Santa Monica College
Mathematics Department Addendum
Math 28 – Calculus 1 for Business and Social Science
Prerequisite Comparison Sheet – exit skills of Math 26 and entry skills for Math 28
Exit Skills for Math 26
Upon successful completion of Math 26, the student will be able to:
A.
Construct the function or equation that best models the description of a
mathematical or practical situation.
B.
Analyze a functional model to determine information relevant to an application.
C.
Solve specific problems relating to, but not limited to, compound interest, supply
and demand, cost, maximizing revenue and profit, and exponential growth/decay.
D.
Solve polynomial, rational, radical, exponential and logarithmic equations.
E.
Use the language and notation of the algebra of functions, including algebraic
combinations and compositions.
F.
Use interval and set builder notation to state the domain and range of functions.
G.
Use algebraic principles of graphing including translations, reflections, expansions,
and contractions.
H.
Graph polynomial, absolute value, rational, radical, exponential, logarithmic, and
piecewise functions without the aid of graphing devices. Graphs must include any
intercepts, holes and asymptotes.
I.
Solve polynomial and rational inequalities in one variable.
J.
Evaluate, manipulate and interpret summation notation using properties of
sequences.
Use geometric sequences and series and related formulas to solve problems
relating to, but not limited to, annuities.
K.
:
L.
Use a scientific calculator to support computations for application problems.
M.
Given an algebraic expression with rational exponents, rewrite it in simplest form
as a product or quotient in which only positive exponents occur.
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Entry Skills for Math 28
Prior to enrolling in Math 28 students should be able to
1.
.2.
Identify & graph different types of functions (polynomial, rational, piecewise,
exponential, logarithmic)
Determine domain and range of functions.
3.
Perform operations (add, subtract, multiply, divide, compose) on functions.
4.
Factor completely algebraic expressions
5.
Solve linear and quadratic equations and inequalities
6.
Solve rational equations and inequalities
7.
Solve higher-order equations
8.
Solve exponential and logarithmic equations
9.
Solve systems of equations
10. Perform operations on exponential and logarithmic expressions
11. Perform operations on polynomials
12. Write algebraic expressions to be used in solving application problems
13. Compute the sum of a geometric sequence
14. Use a calculator to perform basic operations
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Santa Monica College
Student Learning Outcomes
Date: December 2009
Course Name and Number:
Math 28, Calculus 1 for Business and Social Science
Student Learning Outcome(s):
 Individual faculty members will develop and reports on assessments for SLOs.
1.
Given a situation encountered in finance, students will determine the correct finance formula
to solve the problem.
2.
Given a polynomial, rational, exponential or log function, students will analyze the function
using concepts of derivative and create a graph that includes intercepts, holes, asymptotes,
maximum and/or minimum values and points of inflection, if any exist.
3.
Given a situation encountered in business or social sciences, students will determine the
function or equation that best models the situation and solve the problem.
Demonstrate how this course supports/maps to at least one program and one institutional
learning outcome. Please include all that apply:
1.
Program Outcome(s):
The student will demonstrate an appreciation and understanding of mathematics in order to
develop creative and logical solutions to various abstract and practical problems.
As a result of learning about advanced mathematical functions, students will analyze and
solve abstract and practical problems.
2.
Institutional Outcome(s):
As a result of studying instructor feedback given during lecture, or written on homework and
exams, students will evaluate information critically and present solutions in a clear and
logical manner.
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Textbook: Barnett, Ziegler & Byleen, Applied Calculus for Business, Economics, Life Sciences and Social
Sciences, 11th ed., 2008 ,Pearson
A Sample Schedule for Math 28
This schedule assumes a standard meeting schedule of 1 hr 5 min with 4 class meetings per week.
Session
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Text Section/Activity
A-3: Factoring Polynomials
A-4: Operations on Rational Expressions
A-5: Integer Exponents
A-6: Rational Exponents and Radicals
1-1: Linear Equations and Inequalities
1-2: Graphs and Lines
2-1: Functions
2-2: Elementary Functions: Graphs & Transformation
2-3: Quadratic Functions
2-3: Polynomial and Rational Functions
2-4: Exponential Functions
2-5: Logarithmic Functions
Mathematics of Finance
D3-1: Simple Interest
D3-2: Compound & Continuous Compound Interest
D3-3: Future Value of an Annuity; Sinking Funds
D3-4: Present Value of an Annuity; Amortization
D3-4: Present Value of an Annuity; Amortization
Review
Exam 1
3-1: Introduction to Limits
3-2: Continuity
3-3: Infinite Limits and Limits at Infinity
3-4: The Derivative
3-5: Basic Differentiation Properties
3-6: Differentials
3-7: Marginal Analysis in Business & Economics
Review
Exam 2
4-1: The Constant e and Continuous Compound Interest
4-2: Derivatives of Exponential & Logarithmic Functions
4-3: Derivatives of Products and Quotients
4-3: Derivatives of Products and Quotients continued
4-4: Chain Rule
4-4: Chain Rule continued
4-5: Implicit Differentiation
4-6: Related Rates
4-7: Elasticity of Demand
Review
Exam 3
5-1: First Derivative and Graphs
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Session
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
Text Section/Activity
5-1: First Derivative and Graphs continued
5-2: Second Derivative and Graphs
5-2: Second Derivative and Graphs continued
5-4: Curve-Sketching Techniques
5-4: Curve-Sketching Techniques continued
5-5: Absolute Maxima and Minima
5-6: Optimization
5-6: Optimization continued
Review
Exam 4
6-1: Antiderivatives and Indefinite Integrals
6-1: Antiderivatives and Indefinite Integrals continued
6-2: Integration by Substitution
6-2: Integration by Substitution continued
6-4: Geometric-Numeric Introduction to the Definite Integral
6-5: Definite Integral as a Limit of a Sum
6-5: Fundamental Theorem of Calculus
6-5: Fundamental Theorem of Calculus continued
7-1: Area Between Curves
7-1: Area Between Curves continued
7-2: Applications in Business and Economics
7-3: Integration by Parts
7-3: Integration by Parts continued
7-4: Integration Using Tables
Review
Exam 5