Objectives and Suggested Homework for College Algebra
Unit 1—Rules of Algebra (text sections P.1 – P.6)
P.1 Objectives:
Sets of Real Numbers (Natural, Whole, Integer, Rational, Irrational and
Real)
Order and Interval/Inequality Notation
Order of Operations
Algebraic Expressions
Basic Rules and Properties of Algebra (pages 7-8 of text)
Properties and Operations of Fractions
(skip properties of absolute values and distance between two points) |
P.1 Homework (p. 9):
vocabulary 1-9;
problems 1-5 odd, 11-45 odd,
73-95 odd, 97-104, 107, 110, 113 |
P.2 Objectives:
Properties of Exponents (Integer and Rational)
Simplify Expressions—leave answers with only positive exponents
Simplify Square Roots by removing perfect square factors from radicand
(only real numbers in radicand—no variables)
Convert between Radical and Rational Exponent form
Evaluate expressions with rational exponents without using a calculator
Instructor Option: rationalizing denominator/ numerator
(skip scientific notation) |
P.2 Homework (p. 21): vocabulary 1, 3, 4, 5, 9;
problems 1-12, 17-35 odd, 51-56, 63a, 64b, 87-98,
110a-d |
P.3 Objectives:
Define polynomial
Add/Subtract (collect like terms)
Multiply (mostly two binomials, but a few binomials with trinomials)
Special Products (skip cube of a binomial)
Cost, Revenue and Profit Equations |
P.3 Homework (p. 29): vocabulary 1-8;
problems 1-6, 7-19 odd,
23-67 odd, 81, 83, 97, 98 |
P.4 Objectives:
Common Factors
Factor Special Forms (skip sum/ difference of cubes )
Factor Trinomials with Binomial Factors
Factor by Grouping |
P.4 Homework (p. 38): vocabulary 1, 3, 4, 5ac;
problems 5-12, 19-37 odd, 47-71 odd, 79-101 odd |
P.5 Objectives:
Domain
Simplify (factor and cancel)
Multiply and Divide Rational Expressions
Instructor Options: add and subtract rational expressions, complex
fractions |
P.5 Homework (p. 47): vocabulary 1, 2, 4, 5, 6;
problems 1-25 odd, 31, 32, 35-41 odd, 61-67 odd, 68 |
P.6 Objectives:
Recognize and Avoid Common Errors
Rewrite a fraction as a sum of terms with no denominator —see example 6b
in box at bottom page 55 of text
Factor out common factors with Fractional Powers
Simplify expressions that result from quotient rule in calculus |
P.6 Homework (p. 56): vocabulary 1, 2;
problems 1-22, 33-35, 39, 40, 43-48 (rewrite with no denominator),
49-51, 67-69, 71 |
Unit 1 Extra Practice/Review:
p. 70: 1, 2, 5, 6, 13-29, 47-62, 67-70, 73-79, 81, 82, 89-91, 93-95,
97-102
p. 73: 1, 3, 4, 6, 7b, 8, 9, 13, 15-17 |
|
Unit 2—Equations, Inequalities and Functions (text
sections 1.2-1.4, 1.6, 1.7, 2.2 and 2.6)
1.2 Objectives:
Identity vs Conditional Equations
Solve Linear equations by producing equivalent equations
Solve equations that contain fractions, but result in solving linear
equation
—multiply both sides by LCD method
Find Intercepts Algebraically (write them as ordered pairs) |
1.2 Homework (p. 94): vocabulary 1-5;
problems 1-59 odd,
71-77 odd, (Instructor option 81-87 odd), 101, 107 |
1.3 Objectives:
Translating key words and phrases
Application problems involving percentages
Solve a formula for a specified variable
Define variables for a word problem
Translate word problems into a system of equations
(skip similar triangle problems, mixture problems) |
1.3 Homework (p. 105): vocabulary 1, 2;
problems 18, 21, 22, 23, 25, 35-41, 47, 48, 51, 52,
77-83, 87, 101 |
1.4 Objectives:
Solve by Factoring
Solve by Extracting Square Roots
Discriminant
Solve by Quadratic Formula (simplify answers)
(skip completing the square) |
1.4 Objectives:
Solve by Factoring
Solve by Extracting Square Roots
Discriminant
Solve by Quadratic Formula (simplify answers)
(skip completing the square) |
1.6 Objectives:
Polynomial Equations (only those that factor)
Equations with Fractions (multiply both sides by LCD method)
(skip equations of quadratic type, radical and absolute value equations) |
1.6 Homework (p. 140): vocabulary 1;
problems 1, 2, 7-9, 19, 57-64, 120-122 |
1.7 Objectives:
Interval Notation vs Inequality Notation (again)
Determine whether a value is a solution of an inequality
Solve Linear Inequalities (single and double)
(skip absolute value inequalities) |
1.7 Homework (p. 150): vocabulary 1-6;
problems 1-16, 19-39 odd, 40-42, 95-97, 119-122 |
2.2 Objectives:
Define Function
Function Notation
Domain
Evaluate Functions (including piecewise)
Difference Quotient (for linear and quadratic functions) |
2.2 Homework (p. 197): vocabulary 1-6;
problems 1-12, 13-53 odd (skip 29), 57-61, 65-69, 79-82, |
2.6 Objectives:
Arithmetic Combinations of Functions
Composition
Decomposition |
2.6 Homework (p. 238): vocabulary 1-4;
problems 5-8, 11cd, 13-23 odd, 31-53 odd, 69, 73, 74 |
Unit 2 Extra Practice/Review:
p. 165: 31-48, 53, 54, 60 (translate into a system of eqns), 61, 62,
65-74, 95-98,
107, 108, 117-126
p. 169: 7, 8, 9,13
p. 253: 33-42, 44, 45, 47, 53, 107-112;
