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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. An integer is divisible by 4 if...

2. Convert to a percentage: 4/5
80%
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
1/x^n For example - 6-² = 1/6² = 1/36

3. If x² = 144 - does v144 = x?
A line is a 180-degree angle.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.

4. HIGH: What is the median?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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
The # falling in the center of an ordered data set
The total # of possible outcomes.

5. For a bell curve - what three terms might be used to describe the number in the middle?
90 degrees each.
Invert the second fraction (reciprocal) and multiply
360 degrees
The average - mean - median - or mode.

6. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Probability A * Probability B
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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
An integer is divisible by 9 if the sum of its digits is divisible by 9.

7. 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
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.
Example: 1 < x < 10
Multiply numerator times numerator and denominator times denominator.

8. Explain how to calculate an average (arithmetic mean)
180 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.
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

9. HIGH: What is the Pythagorean theorem?

10. HIGH: How do you multiply powers with the same base?
Bh
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 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

11. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
S²

12. Diameter of a circle?
A radius
1/x^n For example - 6-² = 1/6² = 1/36
Not necessarily. This is a trick question - because x could be either positive or negative.
2r

13. Does order matter for a permutation? How about for a combination?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Order does matter for a permutation - but does not matter for a combination.
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 total # of possible outcomes.

14. The three exterior angles of a triangle add up to...
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.
360 degrees
Favorable Outcomes/Total Possible Outcomes
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

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

16. Convert to a percentage: 1/4
(0 -0)
Find a common denominator and make equivalent fractions. Then add or subtract.
25%
80%

17. What do permutation problems often ask for?
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.
Arrangements - orders - schedules - or lists.
Percentage Change = Difference/Original * 100
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. Explain how to divide fractions.
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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
A 90-degree angle.

19. The three interior angles of a triangle add up to...
180 degrees
1/1
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 value that appears most often in a data set.

20. List two odd behaviors of exponents
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.
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. 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.

21. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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%.

22. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
360 degrees
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

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

24. HIGH: What are the percentages for standard deviation?
(x+y)²
S²
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

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

26. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
180 degrees

27. What is the sum of any 'big' angle and any 'Small' angle?
180 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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1

28. What are 'vertical angles'?
'Big' angles and 'Small' angles.
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
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

29. List all the prime numbers that are less than 30:
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.
360 degrees
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

30. How do you divide fractions?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Arrangements - orders - schedules - or lists.
Invert the second fraction (reciprocal) and multiply
Find a common denominator and make equivalent fractions. Then add or subtract.

31. HIGH: What is the unfactored version of x²-y² ?
(0 -0)
(x+y)(x-y)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
S*v2

32. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
Percentage Change = Difference/Original * 100
2
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. Explain how to use an 'Average Pie'
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

34. What is the formula to determine probability?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
(# of possible outcomes that satisfy the condition) ÷ (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.

35. HIGH: Describe how to deal with 2 sets of parentheses.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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)+
Find the total - or whole - first - and then set up a Ratio Box.
2

36. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
3:4:5 5:12:13

37. HIGH: What is the factored version of x² + 2xy + y² ?
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.
(x+y)²
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'.
1.4

38. Probability Formula
Favorable Outcomes/Total Possible Outcomes
Bh
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=pr²

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

40. An integer is divisible by 3 if...
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
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
360 degrees
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.

41. HIGH: What is the formula for the diagonal of any square?
S*v2
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
25%
1/x^n For example - 6-² = 1/6² = 1/36

42. What is the 'distributive law'?
Example: 1 < x < 10
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.
60%
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.

43. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
(a+b)(a-b)
Example: 1 < x < 10
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
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

44. What is the factored version of x² -2xy + y² ?
(x-y)²
25%
3:4:5 5:12:13
180 degrees

45. 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.
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
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
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

46. Define the mode of a set of numbers.
An integer is divisible by 2 if its units digit is divisible by 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.
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
(x+y)²

47. 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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
(0 -0)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

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

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

50. HIGH: What is the unfactored version of (x-y)² ?
Multiply numerator times numerator and denominator times denominator.
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.
x² -2xy + y²
2pr -or- pd