Hey guys, it's Jo! Sorry for the late post, I'm really lazy. During lesson 2 we talked about x and y intercepts. and how to calculate them. When calculating an x intercept y=0 and when calculating the y intercept x=0 so you can use the formula to graph the intercepts. There can be as many intercepts as the degree of the function allows (ex: -4< x^3<7 has a maximum of 3 x intercepts.). We also did an example with a car that was bought (new) for 20,000 and calculated how the value decreased over time, by using the formula V= 20,000-1250t, V being value and t being time, with V on the y axis and t on the x axis. (for example: t (imput) = 3. 20,000 - (1250x3) = 20,000 - 3750 = 16,250 $, therefore V=16250$(output) therefore, the ordered pair is 3,16250)
0 Comments
"You are not spat out of the womb knowing this," says Ms Bjornson, eternal fountain of wisdom. Welcome to domain and range, brought to you by Isolde. Domain and range is all about having an exclusive graph party to which only certain numbers are invited. Domain refers to all possible values of x and range to all possible values of y. To state the domain ya just write D = { all the permissible values of x } and ditto for range, R = { all permissible values of y} Curly brackets are a necessary evil. Don't ask me why. They just look cool, and we all want to look cool when we go to a party. "But what could this possibly be for??" you might ask. "Just letting the world know which x and y values are allowed on your graph." replies Ms B. "But when am I ever going to use this?" "As a barber, of course. To restrict the domain. In other words, give your line a haircut." Instead of always having arrows zooming off to infinity at the edges of graphs, this allows us to make them start and stop somewhere. Katie says restriction is the bouncer at the math party. Analogies aside. The way you state domain and range depends on whether you have a discrete or continuous graph. Check out Anastasia's fantastic post if you have no idea what that means! Inviting Numbers to the Discrete Graph Party. Selected guests, expensive caviar.
IntermissionIn which I remind you that not all numbers are created equal, and there is a way to show that with symbols and stuff. The ravenous math teacher's arm-mouth ever pursues the largest meal. This is also the charade to show that x>n is the same as n<x and it's not a huge deal which way you write it :) Guest List of the Continuous FiestaBecause the line on a continuous graph represents every possible point that line crosses, we need a way of inviting every single weird-decimal number that we want to include without individually naming them like we did for the discrete graph. That would literally take forever. Representing inequalities is the way to go. All the cool kids do it. Simply pretend the x or y axis is a number line, as shown above, wrap those numbers and little beaky symbols in curly brackets, pop a brownie in the microwave, and enjoy your success. If its one of those graphs where the ends are just arrows and you're like ????? how do I find the domain if the x values go on forever???? ? ?? NO PROBLEMO, just write D= {ALL REAL X}, meaning you have just advertised this party on every single social media you have including telephone poles and every x value who is a real number is invited. No limits!!! That wasn't a great explanation, so I'll leave it to my buddy Carlitos here to demonstrate some examples. Hey everyone! Anastasia here. Sorry for the super late post! I'm hoping we didn't do lesson 2 on Friday so that at least my post will be in the right order.
