Cset 1 Prep. Workshop
Summary of Day 1:
On the first day, we began by discussing number systems from the perspective that as humans needed to solve more and more complex equations, they needed to add different types of numbers to their number systems in order to have solutions. We then were able to easily answer all of the questions on the first part of the questionnaire (see below) on number systems. Next, we derived the concept of slope using simiilar triangles in which case we developed the y=mx+b form and reviewed graphing. Then we studied the unique solution, no solution and infinite solution cases by means of graphing and by using matrices (a prelude to linear algebra near the end of the workshop). We concluded our last hour understanding and mastering how to solve linear inequalities in two variables by having workshop participants present various parts of solutions.
Hmk. 1 is below as textbooks have not yet arrived. In addition, a handout for algebra-brushup is included with Day 1.
Standard Proof of quadratic formula:
Summary of Day 2
For the evening session, we began by definining polynomials and then reviewing factoring and sythetic division. Next, we introduced the Factor and Rational Roots Theorems as means to find roots of polynomials, factor polynomials, and create sketchs of the graphs of polynomials.
Summary of Day 3
We continued with the Factor and Rational Roots Theorems, with special emphasis on sketching graphs of polynomials based upon roots and extreme behavior on the x-axis. We also discussed the complex conjugate roots theorem and were able to predict the nature of possible roots based on the degree of a polynomial, its graph, and or the known existing roots
Summary of Day 4
Several proofs on polynomial roots were done (Remainder theorem and Factor theorem), and then we discussed multiple roots, points of inflection, and graphing. After this we tied up some loose ends of chapter 2 by going over sum and product of roots formulas for polynomials, as well as some examples. The remainder of the session dealt with introducing and working with the Binomial Formula and understanding the nCk formula using the 'counting principle' and an example of ordering different types of pizzas, given certain selections of toppings.
Summary of Day 4
Today we worked through Chapter 3, going over many of the homework problems related to the Binomial formula. After that we began Chapter 4 by going over numerous examples of relations and functions, introducing the vertical line test, going over the domain and range concepts and looking at homework problems.
Summary of Day 5
We began this session with the first of many practice CSET 1 problems. We only did the first two pages. The next two are for day 6. After going over the problems, and emphasizing the importance of knowing the 'powers of the imaginary number i,' we delved into inverse graphs, inverse functions and the horizontal line test. We also defined inverses by going into the composition of functions definition, did numerous examples and we learned to procedurally find inverses by switching x and y and then solving for y; however, it was emphasized 'why' this procedure worked by looking at the graph of a function and using the y=x line to get back to x after taking f(x). We went over problems from each area of the homework dealing with inverses and inverse graphs.
Emily was kind enough to provide some notes from the evening.
Summary of Day 9
We began the evening with a review problem and then a discussion of the rules for exponents in the context of why we need to learn exponents to simplify expressions that arise in calculus, such as computing the derivative using the quotient rule. Due to typos, here is a best version of Ch.6. We finished the evening solving equations involving radical expressions and extraneous solutions. Here are my notes for the evening; Ch6_CSET1.
Summary of Day 10
After doing some review of a problem from the section on radical expressions, we delved into a discussion of vector equations which led to the understanding of a 'constructed response' question handed out in the workshop.
Summary of Day 11
We worked through the following practice exam, except for the questions on vectors and matrices (to be covered soon).
Summary of Day 12
On this evening we completed chapter 7on exponential and logarithmic functions. I have recently discovered pdf files from an early version of our text which seem to not have typos, so I am including them here for reference: