Logarithm Properties, Tutoring at RLS

We worked on a problem with exponents and algebra.

Logarithms can be very useful for these problems.

There are three basic properties which are often used, two of them were used in this problem.

The logarithm of a quotient is the logarithm of the numerator minus the logarithm of the denominator.

The logarithm of a product is the logarithm of the first term plus the logarithm of the second term.

And the logarithm of something with an exponent brings the exponent in front of the expression as a multiplication.

Tutoring Law of Cosines, RLS Friday Sheet

We mostly worked on problems with the Law of Cosines. Along with the Law of Sines, this equation can be helpful in figuring out sides and angles of triangles. The Law of Cosines is the Pythagorean Theorem generalized for triangles that are not right triangles.

Also looked at a Friday sheet. One problem with exponents and logarithms was the most involved.

Another involved asymptotes.

Algebra at CSUMB with trig identities- sine, cosine, tangent, cosecant, secant, cotangent

We mostly did problems with trig identities.

SOHCAHTOA
CHOSHACAO

Reduced a few radicals to a simpler form.

Talked about how the 30 60 90 triangle and 45 45 90 triangles have ratios that you should probably know in this context.

Algebra at CSUMB with logarithms

We mostly looked at problems with logarithms.

Used both the properties for the log of a product and the log of a quotient.

Saw how the base, exponent, and result are placed in the equations.

Graphed a few related functions. You can graph functions using an x and y grid and using points. It helps to know the shape in advance, but that’s not completely necessary.

Tutoring math at CSUMB, systems of equations and quadratic equations

We started by looking at systems of two equations with two variables and using substitution to solve.

Then did a few problems with three equations and three variables.

Also used u-substitution to solve a few quadratic equations. If they can be factored, that can be easier. Sometimes quadratic equations cannot be easily factored, in which case it can be useful to use the Quadratic Formula.

Tutoring Algebra at CSUMB, vertical line test and horizontal line test

We looked at functions and inverses of function.

One quick way to see whether something is a function is to do the vertical line test. If a vertical line can ever pass through two points, it’s not a function.

An inverse function switches the x and y values. You can figure out if a function has an inverse that is a function by doing the horizontal line test.

Looked at telling the shape from a few types of equations, especially lines and parabolas.

Graphing Periodic Functions – Sine, Cosine, Amplitude and Period

We looked at periodic functions.

Started most problems by finding the amplitude and the period.

The amplitude is basically the absolute value of the coefficient multiplying the function. If there is no number, the amplitude of a sine or cosine function is 1.

The amplitude can be found by 2π/# the number in front of the x, as in cos(2x) the # is 2.

After that, you should know the basic shape of the sine and cosine functions. You can graph two periods (for this set of problems) and fill in the zeros.

Graphing Hyperbolas, Directrix, Focus

We worked on some upcoming material in the class with periodic functions.

Drew an angle on the unit circle and found the tangent of that angle. You draw the angle and a right triangle then find the ratio using SOHCAHTOA.

Graphed a parabola and looked at the focus and directrix. Also talked about some of the practical purposes of the shape of the parabola. If you forget the equations for these, you can google them if you know what to call them.

Did a problem with a hyperbola. And saw how the sign in front of the variables affects the orientation of the shape.

Looked at a little physics as well. For sound and light with higher wavelengths, the wavelength is shorter.

Preparing for an Algebra Test

We went through the review packet for the test.

One thing to watch for was to only combine like terms, so either numbers or variables with the same exponent.

We saw the difference of perfect cubes more than once, which has a corresponding formula.

You can always multiply by different forms of one to do things like getting a common denominator. Something divided by itself is one.

Need to be careful with parentheses and notation to make the work easy to follow and check.

If the denominators of two equal fractions are equal then the numerators will also be equal, that can save a few steps.

Usually quadratic functions have two solutions, sometimes they have one or none.

Tutoring Trigonometry, Use Trig functions on right triangles!

We went over problems with trig functions.

The functions only work with right triangles.

Looked at both the angle of elevation and the angle of depression in a few problems.

The final two problems were more complicated and involved two equations and two unknowns as well as calculating the tangent function of two angles and factoring as well as multiplying algebraic expressions.