# New GRE Math Terms

## 127 terms · For the new (August, 2011) GRE Math portion - terms and formulas

### HIGH: Area of a triangle?

A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

V=s³

### HIGH: Volume of a cylinder?

V=πr²h (This is just the area multiplied by the height)

### How do you multiply fractions?

Multiply numerator times numerator and denominator times denominator.

### How do you add or subtract fractions?

Find a common denominator and make equivalent fractions. Then add or subtract.

### How do you divide fractions?

invert the second fraction (reciprocal) and multiply

2πr -or- πd

2r

A=πr²

(a+b)(a-b)

### HIGH: What is the median?

The # falling in the center of an ordered data set

### HIGH: What is the mode?

The value that appears most often in a data set.

### Probability Formula

Favorable Outcomes/Total Possible Outcomes

### HIGH: How do you multiply powers with the same base?

Add the exponents, retain the base.
for example, x² + x⁵ = x²+⁵ = x⁷

### HIGH: To divide powers with the same base...

Subtract the exponents, retain the base
For example, x⁹ ÷ x⁴ = x⁹-⁴ = x⁵

### HIGH: x^-n is equal to

1/x^n
For example, 6-² = 1/6² = 1/36

180 degrees

360 degrees

### HIGH: What is the Pythagorean theorem?

For RIGHT triangles only: c² = a² + b²
"c" is the length of the hypotenuse; "a" and "b" are the other two sides ("legs")

bh

### HIGH: How do you calculate the length of an arc?

Length of an Arc = (n/360)(2πr), where "n" equals the central angle (the angle formed by the two edge radii of the arc). For example: if n=60, then n/360 = 1/6, which means the arc formed by the 60-degree central angle will be 1/6 of the circle's circumference. Calculate the circumference as 2πr, and multiply by 1/6.

### What degree angle is a line?

A line is a 180-degree angle.

### How many angles are formed when 2 lines intersect? and what is the sum of these angles?

4 angles are formed. Their sum is 360 degrees

90 degrees each.

### What is a "right" angle?

A 90-degree angle.

360 degrees

### When a pair of parallel lines is intersected by another line, two types of angles are formed. What are they?

"Big" angles and "small" angles.

180 degrees.

### On the GRE, should you ever assume that diagrams are truthful?

No. Never believe what you see, only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

### HIGH: Define the "third side" rule for triangles

The length of any one side of a triangle must be less than the sum of the other two sides. It must also be greater than the difference between the other two sides. So, "A" will always be < B+C, and > B-C or C-B.

### What is a "right" triangle?

A triangle in which one of the three interior angles is 90 degrees.

### HIGH: What is a "right isosceles" triangle?

This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:x√2, where x√2 is the hypotenuse.

### What is an "equilateral" triangle?

Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

### HIGH: What is a "30:60:90" triangle?

This is an equilateral triangle that has been divided along its height. Interior angles are 30:60:90 degrees. Ratio of sides is x:x√3:2x, where x is the base, x√3 is the height, and 2x is the hypotenuse. This allows you to deduce any side, given the value of any other side.

### What causes 80% of errors on the math section of the GRE?

Not reading the problems carefully enough!

### What should you do BEFORE you start to solve a GRE math problem?

Always read the answer choices first. Try to eliminate choices by ballparking or estimating. But watch out for "trap" answers that look temptingly correct at first glance.

### Explain the difference between a digit and a number.

A digit is a number that makes up other numbers. There are ten digits: 0,1,2,3,4,5,6,7,8,9. Every "number" is made up of one or more digits. For example, the number 528 is made up of three digits - a 5, a 2, and an 8.

### Explain the special properties of zero.

Zero is even. It is an integer. It is neither positive nor negative. Zero multiplied by any other number = zero. You cannot divide by zero.

### HIGH: What is "absolute value", and how is it represented?

Absolute value is a number's distance away from zero on the number line. It is always positive, regardless of whether the number is positive or negative. It is represented with | |. For example, |-5| = 5, and |5| = 5.

