We looked at slope intercept form and how m is the slope and b is the y- intercept.
To get the y-intercept, you set x = 0
to get the x-intercept, you set y = 0
To get the slope, you use two points (some are easier to work with than others)
Then take (y2 – y1)/(x2 – x1)
Subtracting a negative two is like like adding two
x – – 2 = x +2
If you have the slope and a point, you can plug in the x and y to get the value for b and then complete the equation.
We reviewed for the test.
Started with parabolas. (h, k) stands for the vertex. The x coordinate being h and the y coordinate being k. In alphabetical order, just like x, y.
The focus is a distance p from the vertex as is the directrix, in opposite directions. The focus is inside the parabola.
If rays of light hit a parabola, they go to the focus.
Also looked at ellipses and hyperbolas.
Amps and current were first thought of with Ben Franklin, so the convention is of positive charge moving.
Ohm’s law is useful when it’s applicable (which is likely throughout this class). V = IR
Power can be a variation of P = I V and power itself is energy divided by time. You can substitute Ohm’s law into that equation for variations.
Opposite charges attract, like charges repel.
Sometimes you will use things like kinematic equations with newer material.
Tutored calculus for a couple of hours the other day, just before the student started Calculus II. Here are some things we went over.
We talked about the purpose of a derivative and how you can optimize things early on and how integrals can find the areas under various curves and on into three dimensions, etc.
Went over how logarithms can be useful, what the natural number e is, and the behavior of the natural logarithm.
How algebra can simplify calculus before doing derivatives or integrals.
How to deal with fractional exponents.
How the order of approach for fractional exponents can simplify things.
Thinking about the behavior of functions for limits.
How exponents like 1/4 and 1/6 work.
How the ln function increases and decreases very slowly.
How to divide by fractions by multiplying by the reciprocal.
Using common denominators.
Going over integration by parts.
Doing some derivatives and keeping track of the sign.
How squared trig functions look.
Factoring out algebraic terms.
Use the product rule when differentiating a product.
Picking u and v for integration by parts won’t always work out, if it seems to not be working, you may want to choose something else.
Doing an integral is taking an anti-derivative and finding something that when you take the derivative of it will give you what you started with between the integral sign and the differential.
Started with sequences. Arithmetic and Geometric. Looked at the relevant formulas then used them.
He needed to figure out whether series were arithmetic or geometric.
And looked at convergence for geometric series.
Also looked at permutations and combinations. Permutations are like a telephone number, the order matters. With combinations, they are more like pizza toppings- mushrooms and olives is like olives and mushrooms, the order does not matter.
Many calculators can compute these.
We mostly looked at functions with polynomials that had asymptotes and holes.
One polynomial had the form of a sum of two cubes, where knowing a related formula is helpful.
To get the coordinates of holes, you plug the x-coordinate that gets a factor of zero in the denominator into the reduced equation.
Finding the behavior close to the asymptote is important, it generally goes up very high or down very low.
To find end behavior, I plug in high magnitude positive and negative numbers. The terms with the highest exponents become more important then.
We mostly looked at hyperbolas.
For the equations, one term (x or y squared) is positive and the other is negative. The graph will be either vertical for positive y or horizontal for positive x.
h,k are the center. The asymptotes will go through the center.
Sometimes associating something with an image can help. I thought of b/a corresponding with the letter b and being horizontal.
For factoring cubic equations, if you have one zero, you can divide using that information and then get to a quadratic function.
Focused mostly on arclength.
The equation used is that for circumference. And then you figure out the fraction of the circle. Which could be any amount, sometimes it was 1/2 for a semicircle.
You can convert between radians and degrees using a conversion factor, just like you would for cm to inches, etc.
Reviewed some common angles in radians, which are often fractions of pi.
2r is the diameter. So if the diameter is given, you can substitute it for 2r.
We started by looking at arithmetic and geometric sequences and sums.
Arithmetic is more like addition, geometric has more to do with multiplication.
Subscripts are used as labels. If the number is next to a letter, it looks like multiplication.
Separating a number with a summation for an exponent into two pieces can be useful.
And either ln or log is often useful for problems with exponents (especially when they are more complicated).
One test problem was worded in a strange way.