Anyhow, on Wednesday we started unit 5, relations & functions. The best part about this unit is that it is completely in worksheets and notes, which means you don't need to bring your text book to school! Your back will thank you! Now, getting into the lesson, we started with a review of the cartesian coordinate plane, which is just a fancy name for a graph, the kind you would plot coordinates [ie- (9,6)] on. We reviewed the x axis (horizontal); and the y axis (vertical); the origin, or "center" of the graph, where the x and y axes meet, (0,0); and the four quadrants that are labeled with roman numerals in counter clock-wise order, starting from the top right, I (+,+), II (-,+), III (-,-) and IV (+,-). *it was also mentioned that in science, we sometimes leave out the arrows on the negative side of the axes (both x and y) to show which side is positive. Next, we talked about relations. A relation in math is a comparison between two sets of numbers. Here are 7 ways a relationship between two quantities can be represented that we will consider in this unit. *pro tip: the last three are the most important! 1. in words 2. a table of values 3. a set of ordered pairs 4. a mapping/arrow diagram (not tested) 5. an equation 6. a graph 7. function notation Then, we talked about independent vs. dependent variables. Independent variables are variables that we control (ie- the left hand side of a table of values, the x axis of a graph, or the input of function notation). Dependent variables rely on the value of the independent variable (ie- the right hand side of a table of values, the y axis of a graph, or the output of function notation). Finally, we discussed discrete vs continuous graphs. Discrete graphs are graphs where a relation only exists for specific coordinates (and it isn't possible to have between values), and the points DON'T CONNECT. Continuous graphs are graphs where a relation exists at specific coordinates and ALL coordinates located between them. Points ARE CONNECTED with a line or a curve. (ex- data collected over a duration or a time would be displayed on a continuous graph) We also started on the homework for this lesson, on the worksheet, p392 #1, 2, 8, 9 and p406 #1, 2ac, 3acf, 4, 5, 6. I've attached some photos below explaining the things that were covered in this lesson; the cartesian coordinate system, independent vs dependent variables (a math-y and then a science-y example) and finally discrete vs continuous graphs. Hope this helps! Anastasia :) Today's lesson focused on negative exponents and reciprocals. An example of a negative exponent is n^-x Negative exponents are the opposite equivalent to positive exponents: where instead of multiplying itself x # of times you would divide the # by itself the number of times indicated. I.E.: 2^-2=2÷2÷2=1/4 (it is easier to write these as fractions rather than decimals); an example given in class is a^-n=1/a^n in the case that there is a negative it can be written like so: -7^-2=-1*7^-2= -1*1/49=-1/49 Another way of writing it is 2^-2=1/2^2=1/4 NOTE: Negative exponents DO NOT make the numbers negative! In case you were wondering what a reciprocal is: a reciprocal is a fraction flipped so that the denominator is now on top. They are used to simplify negative exponents. When you flip the denominator and the numerator the negative exponent is turned into a positive exponent i.e.: 3=3/1. NOTE the exponent is only applied to the numerator and stays with it when it becomes a denominator. 23^-7=(23^-7)/1=1/(27^7)=1/10460353203 -Zane Howdy Y'all, Nathaniel here Today in class Ms B lay some sick beats about exponents and fractions while we simplified integers that are to the power of a fraction. We also covered some homework questions and had a very mini-lesson on radians (but you don't need to know anything about that yet, it was just a fun tangent). Before I start, I'd like to make a note about notation. Due to Weebly's limited equation characters, I will be writing radicals like so n^√x. This means x, nth rooted. For example, 2^√9 = 3, because 3^2 = 9. Let's jump in! Let's say you have a formula that looks like so; x^(m/n). m≠ 0 or 1, n & m are natural, and x is rational. In order to simplify it, you can use the equalities: x^(m/n) = n^√(x^m) = (n^√x)^m. For example: 4^(3/2) = 2^√(4^3) = (2^√4)^3 = 8. Here are some tricks to remember how it works: Flower Power: Picture a flower next to your fraction/exponents. The flower becomes the power, and the roots become the root. x^3/4, 3 = power, 4 = radical or root. Power Up, Root Down The numerator is above the denominator in a fraction, and the power goes up, the root goes down. Thanks for reading! -PM Nathaniel Here are some videos: (You don't need to know the radians one, it's just cool)
For this part of unit four the class was required to make a graphic or diagram representing and presenting information about all the different types of numbers. Making a digital copy and uploading it to the class slide show (which you can access through our google classroom) or making a paper/physical copy and then uploading a photo of it was also suitable. Here is a quick summary of all the different types of Numbers: Real Numbers: All numbers that can be placed on a number line. Rational Numbers: All numbers that can be expressed as a fraction or in a ratio (rational), have decimals that terminate or repeat. Includes Integers, Whole, and Natural Numbers. Is represented with Q. Integers: Any positive or negative numbers without fractional or decimal parts. Includes zero and goes onto infinity. Is represented with I or Z. Whole Numbers: Any numbers that are positive and count upwards to infinity, and do not have any fractional or decimal parts. Includes zero and is represented with W. Natural Numbers: All numbers that are positive and count upwards to infinity and do not have any fractional or decimal parts. Does not include zero and is represented with N. Irrational Numbers: Any number that cannot be expressed as a fraction or ratio and is NOT an imaginary number, have decimals that go on without repeating. Is represented with Q-bar. Imaginary Numbers: Any number expressed in the terms of a negative square root (usually the square root of -1), is represented with i. ARE NOT REAL NUMBERS! I included the required example for the imaginary numbers. As well as math memes and videos. |
| | |
Hey there dudes its Chloe (ollie's here too watching over my shoulder)
Today we started with going over some older blog posts, and watched the first half of a video of decomposing fruit. Also we had a conversation about neon tetras so I included a cute lil video of neon tetras eating food.
