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May 18th

May 18th

# 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 Exp onent 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.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

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.

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 Homework (p. 120): vocabulary 1, 3; problems 1-29 odd (skip 19), 59-83 every other odd, 99- 102, 107, 135-137, 147-154, 156-158 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

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.

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 Homework (p. 228): vocabulary 1, 2, 5, 6; problems 1, 2, 5abd, 7abd, 9-17 odd, 18, 19-22, 25, 26, 29-33, 37, 38, 40, 43-45, 47, 48, 80-88 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

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.

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

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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