### List all the prime numbers that are less than 30:

2,3,5,7,11,13,17,19,23,29. Note that 0 and 1 are not prime numbers.

### An integer is divisible by 3 if...

An integer is divisible by 3 if the sum of its digits is divisible by 3. For example, adding the digits of the number 2,145 (2+1+4+5) = 12, which is divisible by 3.

### An integer is divisible by 4 if...

An integer is divisible by 4 if its last two digits form a number that's divisible by 4. For example, 712 is divisible by 4 because its last two digits (12) is divisible by 4.

### An integer is divisible by 2 if...

An integer is divisible by 2 if its units digit is divisible by 2.

### An integer is divisible by 8 if...

An integer is divisible by 8 if its last three digits form a number that's divisible by 8. For example, 11,640.

### An integer is divisible by 5 if...

An integer is divisible by 5 if its units digit is either 0 or 5.

### An integer is divisible by 6 if...

An integer is divisible by 6 if it's divisible by BOTH 2 and 3.

### An integer is divisible by 9 if...

An integer is divisible by 9 if the sum of its digits is divisible by 9.

### HIGH: What is the order of math operations, and the mnemonic to remember it?

PEMDAS (Please Excuse My Dear Aunt Sally):
P = Parentheses. Solve anything inside of parentheses first.
E = Exponents. Solve these second.
MD = Multiplication, Division. From left to right, do all multiplication and division during one step through the formula.
AS = Addition, Subtraction. Do all addition and subtraction together in one step, from left to right.

### HIGH: How much of your times table should you know, for the GRE?

It will be a great advantage on test day to have your times table memorized from 1 through 15.

### What is the "distributive law"?

a(b+c) = ab + ac
a(b-c) = ab - ac
For example, 12(66) + 12(24) is the same as 12(66+24), or 12(90) = 1,080.

### List two odd behaviors of exponents

1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number.
For example: (1/2)² = 1/4.
2. A number raised to the 0 power is 1, no matter what the number is.
For example: 1,287⁰ = 1.

### HIGH: How do you multiply and divide square roots?

Like any other number.
For example, √3*√12 = √36 = 6
For example, √(16/4) = √16/√4 = 4/2 = 2

### If x² = 144, does √144 = x?

Not necessarily. This is a trick question, because x could be either positive or negative.

1

1.4

1.7

2

### Simplify this: √32

√32 = √16*2. We can take the square root of 16 and move it outside the square root symbol, = 4√2.

### HIGH: Simplify this: √75/√27

√75 = √253 = 5√3, and √27 = √93 = 3√3.
So we have 5√3/3√3. The √3 in the top and bottom of the fraction cancel, leaving 5/3.

### HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x

Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x, x = 3/4.

### How is a range expressed with inequalities?

Example: 1 < x < 10

### HIGH: Describe and define three expressions of quadratic equations, in both factored and unfactored forms. Know these cold.

1. Factored: x² - y² Unfactored: (x+y)(x-y)
2. Factored: (x+y)² Unfactored: x² + 2xy + y²
3. Factored: (x-y)² Unfactored: x² - 2xy + y²

### HIGH: Describe how to deal with 2 sets of parentheses.

Use the FOIL method: First, Outer, Inner, Last. This simply means to multiply every term in the first parentheses by every term in the second parentheses.
Example: (x+4)(x+3) =
First: (xx) + Outer: (x3) + Inner: (4x) + Last: (43)
= (xx)+(x3)+(x4)+(43)
= x² + 3x + 4x + 12
= x² + 7x + 12

(x+y)(x-y)

x² + 2xy + y²

x² -2xy + y²

x²-y²

(x+y)²

(x-y)²

-6

### HIGH: What must be true before a quadratic equation can be solved?

The equation must be set equal to zero. If during the test one appears that's not, before you can solve it you must first manipulate it so it is equal to zero.

