Tutoring Precalculus at CSUMB

We started by looking at some linear equations. One thing he did not remember was that the slope of a line perpendicular to another line is the negative reciprocal of the other line.

Using parentheses for polynomial division can reduce mistakes.

He had a little trouble with radicals.

One problem involved projectile motion and was like a physics equation in that you need to think about what’s going on more than do complex calculations so much.

Precalculus with Interval Notation in My Math Lab – square/curved

We first looked at plotting a function. It helps to recognize the shape of the graph from the equation, but if you don’t, you still move to the next steps you would even if you know the general shape- you plot specific points.

A good point to start with most of the time is the y-intercept, you get that by setting x equal to zero.

From there, plot a few points. If you know there is symmetry, that can make the calculations easier.

Then we looked at linear equations for a while. We saw how the slope is written before the variable (oftentimes x) and that the y-intercept is the number after that (in slope intercept form).

Found the slope using the equation. And also saw that ‘average rate of change’ is the slope.

Went over interval notation a bit. In ‘My Math Lab’, [ are inclusive and ( are exclusive. You use the exclusive brackets for infinity since it’s not a specific point.

Tutoring Precalculus at MPC

We started by looking at how to factor trinomials. One option is to write two sets of parentheses. From there I look first at the first term, then at the third term. And I use the middle term to guide my choices.

There is another method that uses similar ideas but that is laid out in four sections of a large X.

Talked about when the quadratic formula is useful and used it a few times.

Got into algebraic perfect squares.

Did a bit with inequalities.

Saw some complex numbers.

Used the Pythagorean Theorem once.

Looked at a parabola, intercepts, and symmetry.

Graphing Trig Functions

We worked mostly on problems with trigonometric functions.

A few involved graphing the functions. It can help quite a bit to know the shape of the graph in advance. But, if you do not, or even if you somewhat do, then you can use

SOHCAHTOA
CHOSHACAO

Also used some double angle formulas and saw how you can use the trig functions with sums for double angle formulas.

Infinite sums, getting towards the idea of integration

Worked on problems related to the early ideas of calculus today.

The ideas today were closer to integration, finding an area using a summation of infinitely small rectangles using limits.

That meant finding the area of one rectangle and adding up all of them. So a base multiplied by a width.

The actual shape was a triangle and rectangle, but the technique becomes more useful for shapes which are not easy to calculate.

There were quite a few steps, so a single mistake could throw everything off.

RLS Friday sheet Precalculus tutoring – fourth order polynomial with complex numbers

We started by talking about the Lorentz Force Law which makes many problems with forces and magnetism make more sense in my opinion.

Then looked at a Friday sheet.

Did a problem with complex numbers starting with a fourth order polynomial  that had two zeros given. It involved either long division or synthetic division, we used long division.

Another problem had logarithms. e^x and lnx are functions that counteract each other.

The half angle formula was used for another problem.

Starting to look at limits in precalculus

We looked at limits in the context of the last few weeks of precalculus.

All of the functions we saw had a (single) removable discontinuity or hole. The limits were found for that point and two other points. For the limit to exist, it needs to go to the same place from the right and from the left.

It didn’t exactly make sense to find a limit for points that did not have holes, but that was part of some of the problems.

Tutoring Precal for RLS, Double angle formulas and graphing trig functions

We started by looking at homework which used the double angle formula.

The basic approach was to do two things, could start in either order.

1. Draw the angle with a right triangle on the xy axes.
2. Use a double angle formula which is convenient

You can figure out the ratios for the trig functions using
SOHCAHTOA
CHOSHACAO

Then looked at a previous test with graphing trig functions. Should spend more time on that. But one thing you can do most of the time is plot points by plugging in x values and getting y values. You use again,

SOHCAHTOA
CHOSHACAO

It does help quite a bit to know the basic shape of the functions.

Tutoring RLS Precalculus, trig functions and Friday sheet

We looked at some problems with trig functions, especially sum and difference formulas.

For many of them, the angle does not need to be known if the sides of the triangle are known.

Used the half angle formula a bit. Reviewed the quadrants and which trig functions are positive and negative in different positions.

Then got into the Friday sheet which dealt with logarithms a bit.

Tutoring Precalculus, Series and Sigma Notation

We mostly looked at problems with sigma notation. At the bottom of the capital (Greek) letter Sigma, there is a variable with the starting point and at the top a finishing point if it is finite or infinity.

Then the sequence of numbers goes into an equation that are added together.

For a geometric series, there can be a finite sum or it can diverge.

Exponents can be used, and series can also alternate between positive and negative. You can describe the same series in ways that look different.

Looked a bit at combinations and permutations, including one that required a somewhat seldom used formula at least in high school math classes.