In this episode called Math-English dictionary we're going to cover some terms you might need to know for the math section of the SAT and we're also going to talk about how you can take word problems and translate them into symbols that you can use to solve those problems.
Let's have a look at a lot of math terms. So on the math section of the SAT you're going to encounter a good number of word problems and like it or not you're going to have to solve them so it's really important that you be comfortable with deciphering turning the English into the math knowing your symbols. So let's just run through some of these, if you see terms like 'is', 'are', 'same or 'as much as' you need to automatically equate that with the equal sign no pun intended. If you see 'greater than' or 'more than' you need to think of the greater than sign, on the flip side 'less than' or 'fewer than' or 'smaller than' the less than sign and two of the trickier ones if you hear the word 'of' that means 'times' people forget that. So if you hear the word 'of' remember that means 'times' and lastly 'per' or 'for' means divide or make a fraction. Those are all really important in turning words problems into equations that you can solve.
A few more that you will encounter are right here if the problem says 'what', 'what number', 'a number' or 'the number' that means your variable which could 'x' but if you want to go crazy you can make it 'n' you know don't let me stop you. Also 'two less than x', a lot of people get this language part wrong so I want to point out that 'two less than x' is not two minus x which a lot of people automatically think of but it's 'two taken away from x' that's 'two less than x', so 'x minus two'. Keep that in mind and a couple more. Consecutive integers which are numbers like 'one, two, three, four, five' and so on maybe represented in problems as x, x plus 1, x plus 2 and so on because they're all spaced one apart your variables should be all written so that they're one apart and then an even trickier version of that is that some SAT problems talk about consecutive even integers like 'two, four, six, eight' etcetera or consecutive odd integers like 'three, five, seven, nine' and so on and those are written as x for the first one x plus 2 for the next one 'cause it's always two more like five to seven is plus two seven to nine is plus two and the next one two more than that so x plus 4, x plus 6 and so on.
Now let's see this in action. Here's a problem that you might see on the SAT; 'Half of the sum of three consecutive even integers is 10.5. Find the smallest of the three numbers.' So here's how you would set it up, just decode it bit by bit, half means one half of means times the sum means we're going to do some adding we're going to add three consecutive even integers, now you need to remember that that means this the first one's x the second one is x plus 2 and the third one is x plus 4 and all that summed is the problem says 10.5. So that's the problem you would solve and I want to point out the most important things here are 'of' means multiply and three consecutive even integers are written as x, x plus 2 and x plus 4. The step up is the hard part the solving is the easy part.
Let's look at some more terms you need to know. A lot of people forget their numbers so here we go, let's run through some of them. Integers are numbers like '-3, -2, -1, 0, 1, 2, 3' they can be negative they can be zero but they can't be weird fractions or decimals. Next up digits some people think that digits are any number you can think of no they're just the numbers '0, 1, 2' all the way up to nine and some people think there are nine digits 'cause the digits end at nine but you should remember there are ten 'cause you need to count the zero as well. Now the unit's digit or the unit digit is the digits in the ones place so for instance if you had the number 128 the unit's digit would the number that is in the ones place. This is the hundreds place, this is the tens place, this is the ones place so the eight would be unit's digit. That comes into play in some problems; next up prime numbers you should remember are numbers divisible only by themselves and one and one tricky thing about primes is that two is the only even prime number and it's the very first prime number so one is not a prime number two is the first prime number. The numerator is the top of a fraction the denominator is the bottom of a fraction and the reciprocal is what you get when the flip a number upside down. So if you have the number two thirds and you were asked for it's reciprocal that would be not two over three but three over two and here is one tricky version if you're asked for say the reciprocal of the number five. First you take the five and you put it over the number one so then when you flip it you actually have a number that can go on top five has a reciprocal of one fifth.
