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GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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
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

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

3. For a bell curve - what three terms might be used to describe the number in the middle?
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.
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 average - mean - median - or mode.
Favorable Outcomes/Total Possible Outcomes

4. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
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.
2
S*v2

5. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A line is a 180-degree angle.
180 degrees.
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.

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

7. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
4 angles are formed. Their sum is 360 degrees
360 degrees
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.

8. HIGH: Rough est. of v2 =
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
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
1.4

9. HIGH: Describe how to deal with 2 sets of parentheses.
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
Order does matter for a permutation - but does not matter for a combination.
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)+

10. An integer is divisible by 3 if...
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

11. HIGH: How do you multiply and divide square roots?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
40%

12. HIGH: Simplify this: v75/v27
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(x+y)²
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.
'Big' angles and 'Small' angles.

13. HIGH: What are the percentages for standard deviation?
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/x^n For example - 6-² = 1/6² = 1/36
60%
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

14. Define a factorial of a number - and how it is written.
180 degrees.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
360 degrees
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.

15. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
80%
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Not necessarily. This is a trick question - because x could be either positive or negative.
(a+b)(a-b)

16. HIGH: What is the mode?
The value that appears most often in a data set.
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 90-degree angle.
V=s³

17. 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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

18. Probability Formula
V=s³
Favorable Outcomes/Total Possible Outcomes
x² + 2xy + y²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

19. HIGH: Volume of a cylinder?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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
V=pr²h (This is just the area multiplied by the height)

20. Diameter of a circle?
2r
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Not reading the problems carefully enough!
It will be a great advantage on test day to have your times table memorized from 1 through 15.

21. HIGH: What is the side ratio for a 30:60:90 triangle?
40%
V=s³
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

22. What is the name of a line that extends from the center of a circle to the edge of a circle?
A radius
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

23. HIGH: What is a '30:60:90' triangle?
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.
Multiply numerator times numerator and denominator times denominator.
'Big' angles and 'Small' angles.
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

24. Convert to a percentage: 4/5
Order does matter for a permutation - but does not matter for a combination.
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.
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.
80%

25. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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).
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.
Order does matter for a permutation - but does not matter for a combination.

26. HIGH: What is the order of math operations - and the mnemonic to remember it?
(0 -0)
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
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.

27. Convert to a percentage: 2/5
40%
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.
3:4:5 5:12:13
The total # of possible outcomes.

28. How do you solve a combination?

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

30. HIGH: how do you calculate the surface area of a rectangular box?
The average - mean - median - or mode.
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.

31. List two odd behaviors of exponents
An integer is divisible by 5 if its units digit is either 0 or 5.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.

32. HIGH: Area of a triangle?
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.
x² + 2xy + y²
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

33. HIGH: Rough est. of v1 =
1
360 degrees
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

34. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
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 line is a 180-degree angle.
Not reading the problems carefully enough!

35. 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.
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.
Not reading the problems carefully enough!
An integer is divisible by 5 if its units digit is either 0 or 5.

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

37. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
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.
4 angles are formed. Their sum is 360 degrees

38. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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 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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

39. What do combination problems usually ask for?
1.4
The total # of possible outcomes.
V=s³
Groups - teams - or committees.

40. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Probability A + Probability B

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

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

43. HIGH: What is a 'Right isosceles' triangle?
90 degrees each.
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
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.
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.

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

45. What are the side ratios for a 30:60:90 triangle?
A=pr²
S*v2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4 angles are formed. Their sum is 360 degrees

46. How do you solve a permutation?
The # falling in the center of an ordered data set
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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

47. What number goes on the bottom of a probability fraction?
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.
The total # of possible outcomes.
Not necessarily. This is a trick question - because x could be either positive or negative.
(x-y)²

48. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 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.
x²-y²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

49. HIGH: Define the formula for calculating slope.
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.
Multiply numerator times numerator and denominator times denominator.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

50. HIGH: what is the side ratio for a Right Isosceles triangle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Probability A * Probability B
A radius