### What's one way to avoid mistakes on algebra questions in the GRE?

By Plugging In an actual value for the variable(s). This will be quicker, more accurate, you'll avoid built-in traps, and you can use the calculator. When Plugging In, use simple numbers but avoid 1 and 0.

### HIGH: What numbers does ETS hope you'll forget to consider, for quant comp questions?

ZONE-F numbers: Zero, One, Negatives, Extreme values, Fractions

### Explain how to divide fractions.

Turn the second fraction upside down (find its reciprocal) and multiply.
Example: 2/3 ÷ 4/5 = 2/3 * 5/4

### Explain how to solve for 7/¼

This equals 7 ÷¼, or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

### HIGH: Explain a method for quickly comparing fractions with different denominators, to determine which is larger.

Multiply each numerator by the other fraction's denominator.
Example: 3/7 and 7/12. Multiply 312 = 36, and 77 = 49. If you completed the full calculation, you'd also cross-multiply the denominators, but you don't have to in order to compare values.

40%

60%

25%

80%

### HIGH: Explain the process to solve "56 is what percent of 80?"

First, translate into clear math:
56 = x/100(80) ("56 is x one-hundredths of 80")
= 56 = 80x/100
= 56 = 4x/5
Divide both sides by 4/5 (multiply by 5/4)
70 = x, so 70%.

### How do you calculate the percentage of change?

Percentage Change = Difference/Original * 100

### What is the key to dealing with ratio questions?

Find the total, or whole, first, and then set up a Ratio Box.

### Define "proportionate" values

Proportionate values are equivalent.
Example: 1/2 and 4/8 are proportionate, but 1/2 and 2/3 are not.

### Explain how to calculate an average (arithmetic mean)

Total of the elements divided by the number of elements.
Example: (4,6,7) -- add 4+6+7 = 17 and divide by 3

### Explain how to use an "Average Pie"

Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

### HIGH: What are the percentages for standard deviation?

2, 14, and 34. So, a Bell, standard deviation, or normal distribution curve would be segmented:
| 2% | 14% | 34% |average score| 34% | 14% | 2% |

### For a bell curve, what three terms might be used to describe the number in the middle?

The average, mean, median, or mode.

### Explain how to use a "Rate Pie"

This is similar to an Average Pie, and can be used for some story problems. Draw a circle. Top half holds the Distance or other Amount. Bottom left holds Time. Bottom right holds Rate.
Rate * Time = Amount

### What's the most important thing to remember about charts you'll see on the GRE?

That, unlike a normal chart, they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down, read everything, and look carefully for hidden information - asterisks, footnotes, small print, and funny units.

### What are "vertical angles"?

Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

### What is the "third side" rule for triangles?

The length of any one side of a triangle must be less than the sum of the other two sides, and greater than the difference between the other two sides.

3:4:5
5:12:13

s*√2

### How precise do you need to be, using π on the GRE?

Using a simple "3" is usually close enough. Just remember that π is slightly more than 3, if a comparison is called for.

### HIGH: Define the formula for calculating slope.

Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

(0,0)

### In a coordinate system, identify the quadrants and describe their location.

Q 2 is top left.
Q 3 is bottom left.
Q 4 is bottom right.

### HIGH: What is the equation of a line?

y = mx + b -- where:
x,y are the coordinates of any point on the line (allows you to locate)
m is the slope of the line
b is the intercept (where the line crosses the y-axis)
Sometimes on the GRE, "a" is substituted for "m", as in "y = ax + b".

### What is one misleading characteristic of quadratic equations that will be exploited on the GRE?

That they often have not just one answer, but two. For example, solving x² -10x + 24 = 0 factors to (x-4)(x-6)=0, which means x could equal either 4 or 6. Just accept it.

### HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?

The formula is a² + b² + c² = d²
where a, b, c are the dimensions of the figure and d is the diagonal.

