奖金的数学内容

希望我不是使废弃自己太多。如果我告诉你,当我还在高中Makarena真的大了。你可能听说过它,你知道,喜欢跳舞,对,好的。但这里有一个问题谁是艺术家谁写的这首歌?每个人都知道,每个人都知道舞蹈,艺术家是谁?你可能不知道,让我来告诉你为什么,他们从来没有另一个歌,是一个打击。这被称为一个奇迹,在这节课中我们将讨论一个打奇迹的数学部分。他们总是会有一些问题,必定会出现一次。他们看起来有点复杂,除非你知道如何去做。所以它有点像… if it's easy to learn why not learn and you can just nail those questions which you know will appear. In this episode, we're going to take a look at four one hit wonders and then afterwards we'll take a look at SOHCAHTOA which is a trigonometry question that can help you easily answer two out of the four trigonometry questions on the ACT.
一打一打四个奇迹。你总是会看到问题的基本计算本金,关于矩阵的问题,关于一个圆的方程和一个问题测试如果你能找到一个平行四边形的面积。你可能会想哦我的上帝我不知道如何做这些事情只是听起来很复杂。我选择他们的原因是,因为他们学习其实很简单。所以我们要迅速经历这些,你会看到如何真正轻松捡起这些点测试。
首先,基本的计算原则。我在这里在我的壁橱里决定穿什么好。我有3个短裙、5衬衫,6双鞋子和2双袜子。如果我这些元素混合和匹配,总共有多少不同的服装我可以吗?下一个有趣的问题你可能看到过实践检验。这么好的学生做各种各样的事情你知道,他们有多少行动列表,没有必要。基本计算主说你把你所有的不同的选择和组合的总金额。我们去,只是3 * 5 * 6 * 2。好的5 * 6是30 * 2,60 * 3,180。所以3 * 5 * 6 * 2,180年和180年我们有不同种类的服装我可以用这些组合。
让我们看看在一个更困难的问题。偶尔你会看到这些,需要一个额外的步骤,但你仍然可以做到,没有问题。有多少不同的组合可能七位数的电话号码吗?也只是一个有趣的问题,我自己也有点好奇。好吧,好吧,想想我们之前,我们想过多少选择为每个选项我们增加。对我们有……我要3个裙子,2个衬衫,有多少选择为每个然后相乘。我们知道我们有七种不同的选择对吧?所以七个不同数字在我们的电话号码,一,二,三,四,五,六,七。问题是有多少选择每个插槽的号码吗? Okay, this is the part where it's harder; you have to think how many choices are available there? Well for each digit of a phone number, ten choices right, you've got zero, one, two, three, four, five, six, seven, eight, nine, that's ten. So how many different combinations are possible for seven digit number? Well ten options for everyone in the slots, so you would have 10 times 10 times 10 etcetera for each of the seven slots, so really 10 to the seventh power. Okay and we if we do that on a calculator, what would that look like? Well, 10 to the seventh is 10,000,000, okay that's answer choice C, perfect. So 10,000,000 different possibilities for a seven digit telephone number. Again we've found the amount of slots that we need to fill right, seven slots for the seven digits and then how many options for each digit, 10 and then we just did 10 times 10 times 10 times 10 times 10 times 10 times 10. That's the amount of total combinations that we have, great.
下一个奇迹,矩阵。学生往往与这些真正感到了恐惧。看看他们也许已经有一段时间你已经看到它,也许你没见过这个。实际上,他们很容易一旦你知道该做什么。你有这个时髦的形状和一些数字。所有你需要做的就是把他们以任何方式告诉你,你要把每个数字与相应数量的其他方。这里,A + B是什么?这你想添加A和B,你要做的就是将每个数字添加到相应的数量。例如,2 + 0 = 2,3 + 2 = 5,你知道吗,我们先看看答案的选择,只要确保我们甚至要继续。2 + 0 = 2,实际上只有其中的一个甚至有一个2。 So 2 plus 0 is 2 but let's just double check. We said 3 plus 2 is 5, that looks great, 0 plus 1, 1 and negative 1 plus 1 is 0. So this is the solution for this matrix problem. So you see, not that complicated at all, nothing to be intimidated about. And once in a while you'll have subtraction and then you would just subtract each relevant part. So that's a matrix problem.
