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'S one way to avoid mistakes on algebra questions in the GRE?

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2. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
x² -2xy + y²
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


3. 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.
An integer is divisible by 2 if its units digit is divisible by 2.
1/1
A=pr²


4. An integer is divisible by 3 if...
A line is a 180-degree angle.
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.
Example: 1 < x < 10
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


5. How do you multiply fractions?
A radius
Multiply numerator times numerator and denominator times denominator.
1.7
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.


6. Convert to a percentage: 2/5
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Between 0 and 1.
40%


7. For a bell curve - what three terms might be used to describe the number in the middle?
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.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The average - mean - median - or mode.


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

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

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10. An integer is divisible by 2 if...
V=pr²h (This is just the area multiplied by the height)
90 degrees each.
40%
An integer is divisible by 2 if its units digit is divisible by 2.


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

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12. What is the name of a line that extends from the center of a circle to the edge of a circle?
A line is a 180-degree angle.
A radius
360 degrees
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


13. HIGH: What is the Pythagorean theorem?

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14. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
S*v2
Favorable Outcomes/Total Possible Outcomes
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.


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

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16. If x² = 144 - does v144 = x?
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
S*v2
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.


17. Define the range of a set of numbers.
Between 0 and 1.
(x-y)²
2r
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.


18. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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'.
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. 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
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.


19. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.
Favorable Outcomes/Total Possible Outcomes
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.


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

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21. HIGH: What is the factored version of (x+y)(x-y) ?
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.
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.
x²-y²
S²


22. 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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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 -287° = 1.


23. How precise do you need to be - using p on the GRE?

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24. HIGH: To divide powers with the same base...
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


25. HIGH: Volume of a cube?
Invert the second fraction (reciprocal) and multiply
A triangle in which one of the three interior angles is 90 degrees.
S*v2
V=s³


26. Simplify this: v32
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
180 degrees
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
6


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

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28. On the GRE - should you ever assume that diagrams are truthful?
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.
x² -2xy + y²
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.


29. HIGH: How much of your times table should you know - for the GRE?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


30. Define the mode of a set of numbers.
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.
The value that appears most often in a data set.
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%.
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.


31. What degree angle is a line?
A line is a 180-degree angle.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
1
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.


32. Diameter of a circle?
1.7
Groups - teams - or committees.
(x+y)²
2r


33. 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.
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%.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
(x+y)(x-y)


34. HIGH: What is the order of math operations - and the mnemonic to remember it?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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


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

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36. What is the 'distributive law'?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
Favorable Outcomes/Total Possible Outcomes
40%


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

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38. The three exterior angles of a triangle add up to...
2
360 degrees
25%
S²


39. HIGH: Rough est. of v1 =
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
1
80%
A 90-degree angle.


40. What is the equation for a group problem?
4 angles are formed. Their sum is 360 degrees
Probability A + Probability B
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.
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


41. HIGH: Simplify this: v75/v27
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
Order does matter for a permutation - but does not matter for a combination.
Groups - teams - or committees.
V75 = v253 = 5v3 - and v27 = v93 = 3v3. So we have 5v3/3v3. The v3 in the top and bottom of the fraction cancel - leaving 5/3.


42. 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)+
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The value that appears most often in a data set.
Groups - teams - or committees.


43. HIGH: Rough est. of v2 =
Favorable Outcomes/Total Possible Outcomes
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
1.4


44. Does order matter for a permutation? How about for a combination?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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.
2
Order does matter for a permutation - but does not matter for a combination.


45. 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.
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
1.7
S*v2


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

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47. Convert to a percentage: 1/4
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
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
'Big' angles and 'Small' angles.
25%


48. Area of a square?
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.
S²
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


49. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
A=pr²
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
360 degrees


50. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Arrangements - orders - schedules - or lists.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.