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GRE High Frequency Math Terms

Subjects : gre, math

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: How do you multiply powers with the same base?
Between 0 and 1.
1
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
90 degrees each.

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

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

4. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
A radius
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

5. HIGH: What is the formula for the diagonal of any square?
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)+
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.
The average - mean - median - or mode.
S*v2

6. Does order matter for a permutation? How about for a combination?
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 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.
Order does matter for a permutation - but does not matter for a combination.

7. An integer is divisible by 2 if...
V=s³
An integer is divisible by 2 if its units digit is divisible by 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.
The # falling in the center of an ordered data set

8. In a coordinate system - what is the origin?
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
1. Given event A: A + notA = 1.
(0 -0)

9. Explain the difference between handling a permutation versus a combination.
Favorable Outcomes/Total Possible Outcomes
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.
S*v2

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

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

12. HIGH: What are the percentages for standard deviation?
360 degrees
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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
(x-y)²

13. 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
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
(a+b)(a-b)
An integer is divisible by 2 if its units digit is divisible by 2.

14. HIGH: what is the side ratio for a Right Isosceles triangle?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
2r
(x+y)(x-y)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

15. If something is certain to happen - how is the probability of this event expressed mathematically?
90 degrees each.
1/1
A triangle in which one of the three interior angles is 90 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.

16. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
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.
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
90 degrees each.
The average - mean - median - or mode.

17. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
1. Given event A: A + notA = 1.
2pr -or- pd
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

18. 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.
A 90-degree angle.
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
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

19. HIGH: Simplify this: v75/v27
(x-y)²
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
180 degrees
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.

20. HIGH: To divide powers with the same base...
Find a common denominator and make equivalent fractions. Then add or subtract.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2r
The average - mean - median - or mode.

21. HIGH: Describe how to deal with 2 sets of parentheses.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
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)+
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.

22. 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.
The total # of possible outcomes.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
6

23. Define 'proportionate' values
360 degrees
V=pr²h (This is just the area multiplied by the height)
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. 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.

24. HIGH: What is the mode?
60%
The value that appears most often in a data set.
1
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.

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

26. HIGH: How do you calculate the length of an arc?

27. Area of a parallelogram?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
1.4
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Bh

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

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

30. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
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.
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

31. Explain how to use an 'Average Pie'
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(0 -0)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

32. HIGH: What is the factored version of (x+y)(x-y) ?
x²-y²
Find the total - or whole - first - and then set up a Ratio Box.
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
A radius

33. How do you add or subtract fractions?
Arrangements - orders - schedules - or lists.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Find a common denominator and make equivalent fractions. Then add or subtract.

34. An integer is divisible by 3 if...
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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

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

36. HIGH: How do you calculate the circumference of a circle?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
(x+y)²
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.
2pr -or- pd

37. HIGH: Rough est. of v2 =
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
'Big' angles and 'Small' angles.
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.
1.4

38. Probability Formula
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
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Favorable Outcomes/Total Possible Outcomes
x²-y²

39. HIGH: List the two most common side ratios for right triangles
Probability A * Probability B
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
3:4:5 5:12:13

40. Simplify this: v32
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
S²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

41. If x² = 144 - does v144 = x?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.

42. How many degrees does a circle contain?
60%
Percentage Change = Difference/Original * 100
x² + 2xy + y²
360 degrees

43. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
25%
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.

44. Explain how to calculate an average (arithmetic mean)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
(a+b)(a-b)
A radius

45. What causes 80% of errors on the math section of the GRE?
Not necessarily. This is a trick question - because x could be either positive or negative.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Not reading the problems carefully enough!
A line is a 180-degree angle.

46. An integer is divisible by 9 if...
4 angles are formed. Their sum is 360 degrees
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
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

47. What are 'vertical angles'?
4 angles are formed. Their sum is 360 degrees
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%.
(x+y)²
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

48. How do you solve a combination?

49. In a coordinate system - identify the quadrants and describe their location.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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
x²-y²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

50. 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.
2r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28