these are 5 of the most important things I think people should know about Math 10
1. organizing your notes, meaning that you need to have them in the order from the first unit to the last. 2. you need sufficient time for studying before a test i’d give it a week of studying before a test. 3. when studying putting pen to paper is very important because the only way you can learn is if you are learning actively. 4. always be prepared for next days class, Ms. Burton usually puts up the plan of the day, the day before the actual class so you can prepare what you need. 5. when your teacher gives you a chance to review the test you have just taken, I suggest you take it and learn from your mistakes if you’ve made any.
this week I learnt a new method of finding out coordinates, it’s called elimination
what elimination is, is it gives you 2 equations and from those equations you have to find out coordinates so the if you look at the picture you can see the equations I used and then you literally have to eliminate one of the terms, it is recommended that you use addition as much as possible seeing as it is easier to make mistakes with subtraction. Then once you have your single term, which for us is -3y=-33, you isolate for y and find the y coordinate. you take your newfound y coordinate which for us is 11 and you plug it in to one of the very original equations so for me I plugged it into 6x+y=-1 and now you’re trying to isolate x for the x coordinate which gave us -2 and so our coordinates are (-2,11)
these are three equations for a line segment.
slope y-intercept form is fairly simple you have slope which is M and y-intercept which is B and then your X and Y coordinates. General form is just meant to be “pretty” as in it’s supposed to just present the equation in a neat way. point slope form is an equation that is faster to solve than slope y-intercept form, you just have to find the slope and then input the first X and Y coordinate from the slope equation
these are my initials plotted out on a graph and the equations related to each lines
this is the formula for calculating a slope
here we have random coordinates that I picked out and what you do is you put in the coordinates Y with Y and X with X you could put it as Y1 and Y2 or Y2 and Y1 but the Xs have to correspond with that too. Now that you have your coordinates in place you just continue with the formula giving you -1 over -3 or simply 1 over 3 because a negative division equals to a positive,
this is an easy function notation, what it means is basically function of the X coordinate or simply Y
the way it is done is you take the function of 3 in our situation and you put it in place of X which was before the four and you follow the equation to get the answer that the function of 3 or Y=19
this is how to represent a set notation from a graph, I will be showing you domain and range.
first we’ll start with domain and domain uses the x axis, with our graph our line starts at 1 on the x axis and ends at 8 and everything between there is x, not 1 and 8 because the circles are open where the numbers are, giving us domain equaling 1<x<8. moving onto the range being the y axis it starts at 2 and ends at 5 and x being everything in between but not 2 and 5 because again the circles are open which means you don’t include them in x making the range equal to 2<x<5
This is how you figure out an equation to go along with a table of values chart
first you take the difference between the output number and if it’s negative then you put negative and the number along with x but in our case it’s positive 3x then you add or subtract the difference between the result of 3x, x being the input number then you’d get +17 in our case and you’d check to see if the equation works with all 3 or 4 numbers you have and it should.
what we have here is an “ugly” trinomial, it’s basically a normal trinomial but you have to do a little extra work because of the leading coefficient being greater than 1
since the leading coefficient can relate to the other two numbers in the equation (9 and 30) they can be reduced to 3 and 10 because of division leaving us with x4+3×2+10 so then what we did was we just took the lead coefficient out and left us with a simple trinomial to factor so once you factor the trinomial as I did there you are left with the 3 which you put on the left outside of the brackets. If the coefficient didn’t relate with the other 2 numbers it would go to the left but inside the bracket
this is how to figure out if you can factor a simple trinomial or if it even is a simple trinomial
first you look if the the terms have a greatest common factor (GCF). No? that’s ok, now check if you have a difference of squares, remember to have a difference of squares you must have two terms, perfect squares, and it must be a subtraction. If you don’t have a difference of squares that’s still ok, time to check if you got a pattern. In this case we do so we can factor. Check if it is a simple trinomial or if it’s an ugly trinomial, it’s easy to tell because if there is a lead coefficient more than 1 it’s an ugly trinomial and you have to do more work than we do now. Now you just look for what would work with FOIL and that is how you factor