Pre-Calculus
Welcome to Pre-Calculus. Students will spend one more year preparing for calculus, specifically exploring logarithms, trigonometry, algebra, series, and limits.
The syllabus for this class is available as a PDF.
We are using Standards-Based Grading (SBG). 75% of your grade consists of little tests on roughly 35 specific Algebra 2 skills. The skills themselves, along with the dates of the tests, are listed at the bottom of this page.
Homework is assigned each night and is due the next school day. When you are working assignments from the book, be sure to check all of your odd-numbered answers in the back of the book. If you've gotten the wrong answer, go back and do the exercise again until you understand how to do it.
Homework Assignments
The date you see is the date the homework was assigned. It is due the next school day. Most days, I have chosen the homework assignment as practice for the concepts and skills discussed in class. If you are working without distractions, a typical assignment will take you 20 minutes.
Pre-Calculus Skills
The skills listed below are based on the Common Core State Standards.
Second-semester skills
Number | Name | Goal | Textbook section | Tested in class | Notes | |
1 | Adding and subtracting complex numbers | To simplify the sum or difference of two complex numbers. | P.6 | 1/12/17 1/18/17 1/26/17 |
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2 | Multiplying complex numbers | To simplify the product of two complex numbers. | P.6 | 1/12/17 1/18/17 1/26/17 |
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3 | Properties of logarithms | To write a logarithmic expression as a sum of logarithms | 3.4 | 1/12/17 1/18/17 1/26/17 |
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4 | Logistic models | Given a logistic model, to describe some basic characteristics | 3.2 | 1/18/17 1/26/17 2/2/17 2/9/17 |
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5 | Finding an exponential function | Given two data points, to write an exponential function | 3.2 | 1/26/17 2/2/17 2/9/17 |
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6 | Evaluating logarithms | To evaluate a logarithmic expression | 3.3 | 2/2/17 2/9/17 2/18/17 2/22/17 |
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7 | Transformations of logarithmic functions | To describe transformations of the graph of a logarithmic function | 3.3 | 2/2/17 2/9/17 2/18/17 2/22/17 |
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8 | Change of Base formula | To convert a logarithm of unusual base into a quotient of common or natural logarithms, and to simplify using a calculator | 3.4 | 2/9/17 2/18/17 2/22/17 3/1/17 3/9/17 |
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9 | Solving logarithmic equations | To solve a logarithmic equation | 3.5 |
2/18/17 2/22/17 3/1/17 3/9/17 3/16/17 |
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10 | pH of a solution | Given molarity of a solution, to find the pH | 3.5 | 2/22/17 3/1/17 3/9/17 3/16/17 |
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11 | Continuously compounded interest | To use the A=Pert formula to find the missing information in a continuously compounded interest scenario | 3.6 | 3/1/17 3/9/17 3/16/17 3/23/17 |
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12 |
Converting angle measures | To convert between DMS and degrees | 4.1 | 3/9/17 3/16/17 3/23/17 |
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13 | Radian measure | To convert between degrees and radians | 4.1 | 3/9/17 3/16/17 3/23/17 3/30/17 |
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14 | Trigonometric ratios | To find the exact value of one of the six trigonometric ratios, given a right triangle with one side missing | 4.2 | 3/16/17 3/23/17 3/30/17 |
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15 | Right triangle trigonometry | To find the missing part of a right triangle, using trigonometry, and round to indicated precision | 4.2 | 3/16/17 3/23/17 3/30/17 4/6/17 |
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16 | Trigonometric ratios determined by a point | Given a point on the coordinate plane, to find all six trigonometric ratios through the corresponding reference triangle | 4.3 | 3/23/17 3/30/17 4/6/17 4/27/17 |
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17 | Unit Circle (Level 1) | To draw the unit circle, including radian measures and sine and cosine | 4.3 | 3/16/17 3/23/17 3/30/17 4/6/17 4/27/17 |
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18 | Unit Circle (Level 2) | To draw the unit circle, including radian and degree measures and sine, cosine and tangent | 4.3 | 3/30/17
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19 | Graphs of sinusoidal functions | To write a sinusoidal function whose graph meets given characteristics | 4.4 | 3/30/17 4/6/17 4/27/17 |
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20 | Solving a trigonometric equation algebraically | Given a trigonometric function, to solve it algebraically | 4.5 | 4/6/17 4/27/17 |