But wait there is more we have operations to talk about. Sum means add, difference means subtract, product means multiply and quotient means divide. So we also have 'remainder' which some people confuse with 'quotient' but it's really important that you not do that. 'Remainder' is literally the remainder the leftover bit when you do long division so you may have to flash back to fourth or fifth grade now 'cause it's been a while. You can't get the remainder by using your calculator 'cause your calculator gives decimal answers it does do fourth grade style long division. Let me give a quick example if the question said and it won't quite be this simple on the SAT but if the question said what's the remainder when 12 is divided by five the answer is not going to be two point blah blah blah that's a quotient. The remainder is this you take five and divided it into 12 how many times does it go two, two times five is ten you subtract the ten away and you have two left. So what's the remainder the remainder is this bit and let's take a look at our final two terms.
You should know that factor is a number divides evenly into another so for instance three is a factor of 12 because three divides evenly into twelve and lastly we have the term multiple 12 is a multiple of three because 12 can be divided evenly by three and you don't want to get those two terms reversed and what else? Mean and median and mode, the three kinds of averages this is important to know so listen up the mean is the average you're probably used to hearing about also called the arithmetic mean and it's the number you get when you add all the numbers you've got and divide by how many they are and that's what you'll most often tested on the SAT but the other two kinds of averages you should also be aware of. There is also the median and that's the middle number after you place the numbers in order from smallest greatest if you don't do that you're going to get the wrong median and one way to remember what the median is, is that it's sounds kind of like medium so it's easy to remember that it's not the small number, it's not the large number it's the medium number. So that can be a way of remembering and lastly there is the mode and that's simply the number that shows up the most in your list of numbers.
Of course there are the obligatory geometry terms that you need to remember equilateral means all the sides are the same regardless of the shape all the sides are same, could be a triangle could be a quadrilateral surprise me. We also have isosceles that means you're dealing with a triangle generally has two sides the same as each other. Quadrilateral is any four sided figure whether it's a square, a rectangle, a rhombus or something else. Perpendicular means forming a right angle or a 90 degree angle and lastly bisects means cutting something into equal pieces it could be an angle that's getting cut into two equal angles or a line segment that's getting cut into two equally sized line segments and lastly we have some SAT-ese these are things that you may not have come across in math class but they're still really important to know about for the SAT math.
So distinct means unique or different from each other. For instance if I say that x and y are distinct numbers that means that you can't assume that they might three and three 'cause three and three aren't different from each other. Inclusive means including the numbers mentioned so if for instance I said I'm planning an event for thirteen to seventeen year olds inclusive that would mean that everyone in between thirteen and seventeen could come including the thirteen year olds and the seventeen year olds and you remember it because inclusive sounds like include means including the numbers on the ends. In terms of 'a' and 'b' is a common part of SAT questions they'll often say what is 'c' in terms of 'a' and 'b' and all they're really saying is confusing as it is, is that when you get your answer it should include 'a' and 'b' and if you find that language confusing just go ahead and ignore it, it usually will not interfere with your ability actually answer the question. Which of the following is another common part of SAT questions and it's just a hint that says listen in order to answer the question you going to have to look at the answer choices. For instance you can imagine if a question said which of the following is always positive you'd have to look at the choices to figure out which is always positive or which of the following is prime you'd have to look at the answer choices or of course you couldn't answer what's prime and what's not and lastly 'let' something or other 'be defined as' is another common thing that appears on the SAT and all it means is hey I'm giving you something you haven't seen before don't worry about just follow the instructions I'm about to give you and if you do you will be fine. They're basically saying with 'let' this be defined as I'm making something up just stay with on this one.
So let's sum up everything we've covered in this episode. So I know we covered a lot in this episode but I hope you'll go back and recap if you need to or check out the bonus materials where the same stuff is covered because the great thing about all these terms is that they can have a huge pay off. For instance let's say you learned three terms you didn't know before and they all show up on the SAT each one could help you solve one more problem and each of those is going to on average be worth about ten more points so that's 30 points right there and you haven't gotten any better at math you just know a little bit of language you didn't used to know so that's pretty cool. And so you want to learn all these math terms that appear on the SAT because what a bummer to miss points just because you don't know what the question is saying and it's hard to get a question right if you don't know what it's asking but now you can do something about that.