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. HIGH: What is the unfactored version of (x-y)² ?
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.
x² -2xy + y²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
25%


2. v4 =
Not necessarily. This is a trick question - because x could be either positive or negative.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2


3. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


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

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5. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
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


6. What is the name of a line that extends from the center of a circle to the edge of a circle?
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
A radius
80%


7. HIGH: What is the formula for the diagonal of any square?
S*v2
1/1
25%
Multiply numerator times numerator and denominator times denominator.


8. HIGH: What is the Pythagorean theorem?

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9. 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
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 9 if the sum of its digits is divisible by 9.
(x-y)²


10. HIGH: Rough est. of v3 =
(x-y)²
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.
1.7
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


11. Define the range of a set of numbers.
(x+y)²
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.
180 degrees.
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


12. What degree angle is a line?
x²-y²
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
A line is a 180-degree angle.
x² + 2xy + y²


13. HIGH: List the two most common side ratios for right triangles
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
90 degrees each.
180 degrees
3:4:5 5:12:13


14. HIGH: how do you calculate the surface area of a rectangular box?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
(0 -0)
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%


15. HIGH: Rough est. of v2 =
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.
1.4
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
360 degrees


16. List two odd behaviors of exponents
1
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.


17. How do you add or subtract fractions?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
1/1
Find a common denominator and make equivalent fractions. Then add or subtract.
Not necessarily. This is a trick question - because x could be either positive or negative.


18. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Favorable Outcomes/Total Possible Outcomes
Probability A + Probability B
(0 -0)
(x-y)²


19. What do combination problems usually ask for?
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
The average - mean - median - or mode.
Groups - teams - or committees.


20. HIGH: What is the order of math operations - and the mnemonic to remember it?
S*v2
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 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.
Groups - teams - or committees.


21. Explain how to solve for 7/¼
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.


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.
2r
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
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.


23. How do you divide fractions?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
A triangle in which one of the three interior angles is 90 degrees.
360 degrees
Invert the second fraction (reciprocal) and multiply


24. For a bell curve - what three terms might be used to describe the number in the middle?
1.7
The average - mean - median - or mode.
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.
Not reading the problems carefully enough!


25. What is the key to dealing with ratio questions?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Find the total - or whole - first - and then set up a Ratio Box.
V=pr²h (This is just the area multiplied by the height)
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


26. In a coordinate system - identify the quadrants and describe their location.
2r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
360 degrees
Order does matter for a permutation - but does not matter for a combination.


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

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28. What'S the most important thing to remember about charts you'll see on the GRE?
Probability A + Probability B
A=pr²
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.


29. HIGH: To divide powers with the same base...
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The value that appears most often in a data set.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
360 degrees


30. 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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
(x+y)²
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


31. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
Invert the second fraction (reciprocal) and multiply
S²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


32. HIGH: What is the factored version of (x+y)(x-y) ?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
x²-y²


33. How many degrees does a circle contain?
360 degrees
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Groups - teams - or committees.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions


34. 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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
x² + 2xy + y²
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.


35. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
The average - mean - median - or mode.
6
S²


36. 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
The value that appears most often in a data set.
S²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


37. Define 'proportionate' values
Favorable Outcomes/Total Possible Outcomes
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.


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

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39. The three exterior angles of a triangle add up to...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
360 degrees
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


40. 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)+
Not necessarily. This is a trick question - because x could be either positive or negative.
40%
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


41. Explain the special properties of zero.
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
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.
The value that appears most often in a data set.


42. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Invert the second fraction (reciprocal) and multiply
'Big' angles and 'Small' angles.


43. Define the mode of a set of numbers.
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.
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.
3:4:5 5:12:13
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


44. Diameter of a circle?
2pr -or- pd
2r
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.
40%


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

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46. What is a 'Right' angle?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
A 90-degree angle.
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.
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


47. What is a 'Right' triangle?
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.
A radius
A triangle in which one of the three interior angles is 90 degrees.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


48. HIGH: What is a '30:60:90' triangle?
x²-y²
1.4
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28


49. HIGH: How do you calculate the circumference of a circle?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
90 degrees each.
2pr -or- pd
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.


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

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