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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. How do you solve a combination?

2. How do you calculate the percentage of change?
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
S*v2
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
Percentage Change = Difference/Original * 100

3. For a bell curve - what three terms might be used to describe the number in the middle?
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. 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 2 if its units digit is divisible by 2.
The average - mean - median - or mode.

4. An integer is divisible by 9 if...
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
The value that appears most often in a data set.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.

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

6. How do you add or subtract fractions?
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
(a+b)(a-b)

7. What is an 'equilateral' triangle?
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.
The average - mean - median - or mode.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.

8. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
An integer is divisible by 5 if its units digit is either 0 or 5.
60%
2

9. What is the equation for a group problem?
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.
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.

10. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
60%
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.
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
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

11. Define 'proportionate' values
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
x² -2xy + y²
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.

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

13. What'S the most important thing to remember about charts you'll see on the GRE?
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.
360 degrees
Probability A * Probability B
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

14. HIGH: Simplify this: v75/v27
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'.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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
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.

15. HIGH: Volume of a cylinder?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
60%
V=pr²h (This is just the area multiplied by the height)
Find a common denominator and make equivalent fractions. Then add or subtract.

16. Diameter of a circle?
x²-y²
An integer is divisible by 9 if the sum of its digits is divisible by 9.
(x-y)²
2r

17. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
x² -2xy + y²
V=pr²h (This is just the area multiplied by the height)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

18. What do permutation problems often ask for?
40%
V=s³
Arrangements - orders - schedules - or lists.
(x+y)²

19. HIGH: What is the median?
1.7
The # falling in the center of an ordered data set
360 degrees
Between 0 and 1.

20. Area of a parallelogram?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
x²-y²
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.

21. HIGH: Rough est. of v3 =
Between 0 and 1.
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'.
1.7
(0 -0)

22. 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
V=pr²h (This is just the area multiplied by the height)
6
Invert the second fraction (reciprocal) and multiply

23. Explain the difference between handling a permutation versus a combination.
Bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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%

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

25. Explain how to use a 'Rate Pie'
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
1. Given event A: A + notA = 1.
2pr -or- pd
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.

26. The three interior angles of a triangle add up to...
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
180 degrees
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.
x²-y²

27. 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
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A line is a 180-degree angle.

28. List all the prime numbers that are less than 30:
60%
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
1.4
Groups - teams - or committees.

29. HIGH: Define the formula for calculating slope.
A=pr²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

30. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 2.
Multiply numerator times numerator and denominator times denominator.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Favorable Outcomes/Total Possible Outcomes

31. How do you multiply fractions?
A=pr²
Multiply numerator times numerator and denominator times denominator.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.

32. Probability Formula
A triangle in which one of the three interior angles is 90 degrees.
The value that appears most often in a data set.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Favorable Outcomes/Total Possible Outcomes

33. HIGH: Area of a triangle?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
80%
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

34. HIGH: What is a '30:60:90' triangle?
Percentage Change = Difference/Original * 100
1/1
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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

35. HIGH: What is a 'Right isosceles' triangle?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.
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.
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.

36. Define a factorial of a number - and how it is written.
The total # of possible outcomes.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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.
90 degrees each.

37. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
1/x^n For example - 6-² = 1/6² = 1/36
90 degrees each.
Order does matter for a permutation - but does not matter for a combination.

38. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
3:4:5 5:12:13
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.
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.

39. How do you divide fractions?
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.
Favorable Outcomes/Total Possible Outcomes
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
Invert the second fraction (reciprocal) and multiply

40. HIGH: To divide powers with the same base...
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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

41. What number goes on the bottom of a probability fraction?
A triangle in which one of the three interior angles is 90 degrees.
Percentage Change = Difference/Original * 100
40%
The total # of possible outcomes.

42. Define the mode of a set of numbers.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
(x+y)(x-y)
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.

43. Explain the special properties of zero.
Groups - teams - or committees.
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
360 degrees

44. HIGH: what is the side ratio for a Right Isosceles triangle?
Example: 1 < x < 10
90 degrees each.
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

45. Explain how to solve for 7/¼
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%.
A 90-degree angle.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

46. HIGH: How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Find the total - or whole - first - and then set up a Ratio Box.
Multiply numerator times numerator and denominator times denominator.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

47. Convert to a percentage: 1/4
(x+y)(x-y)
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
25%

48. Convert to a percentage: 2/5
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
'Big' angles and 'Small' angles.
40%
V=s³

49. HIGH: What is the Pythagorean theorem?

50. What is the key to dealing with ratio questions?
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.
Find the total - or whole - first - and then set up a Ratio Box.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.