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GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Explain the difference between handling a permutation versus a combination.
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.
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
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.

2. HIGH: What is the unfactored version of (x-y) ?
x -2xy + y
Probability A * Probability B
360 degrees
(0 -0)

3. Explain how to solve for 7/
Groups - teams - or committees.
This equals 7 - or 7/1 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

4. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
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.
3:4:5 5:12:13
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.

5. How many degrees does a circle contain?
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'.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
360 degrees

6. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Not reading the problems carefully enough!
That they often have not just one answer - but two. For example - solving x -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
(x+y)
S

7. Probability Formula
Invert the second fraction (reciprocal) and multiply
Subtract the exponents - retain the base For example - x? x4 = x?-4 = x5
Favorable Outcomes/Total Possible Outcomes
This equals 7 - or 7/1 1/4 = 7/1 * 4/1 = 28/1 = 28

8. a - b is equal to
Find a common denominator and make equivalent fractions. Then add or subtract.
x -2xy + y
An integer is divisible by 9 if the sum of its digits is divisible by 9.
(a+b)(a-b)

9. HIGH: What is the side ratio for a 30:60:90 triangle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Probability A + Probability B
S
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.

10. Explain how to calculate an average (arithmetic mean)
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
1
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

11. Explain the special properties of 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.
Example: 1 < x < 10
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.

12. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
1. Given event A: A + notA = 1.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.

13. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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.
(x+y)
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

14. An integer is divisible by 6 if...
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

15. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.
x -2xy + y
x + 2xy + y

16. If x = 144 - does v144 = x?
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.
60%
Not necessarily. This is a trick question - because x could be either positive or negative.
360 degrees

17. HIGH: What is the factored version of x + 2xy + y ?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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 # falling in the center of an ordered data set
(x+y)

18. Solve this: v6 * -v6 = ?
6
Percentage Change = Difference/Original * 100
That they often have not just one answer - but two. For example - solving x -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
Between 0 and 1.

19. HIGH: How do you multiply and divide square roots?
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.
Probability A + Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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

20. HIGH: Simplify this: v75/v27
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2r
Arrangements - orders - schedules - or lists.
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.

21. An integer is divisible by 9 if...
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 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.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.

22. What is the 'Third side' rule for triangles?
A triangle in which one of the three interior angles is 90 degrees.
x-y
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.
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.

23. HIGH: Rough est. of v1 =
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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.
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

24. HIGH: What is the unfactored version of x-y ?
(x+y)(x-y)
S*v2
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.
A radius

25. What is the sum of any 'big' angle and any 'Small' angle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
180 degrees.
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.
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

26. HIGH: Rough est. of v3 =
1.7
A 90-degree angle.
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

27. HIGH: x^-n is equal to
1/x^n For example - 6- = 1/6 = 1/36
1
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Invert the second fraction (reciprocal) and multiply

28. What degree angle is a line?
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
360 degrees
A line is a 180-degree angle.
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.

29. HIGH: What is the formula for the diagonal of any square?
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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
25%
S*v2

30. What is the formula to determine probability?
x + 2xy + y
For RIGHT triangles only: c = a + b '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) = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287 = 1.
(# of possible outcomes that satisfy the condition) (total # of possible outcomes)

31. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
1.7
(a+b)(a-b)
40%
Probability A + Probability B

32. Define a factorial of a number - and how it is written.
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.
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
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
1. Factored: x - y Unfactored: (x+y)(x-y) 2. Factored: (x+y) Unfactored: x + 2xy + y 3. Factored: (x-y) Unfactored: x - 2xy + y

33. HIGH: Describe how to deal with 2 sets of parentheses.
360 degrees
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)+
2pr -or- pd
(x-y)

34. An integer is divisible by 2 if...
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
An integer is divisible by 2 if its units digit is divisible by 2.
90 degrees each.
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.

35. How do you solve a permutation?
The total # of possible outcomes.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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. Factored: x - y Unfactored: (x+y)(x-y) 2. Factored: (x+y) Unfactored: x + 2xy + y 3. Factored: (x-y) Unfactored: x - 2xy + y

36. How do you solve a combination?
Bh
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
90 degrees each.
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.

37. What is a 'Right' triangle?
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.
The value that appears most often in a data set.
A triangle in which one of the three interior angles is 90 degrees.
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.

38. HIGH: What is the factored version of (x+y)(x-y) ?
Invert the second fraction (reciprocal) and multiply
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. 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
x-y

39. What is the equation for a group problem?
1.4
1.7
Invert the second fraction (reciprocal) and multiply
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

40. Simplify this: v32
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
A=pr
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

41. Convert to a percentage: 2/5
40%
An integer is divisible by 5 if its units digit is either 0 or 5.
1
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.

42. An integer is divisible by 3 if...
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
360 degrees
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.

43. HIGH: How much of your times table should you know - for the GRE?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

44. An integer is divisible by 8 if...
That they often have not just one answer - but two. For example - solving x -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
x-y
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
The total # of possible outcomes.

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

46. HIGH: What is the unfactored version of (x+y) ?
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.
Probability A + Probability B
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.
x + 2xy + y

47. What number goes on the bottom of a probability fraction?
360 degrees
1. Given event A: A + notA = 1.
(0 -0)
The total # of possible outcomes.

48. What is the name of a line that extends from the center of a circle to the edge of a circle?
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.
Between 0 and 1.
A radius
Order does matter for a permutation - but does not matter for a combination.

49. HIGH: How do you multiply powers with the same base?
Probability A + Probability B
Add the exponents - retain the base. for example - x + x5 = x+5 = x7
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.
Order does matter for a permutation - but does not matter for a combination.

50. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
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.
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
4 angles are formed. Their sum is 360 degrees

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