About This Book
- Page ID
- 142675
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This text has been written for use in two courses designed to prepare students for college mathematics at Siena College. These courses are intended to prepare students with learning loss or COVID-19-related knowledge gaps for, primarily, the quantitative courses taken by math and science majors, and to a lesser degree, business or economic topics. They are distinguished by the material focused on geared toward two levels of preparedness for a Calculus I course. The first focuses more on Chapters 1-6, spending more time shoring up fundamental arithmetic and algebra skills needed for all science majors, and as such spends less time on exponential, logarithmic, and trigonometric functions. The second course covers more traditional College Algebra/Precalc, assuming foundational skills and covering mainly Chapters 3-8. Students are encouraged to go directly from the first course into Calculus I and to self-study Chapters 7-8 in preparation, maintaining a disciplined and rigorous study schedule throughout in order to catch up any gaps along the way. Meanwhile, any students who are struggling in the second course are encouraged to review Chapters 1-2 as the course begins, as needed. Suggested section lists to use for each course are given below.
If not indicated otherwise, I have made all graphics myself, using Microsoft Visio, Desmos, Geogebra, Overleaf, Google Workspace, etc.
With questions or corrections (this text was created in the course of a single summer, so it will certainly undergo adjustments over time), please email ldewolf@siena.edu.
Suggested sections for Level I course:
- 1.1 Real Numbers
- 1.2 Working With Fractions
- 1.3 Working With Decimals
- 1.4 Powers and Radicals
- 1.5 Estimation, Common Sense, and Intuition
- 2.1 Algebraic Expressions
- 2.2 Factoring Techniques
- 2.3 Rational Expressions
- 2.4 Algebravaganza (Exam 1 here)
- 3.1 Solving for a Variable
- 3.2 Solving Inequalities
- 3.3 Lines and Circles
- 3.4 Modeling With Equations
- 3.5 Solving Systems of Linear Equations (Exam 2 here)
- 4.1 Functions, Domain, and Notation
- 4.2 Graphing Functions With Transformations
- 4.3 Compositions of Functions
- 4.4 Inverse Functions
- 5.1 Linear Functions and Rate of Change
- 5.2 Quadratic Functions
- 5.3 Polynomial Functions
- 5.4 Roots of Polynomial Functions (Exam 3 here)
- 6.1 Rational Functions
- 6.3 Basics of Exponential Functions
- 6.4 Basics of Logarithmic Functions
- 8.1 Geometry Essentials
- 8.2 Solving Problems With Geometry (Final exam here)
Suggested sections for Level II course:
- 1.5 Estimation, Common Sense, and Intuition
- 2.2 Factoring Techniques
- 2.4 Algebravaganza
- 3.3 Lines and Circles
- 3.4 Modeling With Equations
- 3.5 Solving Systems of Linear Equations
- 3.6 Vectors and Matrices (Exam 1 here)
- 4.1 Functions, Domain, and Notation
- 4.2 Graphing Functions With Transformations
- 4.3 Compositions of Functions
- 4.4 Inverse Functions
- 5.1 Linear Functions and Rate of Change
- 5.2 Quadratic Functions
- 5.3 Polynomial Functions
- 5.4 Roots of Polynomial Functions (Exam 2 here)
- 6.1 Rational Functions
- 6.2 Asymptotes and Limits
- 7.1 Exponential Functions
- 7.2 Logarithmic Functions
- 7.3 Solving Exponential and Logarithmic Equations
- 7.4 Applications
- 8.1 Geometry Essentials
- 8.2 Solving Problems With Geometry (Exam 3 here)
- 8.3 Trigonometry Via Triangles
- 8.4 Trigonometric Functions
- 8.5 More (and Inverse) Trig Functions
- 8.6 Trigonometric Identities
- 8.7 Solving Trigonometric Equations (Final exam here)
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This text was compiled on 12/13/2024