GRE Basic Math Flashcards
What does “and” mean in a word problem?
ADDITION
What does “removed/left” mean in a word problem?
SUBTRACTION
What does “of” mean in a word problem?
MULTIPLICATION
Negative - Positive = ?
Negative + -Positive = Negative #
Positive - Negative = ?
Cancels –> Add Positives
LCD for converting unlike fractions
Find the least common dem. of each fraction presented
Adding Fractions
Add straight across if LCD
Subtracting Fractions
Subtract straight across if LCD
Multiplying Fractions
Cross multiply for any cancellations, then just multiply straight across! Don’t need LCD.
True or False: A ratio is the same thing as a fraction.
TRUE!
Multiplying Exponents
Add exponents together if the base is the same
Dividing Exponents
Subtract exponents if the base is the same
6 (0) exponent = ?
1
6 (1) exponent = ?
6
What is a square root?
A whole number multiplied by itself –> SR of 16 = 4 because 4 X 4 = 16
Adding or Subtracting Square Roots
Only with equal base #s
Multiplying or Dividing Square Roots
Multiply or Divide straight across
Simplifying Square Roots
Break down the base # into numbers that have whole square roots –> SR80 can be broken down into SR4 (which is 2) X SR 20, and simply on down from there.
s with Fractions as Exponents
Base # X the numerator, then take the Square Root of the denom.
Fractions as Exponents quickies…
1/2 = square root of the base # 1/3 = cube root of the base #
Mean
Average = sum of #/total of all #s
Mode
The middle # in a set of numbers listed from highest to lowest
Mode
The # that occurs most often in a series
What does “absolutely value” mean?
The # is ALWAYS positive!
Can you take the Square Root of a Negative #?
NO!
How do you “cancel” the X in an equation?
Apply the opposite operation
When solving algebraic equations, remember to “combine like….”
Terms
Algebra –> Substitution means…
Plug it in like a lightbulb!
Algebra –> How do you treat inequalities?
Just like a normal equation with an = sign
Algebra –> Reverse the equality sign to make a fraction positive when you…
Divide by a negative #
Monomials –> You can perform the operation on #s when the variables & exponents are…
The same!
When do you combine coefficients and variables?
When you multiple 2 or more monomials
When you divide polynomials, you ___ the coefficients and ___ the exponents…
Divide the coefficients and subtract the exponents
Multiplying Binomials –> FOIL
First, Outer, Inner, Last (then combine like terms)
How do you FACTOR MONomials?
Find the largest common monomial and take it out of each section –> 6y(2z + x)
How do you FACTOR TRInomials?
What numbers multiply to the last number, and add to the middle number?
(x +/- #)(x +/- #)
Check each factor with both +/- options to see which one is correct
Reverse FOIL to check your answers
(x-2)(x-3)
How do you solve quadratic equations?
Ones = 0
Find their factors, set each factor to 0, and solve –> you should have TWO DIFFERENT solutions!
Solving an Algebraic equation with fractions –> what do you do?
- Multiply the num. by a common factor
- Divide the coefficients to get a new eq.
- Solve for x
When you feel doubtful about solving an algebraic equation…
Isolate x and solve
Equation - Distance Between 2 points
AB = SR of (Xa - Xb)^2 + (Ya - Yb)^2
Equation - Midpoint of a line
(Xa + Xb), (Ya + Yb) all divided by 2
Equation - Slope of a line
m = Yb - Ya / Xb - Xa
Equation of a line (can also be used to find y-intercept)
Y = mx + b
How do you solve a basic function problem?
Substitute the # given
Trick for solving f(x-4) tricky functions?
Use FOIL
