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

2. HIGH: What is the side ratio for a 30:60:90 triangle?
180 degrees
Not reading the problems carefully enough!
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2pr -or- pd

3. What degree angle is a line?
360 degrees
A line is a 180-degree angle.
1.4
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

4. HIGH: What is the mode?
360 degrees
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
The value that appears most often in a data set.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

5. HIGH: What is the Pythagorean theorem?

6. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
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.
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 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.

7. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
(x+y)(x-y)
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Find the total - or whole - first - and then set up a Ratio Box.

8. An integer is divisible by 3 if...
The average - mean - median - or mode.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
(x+y)²

9. HIGH: x^-n is equal to
1.7
1/x^n For example - 6-² = 1/6² = 1/36
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.

10. The three exterior angles of a triangle add up to...
2
360 degrees
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

11. List two odd behaviors of exponents
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Percentage Change = Difference/Original * 100
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.

12. 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.
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
(x+y)(x-y)
180 degrees.

13. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
(x+y)²
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
2
Probability A + Probability B

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

15. What do combination problems usually ask for?
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.
Groups - teams - or committees.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
An integer is divisible by 2 if its units digit is divisible by 2.

16. 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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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. 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

17. HIGH: How do you calculate the length of an arc?

18. HIGH: Area of a circle
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=pr²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The value that appears most often in a data set.

19. HIGH: What is the unfactored version of (x+y)² ?
An integer is divisible by 2 if its units digit is divisible by 2.
The # falling in the center of an ordered data set
Between 0 and 1.
x² + 2xy + y²

20. HIGH: What are the percentages for standard deviation?
A triangle in which one of the three interior angles is 90 degrees.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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

21. Convert to a percentage: 2/5
2
40%
The value that appears most often in a data set.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

22. HIGH: Area of a triangle?
Between 0 and 1.
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.
Favorable Outcomes/Total Possible Outcomes
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

23. HIGH: Rough est. of v3 =
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2pr -or- pd
1.7

24. HIGH: What is the unfactored version of (x-y)² ?
60%
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

25. How do you solve a permutation?
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
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
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%.

26. What'S the most important thing to remember about charts you'll see on the GRE?
1.4
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.
1.7

27. HIGH: Volume of a cylinder?
1/x^n For example - 6-² = 1/6² = 1/36
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
V=pr²h (This is just the area multiplied by the height)

28. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
Probability A + Probability B
The average - mean - median - or mode.
40%

29. Explain the special properties of zero.
60%
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

30. HIGH: What is the unfactored version of x²-y² ?
6
V=s³
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
(x+y)(x-y)

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

32. What is the formula to determine probability?
S*v2
Find a common denominator and make equivalent fractions. Then add or subtract.
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'.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

33. HIGH: What is a 'Right isosceles' triangle?
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.
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.
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

34. HIGH: Simplify this: v75/v27
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
Favorable Outcomes/Total Possible Outcomes
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.

35. What is the 'distributive law'?
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(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. 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.
Between 0 and 1.

36. Define the mode of a set of numbers.
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/x^n For example - 6-² = 1/6² = 1/36
1. Given event A: A + notA = 1.
Order does matter for a permutation - but does not matter for a combination.

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

38. HIGH: what is the side ratio for a Right Isosceles triangle?
Groups - teams - or committees.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Not reading the problems carefully enough!

39. What is an 'equilateral' triangle?
1.7
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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'.

40. What is a 'Right' angle?
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.
2pr -or- pd
A 90-degree angle.
Between 0 and 1.

41. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
(x+y)²

42. Simplify this: v32
2r
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
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

43. What is the key to dealing with ratio questions?
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.
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
The average - mean - median - or mode.
Find the total - or whole - first - and then set up a Ratio Box.

44. How do you add or subtract 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.
Probability A * Probability B
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Find a common denominator and make equivalent fractions. Then add or subtract.

45. How do you divide fractions?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
Invert the second fraction (reciprocal) and multiply
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

46. What is a 'Right' triangle?
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).
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 triangle in which one of the three interior angles is 90 degrees.

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

48. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 2.
The # falling in the center of an ordered data set
2pr -or- pd
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

49. HIGH: Rough est. of v2 =
It will be a great advantage on test day to have your times table memorized from 1 through 15.
1.4
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
An integer is divisible by 9 if the sum of its digits is divisible by 9.

50. Explain how to use an 'Average Pie'
A=pr²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions