GRE High Frequency Math Terms

Instructions:

• Answer 50 questions in 15 minutes.
• If you are not ready to take this test, you can study here.
• Match each statement with the correct term.
• Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
180 degrees.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3


2. HIGH: Define the formula for calculating slope.
A radius
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
An integer is divisible by 5 if its units digit is either 0 or 5.


3. HIGH: How much of your times table should you know - for the GRE?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The total # of possible outcomes.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.


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

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5. HIGH: Explain the process to solve '56 is what percent of 80?'

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6. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Find the total - or whole - first - and then set up a Ratio Box.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
This is an equilateral triangle that has been divided along its height. Interior angles are 30:60:90 degrees. Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse. This allows you to deduce any side - given


7. How do you add or subtract fractions?
40%
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
Favorable Outcomes/Total Possible Outcomes
Find a common denominator and make equivalent fractions. Then add or subtract.


8. For a bell curve - what three terms might be used to describe the number in the middle?
Length of an Arc = (n/360)(2pr) - 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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
The average - mean - median - or mode.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


9. Area of a square?
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.
S²
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


10. Does order matter for a permutation? How about for a combination?
S*v2
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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.
Order does matter for a permutation - but does not matter for a combination.


11. Explain how to divide fractions.
Find a common denominator and make equivalent fractions. Then add or subtract.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
1.4
S*v2


12. Probability Formula
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.
Favorable Outcomes/Total Possible Outcomes
Find the total - or whole - first - and then set up a Ratio Box.
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 fo


13. An integer is divisible by 2 if...
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
360 degrees
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
An integer is divisible by 2 if its units digit is divisible by 2.


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

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15. 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:xv2 - where xv2 is the hypotenuse.
60%
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Example: 1 < x < 10


16. HIGH: Define the 'Third side' rule for triangles

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17. How many degrees does a circle contain?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Order does matter for a permutation - but does not matter for a combination.
360 degrees


18. HIGH: Rough est. of v1 =
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.
S*v2
1


19. Explain how to use a 'Rate Pie'
The value that appears most often in a data set.
2
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
V=s³


20. What is the sum of any 'big' angle and any 'Small' angle?
Probability A + Probability B
360 degrees
180 degrees.
Order does matter for a permutation - but does not matter for a combination.


21. HIGH: How do you multiply powers with the same base?
90 degrees each.
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.
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)+
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


22. Solve this: v6 * -v6 = ?
40%
6
360 degrees
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28


23. HIGH: What is the unfactored version of (x-y)² ?
25%
x² -2xy + y²
Percentage Change = Difference/Original * 100
An integer is divisible by 9 if the sum of its digits is divisible by 9.


24. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
The total # of possible outcomes.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(a+b)(a-b)


25. Simplify this: v32
1.4
A line is a 180-degree angle.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
1. Given event A: A + notA = 1.


26. In a coordinate system - identify the quadrants and describe their location.
Not necessarily. This is a trick question - because x could be either positive or negative.
Favorable Outcomes/Total Possible Outcomes
An integer is divisible by 5 if its units digit is either 0 or 5.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


27. HIGH: What is the equation of a line?

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28. HIGH: Area of a triangle?
180 degrees.
60%
Probability A * Probability B
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


29. 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
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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Groups - teams - or committees.


30. The three interior angles of a triangle add up to...
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
180 degrees


31. What do permutation problems often ask for?
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.
Arrangements - orders - schedules - or lists.
3:4:5 5:12:13
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


32. HIGH: What is the median?
1/x^n For example - 6-² = 1/6² = 1/36
The # falling in the center of an ordered data set
An isoceles right angle. Remember that interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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


33. Convert to a percentage: 3/5
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.
60%
'Big' angles and 'Small' angles.
An isoceles right angle. Remember that interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


34. If something is possible but not certain - what is the numeric range of probability of it happening?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Find the total - or whole - first - and then set up a Ratio Box.
Between 0 and 1.
90 degrees each.


35. In a coordinate system - what is the origin?
(x+y)²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(0 -0)
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28


36. What are 'vertical angles'?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


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

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38. The three exterior angles of a triangle add up to...
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
360 degrees
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.
Length of an Arc = (n/360)(2pr) - 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


39. What is a 'Right' angle?
360 degrees
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A 90-degree angle.


40. HIGH: Rough est. of v3 =
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Groups - teams - or committees.
1.7
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3


41. Diameter of a circle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
A triangle in which one of the three interior angles is 90 degrees.
2r


42. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

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43. What is the factored version of x² -2xy + y² ?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
(0 -0)
(x-y)²


44. Define the mode of a set of numbers.
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.
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.
Arrangements - orders - schedules - or lists.
180 degrees


45. 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)+
x²-y²
Example: 1 < x < 10
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.


46. HIGH: What is a '30:60:90' triangle?
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 fo
Find the total - or whole - first - and then set up a Ratio Box.
This is an equilateral triangle that has been divided along its height. Interior angles are 30:60:90 degrees. Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse. This allows you to deduce any side - given
3:4:5 5:12:13


47. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
80%
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.


48. 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.
A=pr²
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


49. HIGH: What is the formula for the diagonal of any square?
S*v2
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.
6
(x-y)²


50. HIGH: What is 'absolute value' - and how is it represented?

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