圆的方程。我们去,我们有我们的圆的方程和这样的一个复杂的循环学习,但是一旦你知道该怎么做,你就能得到这个问题肯定会出现。x + y - k - h广场方是r的平方。在这个方程所有你需要知道的,h和k是圆的中心,h是中间点的x坐标和k是中心的y坐标点,r的平方的圆的方程的半径的平方。所以你会看到一个这样的问题。一个圆的半径5是放置在坐标平面上,集中在1、2,这是我们的基本观点,这是我们关心的h和k。圆的方程是什么?好的,所以你要做的就是把这些圆的方程。我们知道中心是h和k, k h x和y坐标,这里我们要插入1,x - 1平方,我们将插入2,y - 2平方和半径是5记住5平方将25。再次让我们看看一些答案的选择,好的我们希望x - 1平方吧,然后我们希望y - 2。 If you look at the answer choices, keep an eye out for this, they know there going to be students who forget the radius has to be squared. So there's always going to be some answer choices with pure un-squared radius. And here we go we already know C and D are out right, they're just 5. Also by the way, when we talked about strategies we talked about getting rid of the misfits and by the way, E is negative and it's the only negative one of all the answer choices, so that can't be right either. Okay, if you look at A and B which one of these fits the equation? Here we go, x minus 1 and y minus 2 right? It was x minus h, y minus k and we plugged in our 1 and our 2 for h and k and here we go we have a radius squared which gives us 5 squared 25. So this is the equation of our circle.
下一个奇迹,平行四边形的面积。这是一个常见的平行四边形面积的问题你会看到。平行四边形的面积ABCD和你有一个平行四边形的边线。学生用这些做一些非常时髦的事情,他们只是忘记了,已经有一段时间,因为你学会了平行四边形的面积。我看到学生瓜分了它,他们把它变成一个正方形两个三角形各种事情没有必要。它很容易找到一个平行四边形的面积。只是底乘以高,所以只是底乘以高。好的我们谈了身高和基地,我们讨论了如何高度基本在90度。这里我们有我们的基地6个,我们有自己的身高,这是在90度角打好。我们知道我们需要找到这个长度,我们谈论时也谈到了三角形几何所以我们这里有一个直角三角形,你有两个方面的你可以找到第三个使用勾股定理。 We know that 3 squared plus this side squared is going to give us 5 squared. Okay let's write this out, so 3 squared or 9 plus, that side that we're missing, we'll call it x squared, is equal to 5 square right so 25 okay. In that case x squared is equal to 25 minus 9. So x squared is equal to 16, so if x squared is equal to 16, x is just equal to 4, x is equal to 4. I'll just write that here and we can write that in and here we go. We've got our height, we've got our base and we can find the area of our parallelogram, just 4 times 6, 24. So B is correct here.
就是这样一个奇迹,你看现在,他们并不像他们看起来吓人。如果你超过这个概念一点,你就可以得到这些问题你就知道将会出现在行动。
让我们继续讨论soh cah toa。所以有四个三角问题,其中两个是简单,其中两个是非常复杂的。最酷的是,如果你知道soh cah toa,我们再谈,你可以很容易地回答四个问题中的两个。现在,如果你感兴趣如何回答其他两个问题,我们有一个很好的教程,在奖金材料。但是现在我们要讨论如何轻松使用soh cah toa找到这两个三角问题更容易。让我们回顾soh cah toa。soh cah toa代表正弦是相反的斜边,余弦是邻斜边和相邻切是相反的。现在,如果你想要写出它在这里。但是很好记住整个缩写,它是如何拼写和代表不同部分。所以我们要想找到正弦,余弦和一个角的正切,问题是你怎么知道的? Students always ask me, how do I know what's opposite? What's adjacent you know for a particular angle? So let me just show you, lets say we care about angle A here and they'll always tell you what angle you need. So you need to know what's the adjacent, what's the opposite, what's the hypotenuse. Well the hypotenuse is always the side opposite the right angle no matter what. So just to review, the opposite side is the side opposite the angle, you'll feel it, it's pretty opposite, it's far on the other side. And adjacent is always going to be connected to the angle you care about. You know you've heard the phrase, let's say the adjacent building, it's connected so that's how you'll know this is your adjacent this is your opposite. Let's take a look at a sample question. What's the cosine of angle B? So keep in mind angle B right here, we'll mark it, is the one we care about. Cosine, where does that come in in SOHCAHTOA? SOH CAH, the middle. C A H right? SOH CAH TOA. Okay, so cosine is adjacent over the hypotenuse, that's what that stands for. So adjacent over hypotenuse okay, in relation to angle B, adjacent remember attached, so 4 over the hypotenuse which would be 5 so your answer would be 4 over 5 answer choice C, great! There's a lot more practice with SOHCAHTOA in your bonus material so if you feel like you need a review you may want to head there next.
让我们回顾一下。我们讨论了一个奇迹,你怎么知道他们会出现,他们并不像看上去的那样令人生畏。所以很好只是有能力能够解决他们测试。和我们谈论soh cah toa,三角函数的概念,可以帮助您轻松地解决两个四个三角的概念你会看到在行动。