GRE Math Rules Flashcards
Equations- Both Sides Rule
You can do anything you want to one side of the equation as long as you also do it to the other side of the equation.
Roots and Exponents
They balance each other out.
Order of Operations
PEDMAS - Parentheses, Exponents, Division, Multiplication, Addition, Subtraction
*when isolating a variable- reverse the order of PEDMAS
Equation Clean Up Moves
1) Get variables out of the denominators (multiple)
2) Simplify grouped terms (distribute)
3) Combine like terms
Fraction Bar Rule
Pretend there are parenthesis around the numerator and denominator of the fraction.
FOIL
First (A+b)(X+y)
Outer (A+b)(x+Y)
Inner (a+B)(X+y)
Last (a+B)(x+Y)
Factoring
pulling out a common term and rewriting the expression as a product
- variables with exponents
- numbers
- expressions with more than one term
Constant vs Coefficient
In a quadratic equation the constant is the third number without an unknown variable while the coefficient is the second number multiplied by variable X. (Ex: x² + 7x + 12 = 12 is the constant and 7 is the coefficient). The possible integers for X will be factors of 12, while the sum of the two possible integers will be 7. Thus the possible integers for X are -3 and -4 because (x+3)(x+4) is the factored version of the quadratic equation.
Quadratic Equation Rules
1) Before you factor a quadratic expression, you must make sure that the other side of the equation is 0.
2) If the sign of the middle term attached to X is positive, then the greater of the two numbers will be positive.
3) If the sign of the middle term attached to X is negative, the greater number will be negative and the smaller number will be positive.
Perfect Square Quadratic
One solution quadratic
(x+4)² = x is -4
(x-3)² = X is 3
0 in the denominator
If 0 is in the denominator, the expression becomes undefined. So 0 cannot be on the bottom of a fraction.
Multiplying and Dividing Inequalities
If you multiple or divide by a negative number, you must switch the direction of the inequality sign.
Absolute value
Describe how far away that number is from zero 0 = |number|. Treat the absolute value symbol like parentheses. |-3| = |3|
Solving:
1) Isolate the absolute value expression on one side of the equation.
2) Set upon the two equations with what’s inside the absolute value sign. Positive and negative versions.
3) Solve. Note there are two possible values for y.
Direct Formulas
The value of each item in a sequence is defined in terms of its item number in the sequence.
Recursive Formulas
Each item of a sequence is defined in terms of the value of previous items in the sequence. An = An-1 + 9
*If you do not know the value of any one term, then you cannot calculate the value of any other. (You need one domino to fall) A1 = 12
Sequence Problems
1) Determine which answer choice corresponds to the correct definition rule for a sequence.
2) Determine the value of a particular item in a sequence.
3) Determine the sum or difference of a set of items in a sequence.
*For the unit digit, use the pattern and just count up until you’ve repeated the pattern to the target number.
Inequality Techniques (Dos)
- DO think about inequalities as ranges on a number line.
- DO treat inequalities like equations when adding or subtracting terms, or when multiplying/dividing by a positive number on both sides of the ineqaulity.
- DO use extreme values t solve inequality range problems, problems containing both inequalities and equations, and many optimization problems.
- DO set terms with even exponents equal to O when trying to solve minimization problems.
Inequality Techniques DON’Ts
- DON’T forget to flip the inequality sign if you multiply or divide both sides of an inequality by a negative number.
- DON’T multiple or divide an inequality by a variable unless you know the sign of the variable.
- DON’T forget to perform operations on every expression when manipulating a compound inequality.
Fraction Denominator Rule
As the denominator of a number gets bigger, the value of the fraction gets smaller.
Common denominator
- Fraction adding and subtracting only works if you can add slices that are all the same size.
- Only the numerator changes once the common denominator is established.
- Then you have to simplify the final form.
Fraction Multiplication
Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.
Reciprocals
Numbers that, when multiplied together, equal 1.
Importance because dividing a number is the exact same thing as multiplying by its reciprocal.
5/6 / 4/7 = 5/6 x 7/4
Fractions between 0 and 1
Multiplying = creates a product smaller than the original #
Division = creates a quotient or result that is larger than the original #
Splitting Up Fractions
You can never split the terms of the denominator.
15+10/5 (can split) = (15/5 + 10/5)
5/15+10 (DON’T SPLIT) = 5/25
15+10/5+2 (simplify but DON’T SPLIT) = 25/7