The expanding method we learned was to expand expressions like (a+b)²
The shortcut was:
"square the first,
multiply the terms and double the product,
square the last."
An example: (3a-2)² = 9a² -12a + 4
Then we learned how to factor perfect square trinomials, which is basically taking the long answer from before and squeezing it down into the small one. In this beautiful method you can skip ALL FACTORING STEPS! NO WORK NEEDS TO BE SHOWN! What more can you ask for?
(there's a video down below about that)
(ms b also said that if you find a method that you're comfy with then stay in your comfy method.)
Next we learned about THE DIFFERENCE OF SQUARES RULE
For this we're gonna have to remember the golden rule of factoring. Then we played a little game of 'spot the difference of squares'. Ms B said that you remember things better when they're silly, so with every answer we'd say "a minus b, a pLuS b!" With the plus being said super high.
You can find a video on this below and also there's notes on google classroom.
Ms B also showed us a 'story so far' review flowchart which is on gc as well.
Also tomorrow is a work block.
Fare thee well folks
Chloe (and also ollie)
Today we started with going over some older blog posts, and watched the first half of a video of decomposing fruit. Also we had a conversation about neon tetras so I included a cute lil video of neon tetras eating food.
The expanding method we learned was to expand expressions like (a+b)²
The shortcut was:
"square the first,
multiply the terms and double the product,
square the last."
An example: (3a-2)² = 9a² -12a + 4
Then we learned how to factor perfect square trinomials, which is basically taking the long answer from before and squeezing it down into the small one. In this beautiful method you can skip ALL FACTORING STEPS! NO WORK NEEDS TO BE SHOWN! What more can you ask for?
(there's a video down below about that)
(ms b also said that if you find a method that you're comfy with then stay in your comfy method.)
Next we learned about THE DIFFERENCE OF SQUARES RULE
For this we're gonna have to remember the golden rule of factoring. Then we played a little game of 'spot the difference of squares'. Ms B said that you remember things better when they're silly, so with every answer we'd say "a minus b, a pLuS b!" With the plus being said super high.
You can find a video on this below and also there's notes on google classroom.
Ms B also showed us a 'story so far' review flowchart which is on gc as well.
Also tomorrow is a work block.
Fare thee well folks
Chloe (and also ollie)
| | |
Hello it's Morgan. Today we learned how to factor trinomials where A does not equal 1. the formula goes like this:
AX^2+BX+C
In the video below you can see the decomposition technique.
Pro tip: imagine decomposing fruit when you do this method
AX^2+BX+C
In the video below you can see the decomposition technique.
Pro tip: imagine decomposing fruit when you do this method
however... there is two techniques for doing factoring where a>1.
Unfortunately I was unable to find a good video detailing the "X" method. But I did manage to find a third technique. it's quite odd but seems to work just fine. You can go quite fast with this method.
Unfortunately I was unable to find a good video detailing the "X" method. But I did manage to find a third technique. it's quite odd but seems to work just fine. You can go quite fast with this method.
Hiya y’all, it’s Lucy! (celebratory trumpets play) Sorry for the late post due to technical difficulties. Hopefully you all had a great spring break and Easter ( if that's your jam) and enjoyed the break and sweet relief of no homework and sleeping in. Well… that's over now! Time to go back to reality and in other words math.
Today our lesson was about factoring trinomials and a brand spanking new technique called the golden rule where you use factor the GCF out of an equation.
For factoring trinomials the main point is to try and imagine how a polynomials two middle terms( the OI in FOIL) would have become the trinomials middle term. For all these questions assume a=1. (Pretend the 2's and 3's next to the x's are squares and cubes)
EXAMPLE
x2+8x+12------------------- We want to find which two numbers can add to 8 and multiply to 12
2 x 6= 12 ---------------- These two numbers work because they both equal the two coloured
2 + 6= 8 numbers. Therefore this equals the OI. 12 x 1= 12
Here is an example for a number that wouldn't work -> 12 + 1=13 not 8
| | -------------- You then take those two numbers and put them into their separate (_+2)(_+6) brackets. Which you can draw under all of your trinomial equations
(x+2)(x+6) ---------------Lastly add the squared variable from the top, in this case its the x.
(x+2)(x+6)
And TA! DA! you are done, give yourself a high five and circle the answer
because you have EARNED it!
EXAMPLE for The Golden Rule
3x3+21x2+30x------------ First thing is you should only use the rule when there a number in
front of the variable at the start EX. 3x3
3x(x2+7x+10)------------- You firstly factor out the GCF of the equation in this case it was 3x
7 10 -------------- Next you identify the two numbers you need to find a multiplicant
5x2=10 5+2=7 and an addition for (for this question it is 7 and 10)
3x(x+5)(x+2)--------------- Finally you put those numbers into your brackets with your GCF and
you're done!
There you have it. Pretty easy right?? Also a few other extra news in today's class was
“Don’t kill the monomial children, that would make you a bad baby sitter”- Mrs. B
Today our lesson was about factoring trinomials and a brand spanking new technique called the golden rule where you use factor the GCF out of an equation.
For factoring trinomials the main point is to try and imagine how a polynomials two middle terms( the OI in FOIL) would have become the trinomials middle term. For all these questions assume a=1. (Pretend the 2's and 3's next to the x's are squares and cubes)
EXAMPLE
x2+8x+12------------------- We want to find which two numbers can add to 8 and multiply to 12
2 x 6= 12 ---------------- These two numbers work because they both equal the two coloured
2 + 6= 8 numbers. Therefore this equals the OI. 12 x 1= 12
Here is an example for a number that wouldn't work -> 12 + 1=13 not 8
| | -------------- You then take those two numbers and put them into their separate (_+2)(_+6) brackets. Which you can draw under all of your trinomial equations
(x+2)(x+6) ---------------Lastly add the squared variable from the top, in this case its the x.
(x+2)(x+6)
And TA! DA! you are done, give yourself a high five and circle the answer
because you have EARNED it!
EXAMPLE for The Golden Rule
3x3+21x2+30x------------ First thing is you should only use the rule when there a number in
front of the variable at the start EX. 3x3
3x(x2+7x+10)------------- You firstly factor out the GCF of the equation in this case it was 3x
7 10 -------------- Next you identify the two numbers you need to find a multiplicant
5x2=10 5+2=7 and an addition for (for this question it is 7 and 10)
3x(x+5)(x+2)--------------- Finally you put those numbers into your brackets with your GCF and
you're done!
There you have it. Pretty easy right?? Also a few other extra news in today's class was
- Today was the last day for the first half of the factoring homework to be handed in unless… you had the wrong worksheet over spring break then:
- You get an extension all those unlucky folk get a one day extension to hand in their homework with the right worksheet filled out
“Don’t kill the monomial children, that would make you a bad baby sitter”- Mrs. B
Author
We are the students of FPC Math 10C.
Where are you from? Find your green dot!
Archives
June 2018
May 2018
April 2018
March 2018
February 2018
January 2018