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21 | Solving a trigonometric equation graphically | Given a trigonometric function, to solve it graphically | 4.5 | 4/6/17 4/27/17 |
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22 | Inverse trigonometric functions | Given two sides of a right triangle, to identify an acute angle | 4.7 | 4/27/17 | ||
First-semester skills
Number | Name | Goal | Textbook section | Tested in class | Notes | |
1 | Simplifying expressions involving powers | To simplify expressions involving powers, meaning (1) each factor appears only once, (2) all exponents are positive, and (3) all exponents and constants are combined as much as possible. | P.1 | 8/25 9/1 9/8 |
These expressions may or may not include fraction bars. | |
2 | Using scientific notation | To convert between standard and scientific notation | P.1 | 9/1 9/8 9/15 |
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3 | Distance Formula | To find the distance between two points on the coordinate plane | P.2 | 9/1 9/8 9/15 9/22 |
Use a scientific calculator on this test. Your final answer may be an approximation. | |
4 | Solving linear equations | To solve linear equations. | P.3 | 9/1 9/8 9/15 9/22 |
These equations have one variable of degree 1. | |
5 | Solving quadratic equations by factoring | To solve quadratic equations by factoring. | P.5 | 9/8 9/15 9/22 9/29 |
These equations have one variable of degree 2. | |
6 | Solving quadratic equations by extracting square roots | To solve quadratic equations by extracting square roots. | P.5 | 9/8 9/15 9/22 9/29 |
These equations have one variable of degree 2. | |
7 | Solving equations by graphing | To solve equations by graphing | P.5 | 9/15 9/22 9/29 10/6 |
These equations have one variable of degree 2. | |
8 | Solving quadratic equations using the Quadratic Formula | To solve quadratic equations using the Quadratic Formula. | P.5 | 9/15 9/22 9/29 10/6 |
These equations have one variable of degree 2. | |
9 | Function characteristics | To model data with a linear function | 1.2 | 9/22 9/29 10/6 10/13 |
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10 | Twelve basic functions | To identify from a graph the following characteristics of a given function: name; formula; domain; range; boundedness; intercepts; intervals where the function is increasing, decreasing, positive, or negative; local extrema; symmetries; end behavior; and periodicity. | 1.3 | 9/29 10/6 10/13 10/20 10/27 |
This is the single most important skill of the semester. | |
11 | Function composition | To compose two functions and report on the resulting domain | 1.4 | 10/6 10/13 10/20 10/27 11/3 |
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12 | Function inversion | To write the inverse of a function and determine whether or not it is a function | 1.5 | 10/13 10/20 10/27 11/3 |
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13 | Confirming inverse functions | To confirm that two given functions are inverses of each other | 1.5 | 10/20 10/27 11/3 |
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14 | Tranforming functions | To write graphical transformations of given functions | 1.6 | 10/27 11/3 |
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15 | Solving for a variable | To solve a formula for a given variable | 1.7 | 10/27 11/3 |
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16 | Completing the square | To rewrite a standard-form quadratic function into vertex form, by completing the square | 2.1 | 11/3 | ||
17 | Line of best fit | To plot given points, and use a calculator to perform linear regression | ||||
18 | Parent functions | To identify the transformation in a graph | ||||
19 | Polynomial long division | To perform polynomial long division | ||||
20 | ||||||
21 | Exponential modeling | To model a real-world situation using an exponential function, and to use given values to find a missing value | 3.2 | |||
22 | Exponential functions | To graph a given exponential function | 3.1, 3.2 | |||
23 | Logistic functions | To use logistic functions | 3.1, 3.2 | |||
24 | Function composition | To compose functions | 1.4 | |||
25 | Inverse functions | To find the inverse of a function | 1.5 | |||
26 | Logarithmic functions | To graph a given logarithmic function | 3.3 | |||
27 | Evaluating logarithms | To evaluate a logarithmic expression | 3.3 | |||
Logarithm operations | To condense a logarithmic expression into a single logarithm | 3.4 | ||||
Exponential equations | To solve an exponential equation using algebra | 3.5 | ||||
Logarithmic equations | To solve a logarithmic equation using algebra | |||||
Change-of-Base Formula | To use the Change-of-Base formula to convert a logarithmic expression to a convenient base | 3.4 | ||||
Graphical transformations | To find the transformations on a graph of adding to, subtracting from, or multiplying by a given value | 1.6 | ||||
28-32 | TBA | |||||