Week8-Math10-Graphs

In week 8 of math10 I learned how to find the slope of a graph.

The slope is how much a graph changes from point to point The way you show a slope is in a fraction the Rise/Run (y/x).
E.X:


The change from the blue point to green point is 1 up in the Y value and 1 to the right on the X value. so the slope is the rise over the run which is 1/1. To make it look better you can just say 1.

Week7-Math10-FunctionVSRelation

In week 7 of Math10, we learned the difference between a function and a relation.

A relation is when there are 2 of the same values for the input but different values for the output. For example.

Input|Output
1 | 3
3 | 4
1 | 2
5 | 1

This means that this is a relation because there are two one’s in the input but have different outputs.

On a graph, it’s easier to see if the graph is a function or relation using the vertical line test.
On a graph this is what it would look something like this.

If you took a ruler and held it up straight and went through the graph you would see that the graph touches the ruler on the same X-axis more than once. Therefore, it is a relation.

Week6-Math10-Polynomials-CollectingLikeTerms

Polynomials are pretty much a bunch of unknown numbers, and it gets very hard to stay organized when dealing with so many variables. Therefore, collecting like terms is very important because it helps you stay organized while doing polynomial math.

What are like terms? Like terms are numbers with the same variable attached to them for example 4X and 2X are like terms. However, 4X and 4X^{2} are not like terms because of the different exponent.

Collecting like terms is adding all the like terms in an equation. For example.

Before collecting like terms.

5X-3-5Y+12X+10Y-23

After collecting like terms.

17X + 5Y – 26.

Week4-Math10-Sine

The sine is a trigonometry function that let’s you find either an angle or the length of a side of a triangle. This is how to find an angle of a triangle with 2 sides given to you (you have to know the length of the opposite side and hypotenuse.)

Let’s say you know that on this triangle the “Opposite” is 10 cm, and the hypotenuse is 16 cm.

So all you do is divide the opposite by the hypotenuse (10/16) and depending on how your calculator works you either press sine and type 10/16 or you type 10/16 then sine.

There you go, you now have the unknown angle!

Week3-Math10-NamingSidesOfTriangle

In week 3 of math10, I learnt how to name all sides of a right angle triangle (Adjacent, opposite and hypothenuse).

step 1:
You have a right angle triangle with 3 sides. You find the little box usually found on the bottom left of a triangle and on the exact opposite side of this box is always going to be the hypothenuse. In the picture, the “c” is the hypothenuse.

step 2:
Now to find the “Opposite” first, you find the unknown angle of the triangle. After, you look at the direct opposite side of the triangle once more and that would be your “opposite”. Depending on where the unknown angle is the “a” or the “b” is the opposite.

step 3:
Now the last side of the triangle is always called the “Adjacent”. The adjacent is the same side as the unknown angle. Depending on where the unknown angle is the “a” or the “b” is the adjacent.

Week2-Math 10-Negative exponents

The most important thing I learned in week 2 of math10 was the negative exponent rule.

#1 The negative exponent rule states that if there is a base with a negative exponent we change the position of that base to the other side of the fraction.

E.X: x^{-2} = 1/ x^{-2}

#2 Then we remove the negative sign and we have completed the negative exponent rule!

E.X: 1/ x^{2}

This rule can go both ways, so if we have a negative exponent at the bottom of the fraction we can move it up top without a negative sign!

E.X: 1/ x^{-2} = x^{2} / 1