GRE-Kaplan Math
area of a trapezoid
(1/2)(b1+b2)h=area
factor a^2 + 2ab+b^2
(a+b)^2
a^2 - b^2
(a-b)(a+b)
a^2 -2ab-b^2
(a-b)^2
0! =
0!=1
what is the sum of the integers from 10 through 50, inclusive?
1. find the average of the two numbers given. 2. determine the number of terms B-A+1 3. find the sum= average x number of terms average=(10+50)/2 =30 number of terms= 50-10+1 sum= 30 x 41 =1230
if $12000 is invested at 6 percent simple annual interest, how much interest is earned after 9 months?
12000 x 0.06 x (9/12) =$540
how to find the sum of all the angles of a regular polygon
180 (n-2)
If a fair coin is tossed 4 times, what's the probability that at least 3 of the 4 tosses will be heads?
2 x 2 x 2 x 2=16 possibilities HHHT HHTH HTHH THHH HHHH = 5 desired results probability = 5/16
how to find the length of an arc in a circle
2*pi*r*(n/360)
How do you recognize the multiples of 2
2: last digit is even
How do you recognize the multiples of 3
3: sum of digits is a multiple of 3
How do you recognize the multiples of 4
4: last two digits are a multiple of 4
How do you recognize the multiples of 5
5: last digit is 5 or 0
How do you recognize the multiples of 6
6: sum of digits is a multiple of 3, and last digit is even
How do you recognize the multiples of 9
9: sum of digits is a multiple of 9
how many integers are there from 73 through 419, inclusive?
B-A+1 = (419-73)+1 = 347
how to find a common multiple of two numbers?
The LCM can be found by finding the prime factorization of each number, then seeing the greatest number of times each factor is used. Multiply each prime factor the greatest number of times it appears. and multiple each factor the greatest number of times it appears in a prime factorization 28=2 x 2 x 7 42= 2 x 3 x 7 LCM= 2 x 2 x 3 x 7 = 84
what is the average of a list of numbers starting with 13 and ending with 77?
The average of evenly spaced number is simply the average of the smallest number and the largest number. The average of all the integers from 13 to 77, for example, is the same as the average of 13 and 77. the answer is 45.
how to find one angle of a regular polygon
[180 (n-2)]/n
factor ab+ac
a(b+c)
how to solve a dilution problem?
balance the equation: n[(% difference btw weaker and desired solution)-weaker percent] = volume of stronger solution[(% difference btw stronger solution and desired)-desired]
how to find a common factor of two numbers?
break both numbers down to their prime factors to see which they have in common. then multiply the shared prime factors to find all common factors.
how to find the range
calculate the greatest value minus the least value
divide roots
handle the inside and outside number seperatly
how to multiply roots?
handle the inside and outside numbers seperately
how to solve a compound interest problem
if interest is compounded, the interest is computed on the principal as well as on any interest earned.
how to find the maximum and minimum lengths for a side of a triangle
if you know n=the lengths of two sides of a triangle, you know that the third side is somewhere between the positive difference and the sum of those two sides.
how to solve a simple interest problem?
interest = (principle) x (interest rate, expressed as decimal) x (time, expressed in years or fraction of a year)
How do you recognize the multiples of 10
last digit is 0
how to add and subtract roots?
make roots common
how to solve a group problem involving both/neither. it's easy to identify this type of question because the words both and/or neither appear in the question.
memorize Group 1 + Group 2 +Neither -Both=total
What formula do you use if you're asked to find the number of ways to arrange a smaller group that's being drawn from a larger group?
permutation formula n= number in the larger group r=the number you are arranging
how to find the area of a sector of a circle
pi*(r^2)*(n/360)
absolute values
represent the possible range for the equation on a number line.
how to solve a group problem involving either/or categories
set up the information in a grid
how to solve a standard deviation problem
standard deviation is a measure of how spread out a set of number is compared to the mean. 1. find the average of the set 2. find the differences between the mean and each value in the set 3. square each of the differences 4. take the positive square root of the average
How do you recognize the multiples of 12
sum of digits is a multiple of 3, and last two digits are a multiple of 4
how to deal with normal distribution curve
the normal distribution curve has divisions of 34, 14, and 2 percent on each side of the mean
how to handle fractional powers
they all relate to roots
how to count the number of possibilities
use multiplication to find the numbers of possibilities.
how to find the diagonal of a rectangular
use the Pythagorean theorem twice, unless you spot "special" triangles
how to solve a combination problem where the order or arrangement of the smaller group that's being drawn from the larger group does not matter
where n= the number in the larger group r=the number you're choosing
(x^m)(x^n) equals what?
x^(m+n)
(x^m)^n equals what?
x^(mxn)
how to solve conditional probability questions for example if 2 students are chosen at random to run an errand from a class with 5 girls and 5 boys, what is the probability that both students chosen will be girls?
you solve through multiplication. you multiple the probability that the first event happens times the probability that the second event happens. (5/10)(4/9)=2/9 the probability of choosing the second girl was affected by another girl being chosen first
