GRE High Frequency Math Terms

Instructions:

• Answer 50 questions in 15 minutes.
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• 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 ?
x² -2xy + y²
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
S*v2
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.


2. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide 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')


3. HIGH: How do you multiply powers with the same base?
Arrangements - orders - schedules - or lists.
The # falling in the center of an ordered data set
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


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

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5. How do you add or subtract fractions?
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 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
Find a common denominator and make equivalent fractions. Then add or subtract.


6. HIGH: what is the side ratio for a Right Isosceles triangle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
6


7. What is the sum of any 'big' angle and any 'Small' angle?
A=pr²
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'.
Favorable Outcomes/Total Possible Outcomes
180 degrees.


8. HIGH: Volume of a cylinder?
180 degrees.
V=pr²h (This is just the area multiplied by the height)
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


9. What is the equation for a group problem?
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.
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
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
A radius


10. What is the 'Third side' rule for triangles?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2r


11. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
60%
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.


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

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13. How many degrees does a circle contain?
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
360 degrees
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.


14. HIGH: Define the formula for calculating slope.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
A radius
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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


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

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16. How is a range expressed with inequalities?
Example: 1 < x < 10
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
3:4:5 5:12:13
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.


17. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
180 degrees.
A triangle in which one of the three interior angles is 90 degrees.
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
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.


18. HIGH: What is the unfactored version of x²-y² ?
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)+
Probability A * Probability B
80%
(x+y)(x-y)


19. Explain the special properties of zero.
Multiply numerator times numerator and denominator times denominator.
180 degrees
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.


20. The three exterior angles of a triangle add up to...
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%.
360 degrees
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.
180 degrees


21. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
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
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


22. Convert to a percentage: 1/4
25%
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


23. 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% |
This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
An integer is divisible by 2 if its units digit is divisible by 2.


24. In a coordinate system - what is the origin?
(0 -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.
3:4:5 5:12:13
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


25. HIGH: How do you calculate the circumference of a circle?
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.
The value that appears most often in a data set.
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.
2pr -or- pd


26. Diameter of a circle?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
25%
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
2r


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

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28. List two odd behaviors of exponents
An integer is divisible by 9 if the sum of its digits is divisible by 9.
A radius
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.


29. HIGH: Simplify this: v75/v27
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.
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.
Invert the second fraction (reciprocal) and multiply
Groups - teams - or committees.


30. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
25%
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.
1/x^n For example - 6-² = 1/6² = 1/36


31. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
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
Not reading the problems carefully enough!
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


32. If something is certain to happen - how is the probability of this event expressed mathematically?
Probability A * Probability B
1/1
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.


33. HIGH: Rough est. of v1 =
Groups - teams - or committees.
1
An integer is divisible by 9 if the sum of its digits is divisible by 9.
2


34. How do you divide fractions?
1.7
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.
Invert the second fraction (reciprocal) and multiply
6


35. How do you calculate the probability of two events in a row? (Probability of A and B)
Not reading the problems carefully enough!
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
x²-y²
Probability A * Probability B


36. HIGH: How do you multiply and divide square roots?
S*v2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


37. HIGH: What is a 'Right isosceles' triangle?
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.
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


38. Explain how to calculate an average (arithmetic mean)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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
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


39. HIGH: What is a '30:60:90' triangle?
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
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
Multiply numerator times numerator and denominator times denominator.
V=s³


40. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
(0 -0)
4 angles are formed. Their sum is 360 degrees
180 degrees


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

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42. An integer is divisible by 2 if...
S*v2
An integer is divisible by 2 if its units digit is divisible by 2.
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.
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.


43. List all the prime numbers that are less than 30:
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
A 90-degree angle.
180 degrees


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

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45. v4 =
2
A=pr²
x²-y²
6


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

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47. HIGH: Rough est. of v3 =
(0 -0)
1.7
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.
(x-y)²


48. HIGH: how do you calculate the surface area of a rectangular box?
Between 0 and 1.
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'.
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.
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.


49. An integer is divisible by 3 if...
x² + 2xy + y²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
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.


50. HIGH: x^-n is equal to
An integer is divisible by 9 if the sum of its digits is divisible by 9.
A=pr²
1/x^n For example - 6-² = 1/6² = 1/36
V=s³