WHAT TO EXPECT IN PRE-CALCULUS SUBJECT? HOW TO PASS AND EXCEL IN PRE-CALCULUS?

Pre-calculus is usually a subject taught in

 Senior High School. As its name says, it’s a 

subject for the preparation in basic calculus. 

Most of the time, students are not eligible to 

sign for calculus courses if they have not 

completed pre-calculus. Some may be eligible 

but it is better to sign up for a pre-cal course 

first as this is a good foundation for the real 

calculus.

If you are already aware that you’ll take up this subject soon, 

you may be interested to know what you should expect in this

subject and how you can pass it or even get a high grade. 

Below are some of the introduction and tips for you!

 

 

WHAT IS PRE-CALCULUS?

Calculus is a field in mathematic formulated by Sir Isaac Newton and Gottfried Wilhelm Leibniz that focuses on continuous function. On the other hand, pre-calculus focuses on mathematical prerequisites for calculus, such elementary and intermediate algebra, trigonometry and elementary geometry.

Though Pre-calculus is far related to the real calculus, it provides the students to learn critical thinking and gain analyzing and problem solving skills. This subject acts as a refresher to the students’ mind to better prepare them to calculus. For example, a pupil will not be taught addition or subtraction if he doesn’t yet know how to write numbers because that will cause information traffic and confusion to that pupil.

WHAT IS THE SCOPE OF PRE-CALCULUS?

·        
          CONIC SECTIONS

Certainly, your teacher will be talking conic and conic and conic every day. In mathematics, according to Wikipedia, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The four conics you’ll be touching in pre-cal are circle, parabola, hyperbola, and ellipse. So expect that you’ll be graphing every day, every quiz or seatwork, every exam, depending on your teacher.


CIRCLE

Under the circle lessons, you should expect to use your background knowledge in the general and standard form of a circle. You will find the center and radius of each form as long as the equation of the circle with center at the origin and center at (h,k) and tangent to a line.

PARABOLA

Under Parabola, you will be tackling the parabola with vertex at the origin and vertex at (h,k) wherein you will find the focus, directrix, vertex, latus rectum. You will also be graphing the result.

ELLIPSE

You will be studying and graphing the standard form of the equation of an ellipse with center at the origin and at (h,k) foci on the x-axis or y-axis.

HYPERBOLA

Included in this conic section are the properties center at (h,k), transverse axis parallel to or coincident with the x-axis (or horizontal transverse axis) and the properties center at (h,k), transverse axis parallel to or coincident with the y-axis (or vertical transverse axis). And just like the other conic sections, you will be graphing in your hyperbola classes.

You should also expect to tackle sequence and series and sigma notation wherein you will also rewrite series to sigma notation and vice-versa.

Binomial theorem is also part of the subject. You will be touching some terms such as Pascal's Triangle and combination.

Trigonometric functions are also included in the subject including the algebraic functions such as quadratic, exponential, polynomial and logarithmic.

The domain and range of functions are covered, along with finding the intervals over which a function increases or decreases and performing transformations on a function.

This is not a complete study map, just the fundamentals. There are much more lessons underlying on it. I recommend you download this pdf file as your reference:

PRECALCULUS COMPLETE LESSONS

or if you want a video tutorial:

PRECALCULUS VIDEO TUTORIAL 


HOW HARD IS THIS SUBJECT?

I can say that  pre-cal is in the middle in terms of difficulty. As long as you have a good stock knowledge in algebra, trigonometry and geometry, you can compare its difficulty when you are still in gradeschool and starting to learn how to divide a whole number by a decimal number or vice versa. You can also take the subject easily and if you really want it to be that way, refresh your old notebooks and textbooks, and begin investing enough time to prepare yourself for it. 

Don’t just rely to the information your teacher provided. Look for video tutorials or ask help from a reliable friend. If you are into teamwork, don’t hesitate to join or even organize study groups.

Unfortunately, this will be tedious subject if you have no prior knowledge in mathematics and what you just know is how to use PEMDAS. If you’re not also into graphing and your teacher wants your graph to be perfect at its finest, it will really be difficult to you.

HOW TO AVOID FAILING IN THIS SUBJECT?

In any subject you are enrolled in, failure grades are inevitable. Every student’s capacity has an extent and you cannot widen it immediately. However, it is relatively easy to keep yourself from this situation. Just do all the best preparation, continue self-educating and always listen to who’s talking in front.

Sometimes, it’s up to the teacher. Some teachers are stricter. Some teachers are more complicated. Don’t just focus on the lessons. You should also adhere to the standards of your teacher and whatever rules they impose in that subject; it’s probably the best way for your advance effective learning. Some teachers prohibit late students to enter the classroom, some prohibit erasures in your test and graphing paper, some may give surprise quizzes. So learn these teachers’ standards to avoid failures in this subject.

Some teachers give many performance tasks related to pre-cal such as making decorations with the circle as the main theme, creating a mini-hyperbolic arc and hyperbolic bridges. If your teacher includes graphing in his teaching, invest money for graphing papers, rulers (and protractor and compass), and pencils. If he or she demands perfect graph, do all your best on it.

CAN I RECEIVE GOOD GRADES FROM PRE-CALCULUS?

Of course! Just be reminded of the tips you have read above but to sum it up, here’s the path:

1.      If you still have time to prepare yourself, look for some help who can teach you the fundamentals in this subject. But remember that it could cause confusion because your real teacher in pre-cal may teach in different manner, may provide different formulas, may give problems harder what you have expected. But at least, you have had gain hints and you can take this as an advantage in your recitation where you can share your knowledge about the lessons.

2.      Know and follow the rules of your teacher as long as it’s for your own good sake. If he prohibits something, avoid doing it. If he commands something, follow it.

3.      Stay connected with and love mathematics, be patience in studying well. These are not requisites but it will maximize your opportunity to get high grades. Do math every day. Learn something new formulas, techniques and trends. Solve and graph problems every day to sharpen your pre-cal skills. Lastly, learn how other people solve the particular problem that is different to your approach.

If you guide yourself with these, pre-cal will just be smooth in passing into your brain. But here’s a word that you shouldn’t omit: ENJOY!