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

2. Explain how to use an 'Average Pie'
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
A 90-degree angle.

3. HIGH: Volume of a cylinder?
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.
Find the total - or whole - first - and then set up a Ratio Box.
80%
V=pr²h (This is just the area multiplied by the height)

4. Convert to a percentage: 3/5
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.
60%
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.

5. What number goes on the bottom of a probability fraction?
A 90-degree angle.
The total # of possible outcomes.
Favorable Outcomes/Total Possible Outcomes
1/x^n For example - 6-² = 1/6² = 1/36

6. An integer is divisible by 4 if...

7. Explain the special properties of zero.
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 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.
Invert the second fraction (reciprocal) and multiply
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.

8. Define 'proportionate' values
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Invert the second fraction (reciprocal) and multiply
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%.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

9. How do you add or subtract fractions?
A line is a 180-degree angle.
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)+
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Find a common denominator and make equivalent fractions. Then add or subtract.

10. HIGH: Volume of a cube?
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
x² -2xy + y²
V=s³
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

11. Convert to a percentage: 1/4
Multiply numerator times numerator and denominator times denominator.
The total # of possible outcomes.
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.
25%

12. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
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.
Probability A + Probability B
S²
(x+y)(x-y)

13. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
Between 0 and 1.
A=pr²
4 angles are formed. Their sum is 360 degrees
Invert the second fraction (reciprocal) and multiply

14. HIGH: What is the unfactored version of (x+y)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.
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.
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.
x² + 2xy + y²

15. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.

16. HIGH: What is a '30:60:90' triangle?
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
Probability A * Probability B
2
40%

17. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
The total # of possible outcomes.
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.
S*v2

18. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Example: 1 < x < 10
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
1. Given event A: A + notA = 1.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

19. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
2r
Arrangements - orders - schedules - or lists.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.

20. The three exterior angles of a triangle add up to...
Groups - teams - or committees.
360 degrees
A radius
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.

21. What is a 'Right' angle?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
A 90-degree angle.
1/1
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. An integer is divisible by 3 if...
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
3:4:5 5:12:13
2pr -or- pd
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.

23. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
1/1
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.
Groups - teams - or committees.

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

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

26. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
S²
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.
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.
Between 0 and 1.

27. What is the equation for a group problem?
1/1
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
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.
1.4

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

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

30. Explain how to calculate an average (arithmetic mean)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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
2pr -or- pd
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

31. List all the prime numbers that are less than 30:
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.
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.

32. What is the 'distributive law'?
2pr -or- pd
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.
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: 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

33. HIGH: What is the Pythagorean theorem?

34. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
A radius
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

35. HIGH: What is the factored version of (x+y)(x-y) ?
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.
x²-y²
Not necessarily. This is a trick question - because x could be either positive or negative.
3:4:5 5:12:13

36. How many degrees does a circle contain?
x² -2xy + y²
A line is a 180-degree angle.
360 degrees
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

37. Area of a square?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
S²
Multiply numerator times numerator and denominator times denominator.
An integer is divisible by 5 if its units digit is either 0 or 5.

38. In a coordinate system - what is the origin?
(0 -0)
An integer is divisible by 2 if its units digit is divisible by 2.
360 degrees
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

39. What do permutation problems often ask for?
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%.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Arrangements - orders - schedules - or lists.
Between 0 and 1.

40. Does order matter for a permutation? How about for a combination?
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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Order does matter for a permutation - but does not matter for a combination.

41. HIGH: What is the order of math operations - and the mnemonic to remember it?
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
2pr -or- pd
Not reading the problems carefully enough!
A line is a 180-degree angle.

42. Diameter of a circle?
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.
V=pr²h (This is just the area multiplied by the height)
2r
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

43. HIGH: What is the mode?
Not necessarily. This is a trick question - because x could be either positive or negative.
60%
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
The value that appears most often in a data set.

44. HIGH: What are the percentages for standard deviation?
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
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 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
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.

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

46. Convert to a percentage: 4/5
Arrangements - orders - schedules - or lists.
80%
A radius
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.

47. Define the mode of a set of numbers.
2
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.
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

48. 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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
A 90-degree angle.
Favorable Outcomes/Total Possible Outcomes

49. What'S the most important thing to remember about charts you'll see on the GRE?
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.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

50. Simplify this: v32
A triangle in which one of the three interior angles is 90 degrees.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Find a common denominator and make equivalent fractions. Then add or subtract.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')