DATE | WEB LESSON | CHANGE |
July 21, 2021 | Length of a Circular Arc (and Related Concepts) | Change ‘Degees’ to ‘Degree’. |
July 21, 2021 | Review of Circles (and Related Concepts) | Typo: change $\,r\,$ to $\,r^2\,$ in definition of interior of circle. |
July 17, 2021 | Graphing Generalized Sines and Cosines | Correct repeated word: ‘the period is the the horizontal...’; |
July 10, 2021 | Fundamental Trigonometric Identities | Add in missing words: the terminal point for $\,t\,$ ... |
June 6, 2021 | The Trigonometric Functions | Remove (missing) link to Drexel (Ask Dr. Math). |
June 5, 2021 | Doubling Time, Half-Life | Change ‘$\,b < 1\,$’ to ‘$\,0 < b < 1\,$’ in three places. |
June 4, 2021 | Solving Exponential Growth and Decay Problems |
Change ‘alternate’ to ‘alternative’ in four places. Reformatting: move the ‘Yuck!’ to be centered in a new row at the bottom. Change ‘solutions steps’ to ‘solution steps’. Fix typo: $P(3\Delta t) = b\cdot P_{\,0}b^2 = P_{\,0}b^3$ (change $\,1\,$ to $\,2\,$ in exponent) |
June 2, 2021 | Solving Exponential Equations |
Change ‘There are NOT ExpTerms’ to ‘These are NOT ExpTerms’. Change ‘Solve (continued)’ to just ‘Solve’. |
May 27, 2021 | Logarithmic Functions: Review and Additional Properties | Change two occurrences of ‘alternately’ to ‘alternatively’. |
May 23, 2021 | Simple Versus Compound Interest | Change ‘compounding periods per years’ to ‘compounding periods per year’. |
May 15, 2021 | Introduction to Average Rate of Change |
Change ‘alternately’ to ‘alternatively’. Change ‘sometime downhill’ to ‘sometimes downhill’. |
May 15, 2021 | The Natural Exponential Function | Formatting change, to agree with the text ‘Clearly, the numbers in the right-hand column at left’. |
May 8, 2021 | Exponential Functions: Review and Additional Properties | Change ‘alternately’ to ‘alternatively’ (two places). |
May 8, 2021 | Introduction to Puncture Points (Holes) | Remove the word ‘it’ in ‘it isn't defined’. |
April 26, 2021 | Introduction to Rational Functions | Change ‘alternately’ to ‘alternatively’. |
April 26, 2021 | Solving Polynomial Equations | Two typos: replace $\,x^2\,$ with $\,x\,$ in Step 5 of example; change ‘and real numbers’ to ‘are real numbers’. |
April 22, 2021 | Multiplying and Dividing Fractions with Variables | Change first occurrence of ‘puncture point’ to a link (suggestion from Ray). |
April 11, 2021 | Greatest Common Factor of Two or Three Numbers |
Mistake: removed entire section titled ‘BONUS: An Efficient Algorithm for Finding the Least Common Multiple’ Also removed link to this section in Finding Least Common Multiples. I have un-published the two Algebra I web books until I decide how I want to address this. |
April 11, 2021 | Arithmetic with Complex Numbers |
Typo: change ‘$\,31\,$’ to ‘$\,3i\,$’ |
March 20, 2021 | Turning Points of Polynomials |
Typo: change ‘$\,x\le 3\,$’ to ‘$\,x\le c\,$’ |
March 20, 2021 | Finding Inverse Functions (switch input/output names method) |
Typo: change ‘which is output from’ to ‘which is an output from’ Typesetting fix: change left single quote to right single quote on the word ‘simple’ |
March 17, 2021 | Finding Inverse Functions (when there's only one $\,x\,$ in the formula) | Clarification: change ‘Here's one. The other is similar.’ to ‘Here's one proof. The other proof is similar.’ |
March 2, 2021 | Max/Min Problems Resulting in Quadratic Functions |
Typos: Insert missing minus signs in $\,\left(-\frac{b}{2a},f(-\frac{b}{2a})\right)\,$ in two places; Re-format ‘Suggested Review’ at beginning (bullets don't work well next to the mathematical cat) |
February 26, 2021 | Piecewise-Defined Functions | Typo: Add a missing space, ‘quadratic,since’. |
February 22, 2021 | Basic Function Models You Must Know |
Typos: change two ‘the the’ to ‘then the’. For exponential functions, change ‘if $\,x = 100\,$’ to ‘if $\,y = 100\,$’. |
February 13, 2021 | Sketching Regions in the Coordinate Plane | Change ‘alternately’ to ‘alternatively’. |
