Letter to Precalc Students
© October 2018, A. Azzolino
By now you should have read my letter and have gotten a feel for who I am.
Soon we see who you are. We see if you are ready at this moment to earn an A, B, or C, to see if you
are a serious and well-prepared student or if you must extend extra effort to become one. You need:
- arithmetic and algebraic proficiency -- the ability to do arithmetic and algebra,
- arithmetic,algebraic, trig, and precalc background -- the ability to recall topics taught in these courses,
- willingness and time to complete homework and study and get help on it if you need help -- remember, 2 hours of homework for
every hour of class time,
- the ability and willingness to get to class on time and without missing classes -- quizzes are often on a daily basis and at the
beginning of class,
- the ability to do well on quizzes, tests, and the final exam -- including proofreading your tests before handing them in.
We go into more detail than in a high school course. It is also a tough course because we have so much
to do so quickly and because there is such a variety of material which is needed for immediate recall.
It is a tough course but the results are fairly consistent from semester to semester. They are also consistent with the grades
given by fellow faculty members in physics and chemistry in their tough courses.
If you earned an A or B in your high school precalc and know how to study you should be fine. If you got a C or D in
high school precalc or if it was a few years ago, you probably will need to make an extra effort.
See how today goes. I do not consider the work today at all difficult. It is precalc at its easiest.
|A few of the skills needed for precalc success include:
- Recall perfectly a formula or equation
- AND KNOW HOW TO USE IT AND WHEN TO USE IT:
- Like the Pythagorean theorem
- Like the quadratic formula
- Like the distance formula
- Like the point-slope form of a line
- Like the standard form for a circle
- Like the a cosine law formula
- But NOT resort to using ANY formula
- Complete a procedure such as:
- Solve a quadratic by using the quadratic formula
- Solve a quadratic by completing the square
- Solve an equation with radicals
- Solve a trig equation which requires use of the quadratic formula.
- Solve an equation:
- You haven't seen since 8th grade.
- You haven't ever seen before.
- Quickly understand and use new symbols
- Like simplify sin(30°)
- Like simplify log2(1/8)
- Like simplify e3x ÷ ex
- Like simplify sec(
- Simplify trig and log expressions
- Graph & point-plot
- Graph unknown functions without a calculator
- Graph or sketch immediately function similar to those you have seen before
- Know what a graph will look like simply by reading its equation
- Understand and use mathematical vocabulary
- Like tangent, hypotenuse, linear coefficient, log
- Like secant, reciprocal, asymptote, end behavior
- Like discontinuity, rational, rational function.
- Show up on time for quizzes tests classes
- Hand in homework when it is due
- Work alone and with others even though no assignment is to be collected
- Use a calculator
- To compute
- To solve
- To graph
- To verify
- Write mathematics
- So a logical progression is shown from step to step,
- Such as an expression, which describes a situation which is familiar.
- Such as an expression, which describes a situation which is new to you.
- Such as an equation, for a situation which is new to you so that you may find an unknown value.
- Such as notes, so you can use them to do a problem similar to the one done in class.
- And be able to proofread your own work
This is why you need a C or better:
- You really need to know the precalc and algebra and trig to use in calculus.
- Most colleges do not give you credit for a course in which you have not earned a C or better.
- If you do not get a C or better, you lose your scholarship money!
Here are possible choices if you do very poorly today.
- Stay in the course and study on your own and see how you do and make a decision later in the semester.
- Stay in the course and as soon as possible spend time in my office doing homework and studying.
- Stay in the course and as soon as possible get tutoring in the tutoring center or with a professional.
- Stay in the course and AT WORST fail it and retake it next semester.
The second grade replaces the first in your overall cumulative average.
- If you wish my second opinion, I can give you another 1-page quiz but the grade will not count.
Study for it. The work (without a calculator) deals with:
graphing, simplifying simple exponents, logs, and trig, and solving equations.
Make a decision once it is graded.
- Stay in the course and if you decide not to continue in the course,
OFFICIALLY drop the course so you do not earn an F by not completing the course.
Good luck and have a good semester.