See exercises 1-29 odd on pp. 163-164.)
3.1.3
Given a
verbal description of a “realistic” situation where two quantities are linearly
related and questions about the relationship formulate and solve appropriate
system linear equations. Identify any
variables you introduce and carefully state your conclusions using complete
sentences.
(See exercises 31-41 odd on pp. 164-167.)
4.1.1
Given a
verbal description of the qualitative properties of a graph, sketch a graph
that has those properties. Demonstrate knowledge of the following terms or
concepts: increasing, decreasing,
concave up, concave down, maximum, minimum, slope, intercept, domain, range,
inflection point. (See exercises 1-19
odd and exercises 43-71 odd on pp. 240-246)
4.1.2
Given a
verbal description of a “realistic” situation where two quantities are related
in a way described qualitatively, sketch an appropriate graph illustrating the
relationship. (See exercises 25-41 odd
on pp.242-244.)
4.2.1
Solve
reciprocal equations and modifications of reciprocal equations. (See exercises 1-19 odd on p. 263.)
4.2.2
Given a
verbal description of a “realistic” situation where a reciprocal or modified
reciprocal relationship exists, formulate and appropriate equation to represent
the relationship. (See exercises 41. 43,
and 45 on pp. 264-265.)
4.3.1
Demonstrate
knowledge and understanding of functional notation. (See exercise 1-33 odd on pp. 276-277.)
4.3.2
Given two
equations whose graphs are related by a shift, describe the shift that would
transform the graph of one into the graph of the other. (See exercises 43 and 45 on p. 277.)
4.3.3
Given an
equation in terms of two parameters c and d for a modified reciprocal
relationship and two points on the graph of the relationship, find the values
of the parameters c and d. (See exercise
51 on p. 277.)
4.4.1
Given
formulas for two functions, write a rule for the composition of the two
functions. (See exercises 1-19 on pp.
291-291.)
4.4.2
Given a
formula for a function, write a rule for the inverse of the function. (See exercises 21-39 odd on p. 292.)
4.4.3
Given a
description of a function for a “realistic” situation, describe the meaning of
the inverse of the given function. (See
exercises 41-47 odd on pp. 292-203.)
5.1.1
Demonstrate
knowledge and understanding of scientific notation. (See exercises 1-19 odd on p. 341.)
5.1.2
Simplify
expressions involving exponents or radicals.
(See exercises 21-81 odd on pp. 241-241.)
5.1.3
Demonstrate
knowledge and understanding of compound growth.
(See exercises 83-89 on pp. 342-343.)
5.2.1
Given a
formula for an exponential function, specify whether the formula describes a
process of growth or decline, and state the rate of growth or decline. (See exercises 27-43 odd on p. 355.)
5.2.2 Given a verbal description of a “realistic” situation involving exponential growth or decline, write an appropriate formula for the relationship and respond to specific questions about the relationship. (See exercises 57-61 on p. 356.)
5.2.3 Given a rule for an exponential function, identify the growth (decay) rate and the growth (decay) factor.
5.4.1 Distinguish between continuous and non-continuous compounding when writing formulas for exponential relationships.
5.4.2 Sketch graphs of exponential functions in continuous compounding contexts. (See exercises 1-33 odd on p. 391.)
5.4.3 Solve problems involving applications involving continuous compounding. (See exercises 34-41 on pp. 391-392.)
5.5.1 Evaluate logarithmic expressions. (See exercises 7-41 on p. 412.)
5.5.2 Invert exponential equations. (See exercises 65-73 on p. 413.)
5.5.3 Utilize the natural logarithmic function (ln) in solving applied problems. (See exercises 84-94 on pp. 413-414.)
6.1.1 Utilize the natural logarithmic function (ln) or a calculator in solving exponential equations. (See exercises 1-17 odd on p. 438.)
6.1.2 Given an exponential relationship, find the half-life or doubling time. (See exercises 1-17 odd on p. 438.)
6.1.3 Solve problem involving applications of exponential relationships. (see exercises 55, 57, 59 on p. 439.)
6.2.1 Examine a data table and determine whether the data suggests an exponential relationship. (See exercises 1-8 on p. 452.)
6.2.2 Given "real" data, use the ratio test to determine whether or not an exponential function might be used to express the relationship in the data. In case an exponential function provides a reasonable fit to the data, specify a rule for the function. (See exercises 51-54 on p. 454 but use the ratio test and not the logarithmic test.)
6.4.1 Sketch graphs of power functions. (Sketch graphs of those functions in exercises 1-11 odd on p. 507.)
6.4.2 Identify power functional relationships in data tables.
6.4.3 When data in a table suggest a power functional relationship, specify a power function that fits the data reasonably well.
(See exercises 54 and 55 on pp. 512-513.)
6.4.4 Solve power functional equations. (See exercises 1-11 odd on p. 507; also sketch graphs of those functions.)
6.4.5 Solve problems involving applications of power functions. (See exercises 41-46 on pp. 508-509.)
7.1.1 Recognize the vertex form of a quadratic function, and identify the information about the function that is revealed in that form. (See exercises 11-14 on pp. 545-546.
7.1.2 Sketch the graph of a quadratic function that is presented in vertex form. (See pp.527-530.)
7.1.3 Recognize the general form of a quadratic function, and identify the information about the function that is revealed in that form. Calculate the coordinates of the vertex from that information. (See exercises 1-9 on p. 544.)
7.1.4 Find the general form equation for a parabola that passes through three known points. (See exercises 15-20 on p. 547.)
7.1.5 Solve applied problems involving quadratic relationships. (See exercises 21, 23, 25 on pp. 546-547.)
7.2.1 Use the method of finite differences, or forward differences, to identify quadratic relationships and then write an equation expressing that relationship. (See exercises 23-26 on p. 567.)
7.3.1 Solve quadratic equations. (See exercises 11-19 odd on p. 589.)
7.3.2 Formulate a quadratic equation for applied problems, an solve the equation to answer questions about the problem situation. (See exercises 25-35 odd on pp. 589-593.)