Room 608

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
 
  2 Multiplying complex numbers To simplify the product of two complex numbers. P.6 1/12/17
1/18/17
1/26/17
 
  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
 

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
 

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
 
  6 Evaluating logarithms To evaluate a logarithmic expression 3.3 2/2/17
2/9/17
2/18/17
2/22/17
 
  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
 
  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
 

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
 

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
 
  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
 

12

Converting angle measures To convert between DMS and degrees 4.1 3/9/17
3/16/17
3/23/17
  13 Radian measure To convert between degrees and radians 4.1 3/9/17
3/16/17
3/23/17
3/30/17
  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
  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

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
  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
 
  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
4/6/17
4/27/17

 

 

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
 
  20 Solving a trigonometric equation algebraically Given a trigonometric function, to solve it algebraically 4.5 4/6/17
4/27/17
 
  21 Solving a trigonometric equation graphically Given a trigonometric function, to solve it graphically 4.5 4/6/17
4/27/17
 

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
 
  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
 

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
  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
  13 Confirming inverse functions To confirm that two given functions are inverses of each other 1.5 10/20
10/27
11/3
  14 Tranforming functions To write graphical transformations of given functions 1.6 10/27
11/3
  15 Solving for a variable To solve a formula for a given variable 1.7 10/27
11/3

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