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## Tips How to Create and Teach a Pre Calculus Course

It is essential to have a pre-calculus course that covers all the topics covered in pre-calculus in a single subject. This subject is overwhelming for many students. This is because they need to have a thorough knowledge of various other subjects. The student must have a solid foundation in algebra, geometry and trigonometry. Pay special attention to the binomial theorem, conic sections, complex numbers, and real numbers.

Calculus is the branch of science that deals with rates of change. In algebra, the student is taught a function that represents a physical quantity, for example, the amount of water in a tank in relation to time. Despite this; in calculus the interest is in the rate at which water changes in a tank in relation to time. It can be clearly seen how calculus completes the picture after algebra. Algebra answers one question and calculus answers a different question and together they give the whole picture.

The calculation requires the student to have a good knowledge of algebra. A good tactic for teaching algebra in a precalculus course is to point out the points that most students have trouble with. Students studying algebra have particular problems with exponents and logarithms.

It is good to use calculators to do lab experiments to get students to understand exponents. For example, the teacher might ask students to use their calculators to find the exponents of 0, 2, 4, 100, and 200. Students will see how the change in the output becomes very steep with small changes in the input. Next, the teacher should ask students to use their calculators to graph an exponent function. Students should examine the curve and see how small changes in the input cause a dramatic change in the output. The same experiments should be done with logarithms. The teacher must choose a base and choose the values to take the logarithms. The teacher should let students try forbidden values such as negative values and see how the calculator responds. Also the teacher should let the students plot a logarithmic function and locate the forbidden values on the graph.

Geometry is very important to calculus. The most important concept in geometry related to calculus is area. The student must see how he can find the area of a shape by cutting it into simpler shapes and adding the individual areas of those shapes. The student should see that we can simplify the calculation of the circumference by simplifying the circumference by considering it a polygon. This simplification causes some margin of error. Despite this; the error decreases as we increase the number of sides of the polygon. The error becomes zero when the number of sides becomes infinite.

Although the need for trigonometry does not come at the beginning of a calculus class, students should know the basic trigonometric functions and their relationships. Students should appreciate that cosine is a sine with a shift and sine is a cosine with a shift. They should view their graphs simultaneously on a calculator.

After knowing what to teach in a pre-calculus course, an appropriate textbook must be chosen to assign to the class. Choosing a textbook is not an easy task. Some students would not do well in a course just because the textbook was not friendly or easy to understand. The textbook should be easy to understand with lots of examples and start from the beginning. The teacher’s explanation of the concepts should be very similar to the textbook so that the students do not get confused.

For each new concept or idea, the teacher must solve several demonstration problems. This really allows the student to follow through on the ideas discussed in class.

The teacher should allow students to ask as many questions as are necessary for understanding. Students need to know that their questions are welcome and that it is important for the teacher to understand the concepts.

Throughout the course students will have to do laboratory experiments using calculators to dissolve the concepts. They would need an algebra calculator, a basic scientific calculator, and a graphing calculator. There are many innovative software calculators like kinematic calculators and many others. These calculators allow the teacher to be creative in how they create math lab experiments.

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