In which quadrant is the point (-5, 4)?

Saw this question, thought it could be best shown with a visual.

The first coordinate is the x-coordinate, the second is the y-coordinate.

coordinate_axes_second_quadrant

How can DMX unintentionally help you with math? Distinguishing between domain and range

We started with some inequality problems and interval notation. The thing we focused on was square brackets vs curved brackets [ and (. One is inclusive, like a closed dot, and the other is exclusive like an open circle on a number line

When boundary points are found, three regions are divided. It’s good to pick convenient numbers in each region to test them.

We also looked at U notation (union) and the upside down version (intersection). Sometimes that is used. Same meanings as the words ‘or’ and ‘and’.

Domain refers to the horizontal (x-coordinates) a trick to remember that is DMX, if you know who DMX is.

Also plotted a few equations using points.

The sum of perfect cubes equation came into play again.

We looked at how the discriminant can determine whether a quadratic equation can be factored.

And u-substitution was used again.

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.

Tutoring Math Friday Sheets at Stevenson School

We worked through the Friday sheet. These sheets are going to be challenging and can include material outside of the normal classwork. I have seen them before for students at RLS.

One important equation to recognize is the sum of perfect cubes and the difference of perfect cubes. One can be turned into the other easily with a little bit of algebraic manipulation.  Probably by looking these up he will memorize them if they continue to pop up, which they likely might. And if you recognize what something is, you can often look it up if you include enough detail “difference of perfect cubes” in Google for example.
With graphing, knowing the basic shape of the graph in advance by looking at the equation can help, especially lines/parabolas at this point.
You often factor when simplifying algebraic equations.

“What is the meaning of “x over y” in mathematics? Does it mean x /y or y/x?”

x_over_y

x is above y in the fraction, hence “x over y”. If you use a / then the two variables are side by side. I almost always recommend using the numerator above the denominator way of writing fractions instead of the slash mark, generally much more functional.

Getting Points from a Linear Equation

Let me know if you have questions.

Square root of 125 simplified

Square root of 125 simplified

First I factor what is within the square root. You could say it’s √(25*5) and then factor again, I went instead to √(5*5*5)

From there you can separate the two pieces in their own square root signs.

Then you have a whole number multiplied by the square root of a prime number.

Simple Factoring, Quadratic Polynomial, Algebra


Factoring a simple quadratic polynomial.

(assuming you can factor it)

First start with two sets of parentheses. Then I look at the first term then the third term and finally the second term.

Synthetic Division of Polynomials

We started by looking  at long division and synthetic division of polynomials.

Long division was familiar, synthetic division was new.

Synthetic division can be faster and less written work, but is more straightforward with certain conditions. You can use one method to check the other.

There is a decent explanation here, but with a mistake in the final example.

http://www.mesacc.edu/~scotz47781/mat120/notes/divide_poly/synthetic/synthetic_division.html

The ‘test zero’ goes on the outside. If you are dividing by (x-2), the test zero is 2, if you are dividing by x+6, the test zero is -6, etc. The test zero is the number that makes the denominator zero when you plug it in.

Synthetic division is straightforward when the coefficient for the variable in the denominator is of the form x + a and the leading coefficient of the numerator’s first term is 1.

Wikipedia describes how you can use it when things get more complicated, but I would probably just use long division if that is the case.

We then looked at some graphing of equations and inequalities. To find the x-coordinate of the vertex of a parabola you use -b/2a.

Also simplified some expressions.

Fractional Exponents, Logarithms, Quartic and Cubic Equations

We started by looking at some current homework which involved factoring. For most of the problems they started with a quartic or cubic equation and then factored into a quadratic and one or two other terms.

Cubic equations can have three solutions, quartic equations can have four.

Talked a little about one application of imaginary numbers since we saw complex numbers in some solutions. And went into more detail about how to do calculations with them.

Talked about fractional exponents for a bit and how to work with them. Also about logarithms. The base being 10 if no other base is shown.

Fractional exponents are almost always easier to work with than ‘cube roots’, ‘fourth roots’ etc. Square roots aren’t too bad but still can be harder to manipulate in some cases.

Last problem we worked on was a three dimensional volume of a cone with the top cut off. Looked at the application of similar triangles and the proportionality of the sides.