### HIGH: how do you calculate the surface area of a rectangular box?

Calculate and add the areas of all of 6 its sides.
Example: for a rectangle with dimensions 2 x 3 x 4, there will be 2 sides each, for each combination of these dimensions. That is, 2 each of 2x3, 2 each of 3x4, and 2 each of 4x2.

### What's a handy rough estimate for a circle's perimeter, if you know it's diameter?

A circle's perimeter is roughly 3x its diameter (the formula is πd).

### What kind of triangle is this: has two sides of equal length, and a 90 degree angle?

An isoceles right angle. Remember that interior angles are 90:45:45 degrees. The ratio of sides is x:x:x√2, where x√2 is the hypotenuse.

### What is the formula to determine probability?

(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

1/1

Between 0 and 1.

### What number goes on the bottom of a probability fraction?

The total # of possible outcomes.

### How do you calculate the probability of two events in a row? (Probability of A and B)

Probability A * Probability B

### How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)

Probability A + Probability B

1.
Given event A:
A + notA = 1.

### Define a factorial of a number, and how it is written.

The factorial of a number is that number times every positive whole number smaller than that number, down to 1.
Example: 6! means the factorial of 6, which = 65432*1 = 720.

### What are the side ratios for a 30:60:90 triangle?

Ratio of sides is x : x√3 : 2x,
where x is the base, x√3 is the height, and 2x is the hypotenuse.

### How do you solve a permutation?

1. Figure out how many slots you have (i.e. there are 3 winning positions in a race - 1st, 2nd, and 3rd)
2. Write down the number of possible options for each slot (i.e. 5 runners in the race, so 5 options for the 1st slot, 4 options for the 2nd slot, and 3 options for the 3rd slot)
3. Multiply the number of options (i.e. 5x4x3 = 60)

### What do permutation problems often ask for?

Arrangements, orders, schedules, or lists.

### What do combination problems usually ask for?

Groups, teams, or committees.

### Does order matter for a permutation? How about for a combination?

Order does matter for a permutation, but does not matter for a combination.

### How do you solve a combination?

1. Figure out how many slots you have (i.e. you're supposed to bring home 3 different types of ice cream)
2. Write down the number of possible options for each slot (i.e. 5 flavors of ice cream at the store, 5 options for the 1st slot, 4 options for the 2nd slot, and 3 options for the 3rd slot)
3. Multiply the number of options (i.e. 5x4x3 = 60)
4. Divide by the factorial of the number of slots (i.e. 3 types to bring home, so 3x2x1=6. 60/6 = 10)

### Explain the difference between handling a permutation versus a combination.

If order matters, then you have a permutation -- do NOT divide. If order does NOT matter, then you have a combination -- divide by the factorial of the number of available slots.

### What is the equation for a group problem?

T = G₁ + G₂ - B + N
Where T = Total
G₁ = first Group
G₂ = second Group
B = members who are in Both groups
N = members who are in Neither group

### Define the median of a set of numbers, and how to find it for an odd and even number of values in a set.

A median is the middle value of a set of numbers. For an odd number of values, it's simply the middle number. For an even number of values, take the average of the center two values.

### Define the mode of a set of numbers.

The mode is the number in a set that occurs most frequently.
Example: for the set {3,6,3,8,9,3,11} the number 3 appears most frequently so it is the mode.

### Define the range of a set of numbers.

The range is the difference between the biggest and smallest numbers in the set.
Example: for the set {2,6,13,3,15,4,9} the smallest number is 2, largest is 15, so the range is 15-2=13.

### HIGH: What is the side ratio for a 30:60:90 triangle?

Ratio of sides is x:x√3:2x, where x is the base, x√3 is the height, and 2x is the hypotenuse.

### HIGH: what is the side ratio for a Right Isosceles triangle?

The ratio of sides is x:x:x√2, where x√2 is the hypotenuse.