February 8, 2021 | Review of Lines and Slopes of Lines |
Change ‘times as fast than the inputs’ to ‘times as fast as the inputs’. Remove section linking to user exercise on lines; no longer working. |
February 2, 2021 | Absolute Value as Distance From Zero | Typos: in two places, change ‘on one side of the equation’ to ‘on one side of the inequality’ |
February 2, 2021 | The Test Point Method for Sentences Like ‘$\,f(x) \gt g(x)\,$’ | Typo: change ‘to indicate than’ to ‘to indicate that’ |
January 31, 2021 | The Test Point Method for Sentences Like ‘$\,f(x) \gt 0\,$’ | Typo: change ‘to indicate than’ to ‘to indicate that’ |
January 13, 2021 | Parallel and Perpendicular Lines | Add the word ‘distinct’ in two places. |
January 1, 2021 | Quadratic Functions and the Completing the Square Technique |
Typos: change ‘can be real number’ to ‘can be any real number’; change ‘hold water’ to ‘holds water’; change $\,a(h-k)^2 + k\,$ to $\,a(x-h)^2 + k\,$; change $\,-\frac{20}{29}\,$ to $\,-\frac{29}{20}\,$ |
December 30, 2020 | Equations of Simple Parabolas | Typo: change ‘the the parabola’ to ‘then the parabola’ |
December 27, 2020 | Parabolas | Typo: change ‘parabola nets narrower’ to ‘parabola gets narrower’ |
November 30, 2020 | Simple Word Problems Resulting in a System of Equations | Change ‘in the following example’ to ‘with the following example’. |
November 30, 2020 | Measures of Spread | Typo: replace $\,x_1\,$ with $\,x_i\,$ in the sentence beginning ‘A reasonable idea is to...’. |
November 14, 2020 | Advanced Set Concepts | Replace ‘alternately’ with ‘alternatively’. |
November 9 and 11, 2020 |
Composition of Functions
, Graphical Interpretations of Sentences Like $\,f(x) = g(x)\,$ and $\,f(x) > g(x)\,$, and Graphical Interpretations of Sentences Like $\,f(x) = 0\,$ and $\,f(x) > 0\,$ |
Typos: change ‘Graphs of Function’ to ‘Graphs of Functions’ in beginning link |
November 7, 2020 | Basic Models You Must Know |
Typos: change ‘Graphs of Function’ to ‘Graphs of Functions’ in beginning link; changed ‘dom’ to ‘ran’ for cubing function; correct symbolic statement of domain for absolute value function; change ‘functions’ to ‘function’: ‘Every constant functions graphs as...’ |
November 2, 2020 | Compound Interest Formula | Typo: changed ‘years’ to ‘year’ (singular) in the Compound Interest Formula box. |
October 29, 2020 | Arithmetic and Geometric Sequences | Changed 12 to 12.5 (twice) in geometric series example. |
October 19, 2020 | More on Exterior Angles in Triangles | Changed ‘with respect to $\,\angle C\,$’ to ‘with respect to the exterior angle at $\,\angle C\,$’. |
October 17, 2020 | Practice with Two-Column Proofs | Typo (two places): change ‘REASONS columns’ to ‘REASONS column’ (singular). |
October 11, 2020 | Relationships Between Angles and Sides in Triangles | Typo: changed ‘$\,B\Leftarrow A\,$’ to ‘$\,A\Leftarrow B\,$ (that is, $\,B\Rightarrow A\,$)’. |
October 11, 2020 | Triangle Congruence | Changed ‘alternately’ to ‘alternatively’. |
October 11, 2020 | Angles: Complementary, Supplementary, Vertical, and Linear Pairs | Removed the cursor from the vertical angle image. |
October 3, 2020 | Introduction to the Two-Column Proof | Typo: changed ‘in written in’ to ‘is written in’. |
October 3, 2020 | Proof Techniques | Typo: changed ‘the only time than an’ to ‘the only time that an’. |
September 28, 2020 | Quadrilaterals | Changed ‘containing’ to ‘connecting’ in the definition of convex; much clearer. |
September 19, 2020 | More Practice with Function Notation | Missing factor of $\,2\,$ in displayed equation; corrected in online (not print) version. |
September 14, 2020 | Finding Slant Asymptotes | Added a ‘real-life’ example of a slant asymptote to online version, per user request. |
September 14, 2020 | Finding Vertical Asymptotes | Added ‘real-life’ examples of vertical asymptotes to online version, per user request. |