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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: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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

2. On the GRE - should you ever assume that diagrams are truthful?
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.
(0 -0)
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

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

4. In a coordinate system - what is the origin?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
40%
(0 -0)
2pr -or- pd

5. How many degrees does a circle contain?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
1. Given event A: A + notA = 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.
360 degrees

6. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
4 angles are formed. Their sum is 360 degrees
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.

7. HIGH: What is the unfactored version of (x-y)² ?
An integer is divisible by 5 if its units digit is either 0 or 5.
x² -2xy + y²
(x+y)(x-y)
25%

8. HIGH: What is the unfactored version of (x+y)² ?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
The value that appears most often in a data set.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x² + 2xy + y²

9. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
x²-y²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
An integer is divisible by 5 if its units digit is either 0 or 5.

10. Does order matter for a permutation? How about for a combination?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
1. Given event A: A + notA = 1.
Order does matter for a permutation - but does not matter for a combination.

11. HIGH: What is the factored version of (x+y)(x-y) ?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
An integer is divisible by 9 if the sum of its digits is divisible by 9.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
x²-y²

12. HIGH: What are the percentages for standard deviation?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A line is a 180-degree angle.
Find a common denominator and make equivalent fractions. Then add or subtract.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

13. An integer is divisible by 5 if...
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.
A triangle in which one of the three interior angles is 90 degrees.
An integer is divisible by 5 if its units digit is either 0 or 5.
Multiply numerator times numerator and denominator times denominator.

14. Define the mode of a set of numbers.
'Big' angles and 'Small' angles.
Multiply numerator times numerator and denominator times denominator.
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.
80%

15. Convert to a percentage: 3/5
60%
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
4 angles are formed. Their sum is 360 degrees
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.

16. HIGH: x^-n is equal to
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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/x^n For example - 6-² = 1/6² = 1/36

17. v4 =
Find a common denominator and make equivalent fractions. Then add or subtract.
2
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
3:4:5 5:12:13

18. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
Order does matter for a permutation - but does not matter for a combination.

19. HIGH: What is the mode?
V=s³
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The value that appears most often in a data set.
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.

20. What do permutation problems often ask for?
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.
60%
(x-y)²
Arrangements - orders - schedules - or lists.

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

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

23. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

24. HIGH: What is the formula for the diagonal of any square?
Order does matter for a permutation - but does not matter for a combination.
25%
1.4
S*v2

25. Explain how to solve for 7/¼
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)+
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.

26. HIGH: To divide powers with the same base...
180 degrees
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

27. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?

28. a² - b² is equal to
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.
360 degrees
(a+b)(a-b)
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.

29. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
Find a common denominator and make equivalent fractions. Then add or subtract.
The # falling in the center of an ordered data set
A line is a 180-degree angle.

30. What is the formula to determine probability?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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 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.
Favorable Outcomes/Total Possible Outcomes

31. Explain how to calculate an average (arithmetic mean)
Favorable Outcomes/Total Possible Outcomes
(a+b)(a-b)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
'Big' angles and 'Small' angles.

32. HIGH: What is the factored version of x² + 2xy + y² ?
Multiply numerator times numerator and denominator times denominator.
(x+y)²
360 degrees
The value that appears most often in a data set.

33. HIGH: Define the formula for calculating slope.
Probability A * Probability B
Bh
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.

34. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
1
25%

35. An integer is divisible by 9 if...
1/x^n For example - 6-² = 1/6² = 1/36
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Bh
Probability A * Probability B

36. What degree angle is a line?
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 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.
A line is a 180-degree angle.
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.

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

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

39. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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
90 degrees each.
S²

40. HIGH: How much of your times table should you know - for the GRE?
Favorable Outcomes/Total Possible Outcomes
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
2
It will be a great advantage on test day to have your times table memorized from 1 through 15.

41. HIGH: List the two most common side ratios for right triangles
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a+b)(a-b)
3:4:5 5:12:13
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.

42. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

43. An integer is divisible by 2 if...
(x+y)²
Probability A * Probability B
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
An integer is divisible by 2 if its units digit is divisible by 2.

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

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

46. Explain the special properties of zero.
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=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.
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

47. HIGH: Volume of a cube?
Between 0 and 1.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
V=s³

48. Convert to a percentage: 4/5
80%
The average - mean - median - or mode.
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

49. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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
An integer is divisible by 5 if its units digit is either 0 or 5.

50. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
(0 -0)
90 degrees each.
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 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.