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Math SAT Preparation - Basic Algebra
Welcome to a Math SAT Preparation Lesson. In this lesson we will go over really simple, basic algebraic and numerical concepts.
First of all, make sure you remember your basic grade 1 math:
Numbers - these are the symbols we use to do math. For example, 3, -289, 0, five. Operations- these represent actions you can perform with your numbers. The basic operations are:
a. Addition: for example,
b. Multiplication: for example,
There are other minor variations of these operations:
c. Subtraction, adding a negative:
d. Division, multiplying by an inverse:
.
Division also involves quotients and remainders. Every number
can be
divided by some smaller number
in such a way that
, where
is your quotient and
is your remainder. For
example, when 19 is divided by 6, the quotient is 3 since 6 goes
into 19 3 times, while the remainder is then 1.
Thus, we write: .
Addition and multiplication have some nice properties - they are
commutative, associative and distributive. This means that, for
addition:
,
and
There are special types of numbers we have to consider:
a. Negative numbers - all numbers less than 0, such as -7
b. Even numbers - numbers divisible by 2, such as 166712
c. Odd numbers - numbers not divisible by 2, such as 5
d. Prime numbers - numbers divisible only by 1 and themselves, such as 2,3 and 5.
We should also recall fractions, which are division that aren't
clean and don't represent whole numbers, such as:
Fractions can be represented as decimal numbers, for example:
An additional concept is the percentages. These are fractions that are always over 100. For example, 20% of the number 15 is equal to:
Good stuff so far.
Another important tool in algebra is a variable. Variables are usually represented by
letters (most often ), and they denote an unknown number.
Variables are highly useful in equivalence relations, or any
expression that uses an "" sign. For example:
Which can be solved for to find that
.
We can have expressions with multiple variables, such as:
The answer is and
in this case, which can be denoted as
.
Equations that use degree one variables, such as the one we saw earlier, are called linear equations, as they represent lines in the classic 2-D XY plane. Equivalence relations do not have to be linear, however, and raising the degree of our variables is possible.
For example, the equation has solutions
.
Higher degrees, called exponents, have
exponent rules:
a.
b.
c.
d.
e.
![x ^ {\frac{1}{a}}=\sqrt[a]{x}](http://texhub.com/b/IHggXiB7XGZyYWN7MX17YX19PVxzcXJ0W2Fde3h9IA== "x ^ {\frac{1}{a}}=\sqrt[a]{x}")
Word problems are something to watch out
for.
These problems usually define a situation which requires you to define your own equivalence relations. For example:
If Lucy has 5 apples more than Jack, we can say that if L
represent Lucy's apples and J represent Jack's, then . Once
equations are set up, they can be solved to reach a solution.
These are all basic topics you should be aware of and comfortable with from your math classes. Here are a few notes and tips on how to deal with questions involving such topics when writing your SATs:
Feel ready?
Think you've mastered your basic algebra? Try the basic algebra test.
For a lot more algebra, check out the Welcome to Algebra Series in the Algebra community:
Image Credit jurvetson
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Oren, Is the SAT administered in Canada? Also, in strategy 1. near the end, “Remember to take it slow and think through your answer.” One stratgey I tell my student is the one of triage, that is, go through the questions fairly quickly and if you think you can anser it quickly do so; make note of the ones you passed over, and make a second or third cycle through the unanswered ones.
The SAT is administered all over the world. However, it is only required for admissions into schools in the US, Canadian universities do not require it (is that a good or bad thing? Up to you to judge).
Personally, I think that leaving questions you’re unsure of until you’ve gone through the test once is a good idea, especially in multiple choice tests like the SATs where you can just guess those questions you don’t know and still have a 20% chance of getting them right. On the other hand, going quickly through the questions does often lead to situations when you make a small mistake, like miss a minus sign, and you’re unaware of it, so you’re still confident your answer is right and you’re not likely to change it even if you check your answers.
My suggestion is to leave questions that you know you don’t know to the end, but take some time to ensure that when answering those questions you’re sure of, you get them right.
I don’t recall having to take an entrance exam when I went to Queen’s. I did have to have pretty good marks though. Having mentored high school students for four years now in the US, I think the SAT & ACT are good. If you’re good at either one, it means you know basic things well and it also means that you can strategize. I knew nothing about strategizing at that age.
hey guyz plz help me,,actually i want to study undergraduate course in usa..can u tell me what exams i have to give for scholarship,plz guyz help me and also tell what i have to do if i go there to do mba?
To study in the USA you will need to take the SAT and the TOEFL. Join the Study in the US Community to learn more about the process. For scholarship information, you can join the scholarship community.
To get an MBA later on you will need to take the GMAT test.
I would like to study in the us and I am taking the SAT..but is it necessary for me to take the TOEFL too..I am from India so English would be a foreign language..but i speak it at home and am fluent…??
While not every US school would require the TOEFL and some would accept the SAT writing section as replacement for the TOEFL, other schools will require it. If you studied in an English institute for at least 2 years, the TOEFL may be waved by most colleges.
I would advice you to take the TOEFL anyway, just to make sure you satisfy the conditions of as many colleges as possible. If you’re fluent in English it shouldn’t be a problem, most people find the TOEFL easier than the SAT.
i want to take admission in B.E. after 12th sci. in america. Is SAT exam is required 4 that?
plz help me
Yes, the SATs are generally required for pretty much all Bachelor degree programs in the US. I would advise you to make sure by checking on the specific college or university you are interested in, but I believe that chances are you’ll need an SAT score, and possibly a TOEFL score as well.
i want 2 do engineering in japan or singapore how can i gt admition…
Hey r4u. You should post your question in our Study in Singapore community, where you’ll find lessons that can guide you on how to get admission into a great institute in Singapore, which is an amazing place for studying engineering and a lot of other programs as well.
Singapore and Japanese admissions are not very likely to require an SAT score, since the SAT is primarily used in the United States for admission, and I don’t think it’s used by a lot of other countries. However, a TOEFL or IETLS test would probably be required. You can find out more in our TOEFL Prep Community. Good luck on finding a great university!
if sat…then how can i gt application form of it….
If you’re looking for information on how to register for the SAT, follow this comrehensive lesson which will guide you through finding the forms (either online or sending them in by mail), and sending them off so that you can register and write the SAT.
You can apply to Canada’s international renowned universities right now without an SAT score. Its free & easy:
Knowing is not enough; we must apply. Willing is not enough; we must do.
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me a juniour college student who is now in std 11th. i want to do engineering in US. i was told by someone that for applying to universities in US I have to give SAT. but i don’t have any clue about this SAT can you help me with what i should do and how i should go about this?
yours’
raunak ajmani