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Precalculus

Course Description:
Major emphasis is on the concept of functions. Study polynomial, rational, exponential, logarithmic,
trigonometric and inverse trigonometric functions, their properties, graphs, and related equations and
applications. Additional topics include systems of equations , matrices, conic sections , sequences and series,
and probability. A graphing calculator is required and used extensively. Prerequisite: MTH 131

Core Course Objectives:

1. Simplify polynomial , radical, and rational expressions, and algebraic ex pressions involving radicals,
integer exponents, rational exponents, trigonometric functions, combinations, permutations, factorials ,
series, sequences, and matrices using appropriate algebraic skills, and logarithmic processes. (ADO 3.2)

2. Use appropriate algebraic processes to solve:
• linear, absolute value, quadratic, radical, rational, exponential, and logarithmic
equations.
• linear, absolute value, polynomial, and rational inequalities.
• linear and non-linear systems of equations.
• trigonometric and inverse trigonometric equations (ADO 3.2)

3. Manipulate and identify functions graphically, symbolically , and numerically . (ADO 2)

4. Solve application problems involving many different subject areas using algebraic
processes, counting technologies, and the binomial theorem. (ADO 4)

5. Apply fundamentals of right triangle trigonometry and solve applications problems.
(ADO 3.2)

6. Use appropriate technology (such as the graphing calculator) to enhance the understanding
of the previously stated objectives. (ADO 7)

7. Have an awareness of the historical background of topics covered in the course. (ADO 15)

Associate Degree Outcomes:
ADO 2. The ability to comprehend and use information including written and oral forms
ADO 3 Computational skills and understanding appropriate to the program of study
ADO 4. Critical thinking and problem-solving
ADO 7 Facility in the use of computers and other technologies appropriate to the program of study
ADO 15 An historical perspective

Day Section Topic Practice HW
12 Jan   Introduction  
  R.1 The Real-Number System 11-28,59-78
  R.2 Integer Exponents, Scientific Notation,
and Order of Operation
1-90
13 Jan R.3 Addition, Subtraction , and Multiplication
of Polynomials
1-53
14 Jan R.4 Factoring 1-138
  R.5 Rational Expressions 1-74
15 Jan R.6 Radical Notation and Rational Exponents 1-130
  R.7 The Basics of Equation Solving 1-64
       
19 Jan   No Class  
20 Jan 1.1 Introduction to Graphing 1-134
  1.2 Functions and Graphs 1-89
21 Jan 1.3 Linear Functions, Slope , and Applications 1-72
  1.4 Equations of Lines and Modeling 1-94
22 Jan 1.5 More on Functions 1-87
  1.6 The Algebra of Functions 1-106
       
26 Jan 1.7 Symmetry and Transformations 1-102
27 Jan ˜˜˜˜˜˜ CBR Lab  
28 Jan ˜˜˜˜˜˜ Review for Exam #1  
29 Jan ˜˜˜˜˜˜ Exam #1 on Chapters R&1  
       
2 Feb 2.1 Linear Equations, Functions, and Models 1-88
3 Feb   Project Success Day  
4 Feb 2.2 Complex Numbers  
5 Feb 2.3 Quadratic Equations , Functions, and Models 1-147
  2.4 Analyzing Graphs of Quadratic Functions 1-66
       
9 Feb 2.5 More Equation Solving 1-114
  2.6 Solving Linear Inequalities 1-81
10 Feb 3.1 Polynomial Functions and Modeling 1-86
11 Feb 3.2 Graphing Polynomial Functions 1-52
12 Feb 3.3 Polynomial Division 1-9,64-70
      1-48
       
16 Feb 3.4 Theorems about Zeros of Polynomial
Functions
 
17 Feb 3.5 Rational Functions  
18 Feb 3.6 Polynomial and Rational Inequalities 1-94
19 Feb 3.7 Variation and Applications 1-88
  ˜˜˜˜˜˜ Review for Exam #2 1-49
       
23 Feb ˜˜˜˜˜˜ Exam #2 on Chapters 2&3  
24 Feb 4.1 Inverse Functions 1-98
  4.2 Exponential Functions and Graphs 1-101
25 Feb 4.3 Logarithmic Functions and Graphs 1-114
26 Feb 4.4 Properties of Logarithmic Functions  
       
2 Mar 4.5 Solving Exponential & Logarithmic Eqns 1-86
3 Mar 4.6 Applications and Models: Growth and
Decay, and Compound Interest
1-43
4 Mar ˜˜˜˜˜˜ Review for Exam #3  
5 Mar ˜˜˜˜˜˜ Exam #3 on Chapters 4  
       
16 Mar 5.1 Trigonometric Functions of Acute Angles 1-116
16 Mar 5.2 Applications of Right Triangles 1-44
18 Mar 5.3 Trigonometric Functions of Any Angle 1-106
19 Mar 5.4 Radians, Arc Length, and Angular Speed 1-79
       
23 Mar 5.5 Circular Functions: Graphs and Properties  
24 Mar 5.6 Graphs of Transformed Sine and Cosine
Functions
 
25 Mar 6.1 Identities: Pythagorean and Sum and
Difference
1-76
26 Mar 6.2 Identities: Cofunction, Double-Angle,
Half-Angle
1-52
       
30 Mar 6.3 Proving Trigonometric Identities 1-51
31 Mar 6.4 Inverses of the Trigonometric Functions 1-86
1 Apr 6.5 Solving Trigonometric Equations 1-66
2 Apr 7.1 The Law of Sines 1-48
       
6 Apr 7.2 The Law of Cosines 1-48
7 Apr ˜˜˜˜˜˜ CBR Lab  
8 Apr ˜˜˜˜˜˜ Review for Exam #4  
9 Apr ˜˜˜˜˜˜ Exam #4 on Chapters 5,6&7  
       
13 Apr 8.1 System of Equations in Two Variables 1-86
14 Apr 8.2 Systems of Equations in Three Variables 1-55
15 Apr 8.3 Matrices and Systems of Equations  
16 Apr 9.1 The Parabola 1-49
       
20 Apr 9.2 The Circle and The Ellipse 1-71
21 Apr 9.3 Hyperbola 1-55
22 Apr 9.7 Parametric Equations 1-46
23 Apr 7.4 Polar Coordinates and Graphs 1-98
       
27 Apr   Review for Exam #5  
28 Apr   Review for Exam #5  
29 Apr   Exam #5 on Chapters 8,9,&7.4  
30 Apr   Comprehensive Review  
       
4 May   Comprehensive Review  
5 May   Comprehensive Review  
6 May   Final Exam  
7 May   Final Exam  
       
11 May   Course Review  
12 May   Course Review  
       

 

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