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:
- 1. These questions seem really easy, which may cause you to feel over-confident and thus make small, silly mistakes. Remember to take it slow and think through your answer.
- 2. Watch out for the minus signs.
- 3. Calculators are allowed, so use them well. Always be familiar and comfortable with your calculator.
- 4. When solving equations, remember that you can check your answers by plugging them into the variables.
- 5. Word problems can get tricky. Don't forget to define your variables clearly and set up the relationships correctly before solving the equations.
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
Post Comments
raunak said – Sat, 16 Aug 2008 06:22:24 -0000 ( Flag Edit Link )
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