The slope is the steepness of a line. On positive slopes the line rises from left to right where as on negative slopes the line decreases from right to left. (M) is the variable for slope and rise is (X) and run is (Y)
M= Rise (x) / Run (y)
M= y1-y2 / x1-x2
This week we learned about domain and range. In the beginning I didn’t really know what to do with inputs and outputs but when we got deeper into the lesson and did more examples I started to get it a little more. Abide by the BEDMAS rule when solving a function, you also replace the variable with the number given for the (x) value.
Domain: the independent(input) variable in the relation.
Range: the set of all numbers for the dependent(output) variable in the relation.
Function: a special realtion where every input(x) has only one output(y).
To find the X intercept you make Y equal to 0. Essentially you want to isolate X in order to find what it is equal to. When finding the Y intercept it is nearly the same thing except you replace X with 0 in order to isolate Y to find what it is equal to.
When you write the X intercept in ordered pair form you but the X value first followed by Y (which should be 0).
ie: (-4, 0)
Same with if you’re writing out the Y intercept in ordered pair form, you put the Value as 0 and plug in the Y value.
ie: (0, 13)
When you have these two points you can begin to place them on a graph.
I chose to go over the distributive property because I forgot about this unit when going over the review package as well as the numbers unit. In distributive property you multiply the constant by the contents inside the brackets. Make sure your work is neat and tidy so you don’t get lost in bigger equations. I like to colour coordinate my terms so Its easier for me to decipher which terms I can group and which I cannot.
This week we learned how to factor trinomials. When factoring trinomials you want the first and last term to be the product of two numbers and the middle term to be the sum of two numbers. if there is no number that can add up to the number in the middle and multiply to the last term then the trinomial is unfactorable.
The first thing you want to do when removing the GCF in a trinomial is find all the factors of each number. Each number that has similar factors you can begin to remove, you want to place the factor you chose and move it outside of the brackets as well as dividing that number out of the trinomial, the number you get from dividing the factor goes inside the brackets. This makes factoring much easier. I chose simple examples which in my first example my numbers were 5, 15, and 10 and the factor I removed and divided by was 5x because in the trinomial each number had (X) in it. In my second example I had numbers 6, 9, and 18 and I removed 3 and divided each number by 3.
We learnt the basics of trigonometry. Finding the missing sides and angles through SOH CAH TOA. Trigonometry was introduced to us this year which I found difficult at first as there is so many functions and an acronym to remember but once I got the hang of it I found it very easy.
In this lesson of polynomials we learned how to FOIL. Its a method used when multiplying using the distributive property that is very easy and the way you write it out makes it very easy to understand when looking at it rather than trying to do it in your head.
In our seventh lesson of measurement we learned how to find the surface area and volume of a rectangular based pyramid. its a long process and you have to make sure that your formulas and steps are correct in order to receive the correct answer. I like to write out everything i do. I like to draw the shape of the face that I am trying to calculate the area of. This helps to keep track of everything i do and makes it easier to visually see as well as keeping it neat and tidy.
- First you have to find the two slant heights of the pyramid. A rectangular based pyramid has two slant heights because the base side lengths are not the same. You find the slant heights by using pythagorean theorem on each triangular face.
- Once you find the two slant heights, you find the area of each triangular face. Then you add those to the base area. (Make sure to put the coefficient 2 in front of each triangular face’s area. You do this because it tells you that two of the four triangular faces have the same area.)
- You add the each face by writing out how to get the area of each triangular face and then the area of the base. You write them all out side by side and simplify where you can. Lastly you multiply the numbers left after you have simplified.
- The number that is left is the surface area of the rectangular prism.
I know this sounds hard and has a lot of steps, but I hope this example will make it easier to understand.
- To find volume of a rectangular based pyramid you multiply 1/3 by the area of the base by the height of the pyramid.
- You should already have the area of the base from finding the surface area, so we just use that to easily find the volume. (You should be able to plug in the whole equation on your calculator.)
Here is an example using the same dimensions that I used for finding the surface area above.
The measurement unit for me was a little difficult as there us so many units to convert and its a long process going from a bigger unit to smaller ones or switching metric to imperial or vice-versa. I found this unit very easy to make a little mistake on. the imperial system in mainly used in the US but we still use certain measurements like when we when we use our height or weight.