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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 do permutation problems often ask for?
3:4:5 5:12:13
180 degrees.
1
Arrangements - orders - schedules - or lists.

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

3. HIGH: Rough est. of v3 =
1.7
V=s³
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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

4. What is the 'Third side' rule for triangles?
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
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

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

6. How do you add or subtract fractions?
A triangle in which one of the three interior angles is 90 degrees.
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
x²-y²

7. 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%.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

8. HIGH: Volume of a cylinder?
40%
(0 -0)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
V=pr²h (This is just the area multiplied by the height)

9. What is an 'equilateral' triangle?
Not necessarily. This is a trick question - because x could be either positive or negative.
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
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Bh

10. HIGH: Simplify this: v75/v27
A radius
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

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

12. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
'Big' angles and 'Small' angles.

13. What is a 'Right' angle?
60%
Probability A + Probability B
A 90-degree angle.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

14. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
(a+b)(a-b)
Groups - teams - or committees.
1. Given event A: A + notA = 1.

15. If x² = 144 - does v144 = x?
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
6
Not necessarily. This is a trick question - because x could be either positive or negative.

16. HIGH: What is the unfactored version of (x+y)² ?
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.
x² + 2xy + y²
The average - mean - median - or mode.
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.

17. HIGH: What is a '30:60:90' triangle?
1/1
1.7
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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

18. HIGH: How do you multiply powers with the same base?
Find a common denominator and make equivalent fractions. Then add or subtract.
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
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

19. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
60%
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A=pr²
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.

20. 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
3:4:5 5:12:13
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
An integer is divisible by 2 if its units digit is divisible by 2.

21. HIGH: What is the unfactored version of x²-y² ?
(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.
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

22. HIGH: What is the order of math operations - and the mnemonic to remember it?
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
80%
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.
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

23. In a coordinate system - identify the quadrants and describe their location.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
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.

24. HIGH: how do you calculate the surface area of a rectangular box?
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.
A=pr²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

25. HIGH: What are the percentages for standard deviation?
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
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.
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

26. HIGH: How do you multiply and divide square roots?
1
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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%.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

27. An integer is divisible by 4 if...

28. What'S one way to avoid mistakes on algebra questions in the GRE?

29. How do you calculate the probability of two events in a row? (Probability of A and B)
Not reading the problems carefully enough!
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.
Probability A * Probability B
A line is a 180-degree angle.

30. The three exterior angles of a triangle add up to...
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
360 degrees
An integer is divisible by 5 if its units digit is either 0 or 5.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

31. 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.
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.
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

32. What'S the most important thing to remember about charts you'll see on the GRE?
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.
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.
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.
Favorable Outcomes/Total Possible Outcomes

33. How do you solve a combination?

34. The three interior angles of a triangle add up to...
180 degrees
A triangle in which one of the three interior angles is 90 degrees.
25%
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'.

35. Area of a parallelogram?
Bh
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.
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
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.

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

37. How is a range expressed with inequalities?
Not necessarily. This is a trick question - because x could be either positive or negative.
Multiply numerator times numerator and denominator times denominator.
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.
Example: 1 < x < 10

38. Convert to a percentage: 3/5
V=pr²h (This is just the area multiplied by the height)
60%
Probability A * Probability B
S*v2

39. Area of a square?
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
S²
(a+b)(a-b)

40. HIGH: How do you calculate the circumference of a circle?
1/x^n For example - 6-² = 1/6² = 1/36
2pr -or- pd
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.
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

41. HIGH: Area of a circle
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
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.
A=pr²

42. HIGH: What is the mode?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Example: 1 < x < 10
Percentage Change = Difference/Original * 100
The value that appears most often in a data set.

43. If something is certain to happen - how is the probability of this event expressed mathematically?
180 degrees
1/1
2r
2

44. An integer is divisible by 9 if...
Groups - teams - or committees.
Order does matter for a permutation - but does not matter for a combination.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
S*v2

45. v4 =
2
x² -2xy + y²
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

46. HIGH: List the two most common side ratios for right triangles
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
3:4:5 5:12:13
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.

47. How do you solve a permutation?
S*v2
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
Favorable Outcomes/Total Possible Outcomes
'Big' angles and 'Small' angles.

48. In a coordinate system - what is the origin?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(0 -0)
1.4
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.

49. If something is possible but not certain - what is the numeric range of probability of it happening?
S²
Between 0 and 1.
(x+y)(x-y)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

50. What is the 'distributive law'?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
80%
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.