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. v4 =
2
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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


2. Convert to a percentage: 2/5
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.
180 degrees
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.
40%


3. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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
Probability A + Probability B
V=s³


4. a² - b² is equal to
'Big' angles and 'Small' angles.
(a+b)(a-b)
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
1.4


5. How do you add or subtract fractions?
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
Find a common denominator and make equivalent fractions. Then add or subtract.
1/1
Invert the second fraction (reciprocal) and multiply


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

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7. 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.
Between 0 and 1.
1/x^n For example - 6-² = 1/6² = 1/36
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.


8. What is a 'Right' angle?
A 90-degree angle.
(x-y)²
Order does matter for a permutation - but does not matter for a combination.
Favorable Outcomes/Total Possible Outcomes


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


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

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11. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
The # falling in the center of an ordered data set
Groups - teams - or committees.
3:4:5 5:12:13


12. HIGH: What is the formula for the diagonal of any square?
3:4:5 5:12:13
S*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.
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.


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

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14. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Example: 1 < x < 10
3:4:5 5:12:13
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
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


15. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
Between 0 and 1.
(0 -0)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The value that appears most often in a data set.


16. What is the factored version of x² -2xy + y² ?
Probability A + Probability B
(x-y)²
2pr -or- pd
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions


17. HIGH: Define the formula for calculating slope.
6
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.
Multiply numerator times numerator and denominator times denominator.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


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

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19. How do you calculate the percentage of change?
Invert the second fraction (reciprocal) and multiply
Percentage Change = Difference/Original * 100
Bh
An integer is divisible by 5 if its units digit is either 0 or 5.


20. 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% |
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
Find the total - or whole - first - and then set up a Ratio Box.


21. HIGH: what is the side ratio for a Right Isosceles triangle?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
90 degrees each.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x² -2xy + y²


22. If something is possible but not certain - what is the numeric range of probability of it happening?
6
Between 0 and 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.
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.


23. Convert to a percentage: 4/5
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'.
80%
The total # of possible outcomes.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28


24. How do you divide fractions?
Invert the second fraction (reciprocal) and multiply
V=pr²h (This is just the area multiplied by the height)
60%
Not necessarily. This is a trick question - because x could be either positive or negative.


25. An integer is divisible by 3 if...
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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 -2xy + y²


26. HIGH: How much of your times table should you know - for the GRE?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
(a+b)(a-b)
2pr -or- pd


27. HIGH: What is the factored version of (x+y)(x-y) ?
x²-y²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Invert the second fraction (reciprocal) and multiply
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'.


28. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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
6
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
1. Given event A: A + notA = 1.


29. HIGH: What is the mode?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
The value that appears most often in a data set.
Invert the second fraction (reciprocal) and multiply
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28


30. What is the 'distributive law'?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.
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%.
Order does matter for a permutation - but does not matter for a combination.


31. HIGH: Volume of a cylinder?
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.
V=pr²h (This is just the area multiplied by the height)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


32. HIGH: What is the unfactored version of (x-y)² ?
x² -2xy + y²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A line is a 180-degree angle.


33. Explain the difference between handling a permutation versus a combination.
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.
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.
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.
1


34. HIGH: Volume of a cube?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
V=s³


35. An integer is divisible by 5 if...
(0 -0)
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
An integer is divisible by 5 if its units digit is either 0 or 5.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


36. HIGH: List the two most common side ratios for right triangles
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.
180 degrees
An integer is divisible by 5 if its units digit is either 0 or 5.
3:4:5 5:12:13


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

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38. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
90 degrees each.
x²-y²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.


39. What are 'vertical angles'?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
'Big' angles and 'Small' angles.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.


40. 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.
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.
Arrangements - orders - schedules - or lists.
6


41. How do you solve a combination?

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42. What are the side ratios for a 30:60:90 triangle?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
x² + 2xy + y²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


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

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44. 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.
6
2pr -or- pd
1.4


45. What number goes on the bottom of a probability fraction?
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 total # of possible outcomes.
A triangle in which one of the three interior angles is 90 degrees.
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.


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

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47. What'S the most important thing to remember about charts you'll see on the GRE?
'Big' angles and 'Small' angles.
3:4:5 5:12:13
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


48. If x² = 144 - does v144 = x?
Between 0 and 1.
Favorable Outcomes/Total Possible Outcomes
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.
Not necessarily. This is a trick question - because x could be either positive or negative.


49. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
V=s³
1/1


50. Define 'proportionate' values
Multiply numerator times numerator and denominator times denominator.
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.
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.