奖金的数学内容

希望我没有太过过时。如果我告诉你我在高中的时候马卡雷纳真的真的很大。你们可能听过，那支舞就像，好吧。但有个问题是写这首歌的艺术家是谁?每个人都知道，每个人都知道这种舞蹈，谁是艺术家?你可能不知道，让我告诉你为什么，他们从来没有做过另一首热门歌曲。这就是所谓的“一鸣惊人”，这一集我们将在数学部分讨论“一鸣惊人”。总会有一些问题每次都会出现。它们看起来有点复杂，除非你知道怎么做。所以这有点像… 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.
四个一击中一个击中奇迹。你总会遇到一个关于基本计数原理的问题，一个关于矩阵的问题，一个关于圆方程的问题以及一个关于平行四边形面积的测试问题。你可能会想，天哪，我不知道怎么做这些事情听起来真的很复杂。我挑选它们的原因是它们其实很容易学。所以我们将快速地浏览这些，你们会看到如何在测试中很容易地找到这些点。
一、基本计数原理。我在衣橱里决定穿什么。我有3条裙子，5件衬衫，6双鞋子和2双袜子。如果我混合和搭配这些元素，我总共可以做多少套不同的衣服?你们可能在练习测试中见过一个有趣的问题。学生们做各种各样的事情，列出他们有多少行动，没有必要。基本计算原理是，你只要把所有不同的选项相乘就得到了所有组合的总数。就是3乘以5乘以6乘以2。好的5乘以6等于30乘以2 60乘以3 180。所以3乘以5乘以6乘以2 180我可以用这些组合做出180种不同的衣服。
让我们看看一个更困难的问题。一旦你会看到这些，这些都需要额外的步骤，但你仍然可以没有问题。七位数电话号码可能有多少种组合？也只是一个有趣的问题，我自己好奇了。好吧，好的，想想我们以前所做的事情，我们想到了我们对每个选项有多少选择，我们乘以这一点。我们有......我会带3个裙子，2件衬衫，所以每个人有多少选择，然后乘以它们。在这里我们知道我们有七种不同的选择吗？所以我们的电话号码中的七个不同的数字，一个，二，三，四，五，六，七。问题是该号码每个插槽中的每个插槽有多少选择？好的，这是它更难的部分; 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.
下一个热门奇迹，矩阵。学生们对这些东西很害怕。他们看着它们也许你们已经有一段时间没看到了，也许你们根本没见过。事实上，一旦你知道该怎么做，它们真的很容易。你得到了这些时髦的形状，里面有一些数字。你所要做的就是按照题目告诉你的方式把它们组合起来然后把每一个数和另一个正方形中相应的数组合起来。这里，A + B等于多少?好的，这里你想要加A和B你要做的就是把每个数加到相应的数上。举个例子，2 + 0 = 2 3 + 2 = 5，我们先来看看选项看看我们是否还需要继续。2 + 0 = 2实际上这里只有一个是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.
关于圆的方程。好了，我们得到了圆的方程这是一个复杂的圆，但一旦你知道怎么做，你就能得到这个问题它肯定会出现的。(X - h)方加上(y - k)方等于r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。你们会看到这样一个问题;一个半径为5的圆放在坐标平面上以点(1,2)为圆心，这是我们的本质点，这是我们关心的h和k。这个圆的方程是什么?你要做的就是把这些代入到圆的方程中。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。让我们看一些选项，好的，我们想要x - 1的平方，然后我们想要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.
下一个击中奇迹，平行四边形区域。因此，这是您将看到的常见平行四边形区域问题。什么是地区平行四边形ABCD，你有一个平行四边形，其中一些侧线。学生用这些学生做一些非常时髦的事情，他们只是忘记了，自从你学到了平行四边形的区域已经有一段时间了。我见过学生将其分开，他们将其变成一个正方形，两个三角形都没有必要。找到平行四边形的区域很容易。它只是基数高度，所以只是基准时间高度。好吧，我们谈到了一个高度和一个基地，我们谈到了高度如何在90度点击基地。所以在这里，我们已经得到了我们的基地，我们得到了我们的高度，它以90度角击中。所以我们知道我们需要找到这个长度，我们也谈到了三角形的时候，当我们谈到几何时，我们在这里有一个正确的三角形，你有两个方面你可以找到使用毕达哥拉斯定理的第三个方面。 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.
这就是昙花一现的奇迹，现在你看，它们并不像看起来那么吓人。如果你们再复习一下这些概念，你们就能得到这些问题，你们知道这些问题会出现在ACT考试中。
我们继续讲SOHCAHTOA。ACT考试中有四个三角问题其中两个很简单，另两个很复杂。很酷的是，如果你知道SOHCAHTOA我们马上会讲到，你可以很容易地回答四个问题中的两个。现在如果你对如何回答另外两个问题感兴趣，我们在额外的材料中有一个很好的教程。但是现在我们要讨论的是如何用SOHCAHTOA来求这两个更简单的三角问题。我们来复习一下SOHCAHTOA。SOHCAHTOA表示sin是对边比上斜边，cos是邻边比上斜边tan是对边比上邻边。如果你想把它写出来，在这里。但是最好记住整个缩写词，它的拼写和不同部分代表的意思。我们要求一个角的正弦，余弦和正切问题是，你怎么知道? 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。我们讨论了一个热门的奇迹，你如何知道他们会出现，他们并不像他们看起来那么可怕。所以有能力在测试中解决这些问题是很好的。我们讲过SOHCAHTOA，这个三角概念可以帮助你轻松解决ACT中四个三角概念中的两个。