Tutoring Chemistry, pH Ka, Acids & Bases

You can find the pH by taking the negative log of the concentration of H+ or H3O+ and the pOH by taking the negative log of the OH-

There are various ways to do calculations with Ka and the pH.

We checked out Bronsted-Lowery acids and bases and the theory with proton donors/acceptors.

Also, with chemistry, you want to be very careful with the names since changing them slightly can mean a different substance.

And rounding early is not a good plan since it can introduce inaccuracy.

Tutoring SAT Math Calculator Section

We focused on questions in the calculator section that she was having trouble with.

The first had a bag of marbles and was about finding probabilities. The basic idea is to find the number of specific option(s) you want and divide by the total number of options. There are variations on that.

For another problem, the vertex of a parabola was needed. You can use -b/2a to get the x-coordinate. That can also be derived using calculus by taking the derivative of ax^2 + bx + c and setting it equal to zero since the slope at the vertex is zero.

Sometimes using different forms of an equation, including what is originally listed, can be more useful for certain applications than a derived form.

Getting a common denominator is important for some problems.

The SAT often has answers that you would arrive at by making common mistakes.

Mean, median, and mode can show up. Most common would be mean (average).

sin^2x + cos^2x = 1, that showed up in practice.

SAT Math, Adding 10% more efficiently

Alejandra seems to have a good foundation in math. With the SAT though, there are some topics which she has not seen in a few years which are less familiar. Also, the test often includes answers that you would arrive at if you make a common mistake.

For example, on the first problem we looked at, she went through the problem quickly but made a small mistake with overlooking a negative sign. That means she understands the process, however, she would have gotten the wrong answer there.

We went over the formula to get the sum of the interior angles of an n-gon, something like that could show up.

Also went over how adding 10% can be done more efficiently by multiplying by 1.1, etc. That was a useful technique for the test at times.

Why is Tan(90°) Wrong? (Undefined)

I’ve drawn a triangle that has an angle close to 90°, it’s looks more like 85°. That is to make it look like a triangle rather than a degenerate triangle (straight line). But I have used the values of the sides for when the triangle has a ninety degree angle.

tan_90

As you go from 85° to 90°, the adjacent side goes from being small to being zero.

Using SohCahToa, you can get the tangent of theta by dividing the opposite by the adjacent side.

1/0

Which is either undefined (in earlier classes) or something like ∞. The limit from the right and left changes the sign though.

SAT Triangle Maximum Area

For an SAT Math question that gives two sides of a triangle 7, 10.

triangle_maximum_area

You could pick any kind of triangle you want, but I would recommend thinking about a right triangle, if you do that, you don’t need to use any trig functions. And that is the type of triangle that it turns out will maximize the area.

It could help to sketch this out.

You also need to know the formula for the area of a triangle.

So I imagined the bass as 7 and the height as 10, you don’t need to know what the hypotenuse is.

So (7*10)/2 = 35, which is a possible choice.

You could get less area, but not more for the given dimensions.

The choices that are larger than 35 are much larger. 70 might reflect the mistake of not multiplying by 1/2.

I think it really comes down to knowing the equation for area of a triangle.

Greater and ‘Greator’ with ‘or’, Tutoring Algebra II

Today we looked at inequalities, plotting them on number lines and interval notation.

One trick is to use the similarity between the word ‘greater’ and ‘greator’ with an ‘or’, most times inequalities with absolute value and a greater or greater/equal symbol will result in a solution set that includes the word or.

Absolute value is the magnitude, the distance from zero, always positive.

Cannonball Problem Diagram and Equations

cannon-problem-physics

The two equations are the two basic equations used in most kinematics problems for the first few chapters of a physics book generally.

Do you know what to do next?

How Chocolate Can Help You Learn Trigonometric Functions cosecant, secant, cotangent

chocolate_01400

Why would chocolate help you with the trig functions?

If you know SOHCAHTOA, which you should learn if you are taking math, you know the ratios for three trig functions.

There are three other functions that have the reciprocals of the ratios of those functions.

I remember mixing up secant and cosecant sometimes, which one was paired with sine and which with cosine.

If you know SOHCAHTOA, you could learn CHOSHACAO. But more simply than that, if you know SOHCAHTOA, you can just remember Chocolate.

CHO is the first part and if you line them up like this:

SOHCAHTOA

CHOSHACAO

The first of the lesser known trig functions lines up with Sine. So the ratio for cosecant is the reciprocal of the ratio for sine.

It’s fairly easy to remember that cotangent and tangent line up. Therefore you now know two of three so secant has to line up with cosine.

choshahcao_chocolate

What is the sin of 90 degrees, Tutoring Precalculus

We looked at coordinates and their rays from the origin and the six trigonometric functions. To do that, we used SOHCAHTOA and to remember the other three functions, you can use the word ‘chocolate’ since CHO, cscx=H/O is the reciprocal of sinx.
To visualize the ‘triangles’ for the two directions on the x-ax and the two directions on the y-axis, I’ll draw something like 85 degrees instead of 90 since it’s fairly close and then label one side of the triangle as zero and the other two as equal values (1 usually works well).

choshahcao

Tutoring Physics 2A at MPC Before Test 1

We looked at how two of the kinematic equations are most fundamental to the problems for the first three chapters. Also looked at how the summation of the forces will be zero if there is no acceleration.
For one problem, it could be solved with the quadratic formula or in a different order without it.
Drawing a diagram and then writing the general equations would be one way to start many of the problems.

The first test covers the first five chapters.