p. 257: 4, 5, 17 |
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Unit 3—Graphing (text sections P.7, 1.1, 2.1, 2.3-2.5,
3.1 and 3.2)
P.7 Objectives:
Quadrants
Point Plotting
(skip distance and midpoint formulas and scatter plots) |
P.7 Homework (p. 64): vocabulary 1, 2;
problems 1-20, 51-55 |
1.1 Objectives:
Make a Table of Values for an equation in two variables (do not sketch)
Determine whether a point lies on the graph of an equation
Intercepts of a Graph (visually—already did algebraically)
Choose appropriate scales for axes based on table of values
(skip symmetry and circles) |
1.1 Homework (p. 86): vocabulary 1-3;
problems 1-11 odd, 63, 73, 74 |
2.1 Objectives:
Slope-intercept form for equation of a line
Slope formula
Write equation of Line
Parallel and Perpendicular lines
Instructor Option: Finding Point of Intersection for two lines |
2.1 Homework (p. 183): vocabulary 1-5, 7;
problems 1-25 odd, 29-47 odd, 51-57 odd, 61-75 odd, 133-135 |
2.3 Objectives:
Vertical Line Test
Domain and Range from a graph
Zeros of a Function
Intervals where increasing, decreasing, constant
(skip even/odd functions and average rate of change) |
2.3 Homework (p. 210): vocabulary 1-5;
problems 1-14, 15-21 odd, 31-37, 55, 56, 107-113, 115, 116 |
2.4 Objectives:
Parent Functions (Constant, Identity, Absolute Value, Square Root,
Quadratic, Cubic and Reciprocal—graphs a-g on page 219)
Piecewise Functions (linear pieces only)
(skip step and greatest integer functions) |
2.4 Homework (p. 220): vocabulary 2-9;
problems 1-7 odd, 43, 44, 65, 69, 71, 73-76 (memorize functions a-g on
p. 219) |
2.5 Objectives:
Shift Graphs of parent functions from section 2.4
Reflect Graphs of parent functions (x-axis reflections only)
(skip vertical and horizontal stretching/shrinking) |
2.5 Objectives:
Shift Graphs of parent functions from section 2.4
Reflect Graphs of parent functions (x-axis reflections only)
(skip vertical and horizontal stretching/shrinking) |
3.1 Objectives:
Quadratic Functions using f(x)= ax2 + bx + c
(skip f(x) = a(x - h)2 + k; do problems given in that form by shifting)
Open up/down; Narrower/Wider than quadratic parent function from 2.4
Find vertex using formula on page 269 of text
Graph by shifting (like 2.5) and/or using vertex and x-intercepts |
3.1 Homework (p. 270): vocabulary 1-5;
problems 1-8, 13-27 odd,
53-56, 89, 90, 93, 95-104 |
3.2 Objectives:
Instructor Option: Power Functions and graph by shifting
Max number of turning points
Leading Coefficient test
Zeros and Multiplicity
Graph using end behavior, zeros, multiplicity, and plotting a few
additional points |
3.2 Homework (p. 284): vocabulary 1-6;
problems 1-8, 13-21 odd,
27ab-37ab odd, 41, 42, (Instructor option 47-53), 67-79 odd, 99,
101-102, 105-112, 117-120 |
Unit 3 Extra Practice/Review:
p. 72: 103-106
p. 165: 1-4 (do not sketch), 11, 12
p. 253: 1-10, 13-28, 55-64, 77, 78, 81-84, 89, 91-98, 100
p. 257: 1, 3, 15
p. 326: 1, 3-12 (use vertex and x-intercepts to graph), 31-39, 42
p. 330: 1, 2, 9, 10 |
|
Unit 4—Exponential and Logarithmic Functions (text
sections 5.1-5.4)
5.1 Objectives:
Basic Exponential Function (increasing and decreasing)
One to One Property
Graph of basic Exponential function including asymptote
Shifting graph of basic exponential function (including asymptote)
(Skip compound interest) |
5.1 Homework (p. 392): vocabulary
1-3;
problems 7-10, 17, 19,
45-51 odd, 71-77 odd |
5.2 Objectives:
Basic Log function
Convert from Log form to Exponential form
Common Log, Natural Log and Properties (pages 396 and 400)
Graph of basic log function including asymptote
Shifting graph of basic log function (including asymptote) |
5.2 Homework (p. 402): vocabulary
1-5;
problems 1-21 odd, 27-41 odd (omit 37), 45-59 odd, 65-69 odd, 79-85 odd,
92, 103-107 odd |
5.3 Objectives:
Properties of Logs ( condense and expand )
Evaluate logs without a calculator
Instructor Option: Change of Base Formula |
5.3 Homework (p. 409): vocabulary
3-5;
problems 17-79 odd, 87, 103-105, 107-110 |
5.4 Objectives:
One to One and Inverse Properties
Solve Exponential Equations (leave answers exact)
Solve Log Equations (leave answers exact)
(skip doubling time) |
5.4 Homework (p. 419): vocabulary
1-3;
problems 9-20*, 21-49* every other odd, 51, 63*, 65*,75*, 79*, 93-99*
odd, 119-122 *leave answers exact—do not approximate with a calculator |
Unit 4 Extra Practice/Review:
p. 437: 7-14, 23-26, 41-58, 65, 66, 75-94, 97-112*, 123*, 127-130*
p. 441: 15-20, 21*, 22*, 24*, 26*
*leave answers exact—do not approximate with a calculator |
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Note: Objectives listed as Instructor Option may be
covered on Unit tests at the instructor’s discretion, however, they will not be
covered on the Departmental Final Exam.
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