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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 is a range expressed with inequalities?
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.
Probability A + Probability B
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.
Example: 1 < x < 10

2. What is a 'Right' angle?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A 90-degree angle.
(x-y)²
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.

3. What is the equation for a group problem?
4 angles are formed. Their sum is 360 degrees
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
Arrangements - orders - schedules - or lists.
180 degrees.

4. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
25%
4 angles are formed. Their sum is 360 degrees
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

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

6. On the GRE - should you ever assume that diagrams are truthful?
Order does matter for a permutation - but does not matter for a combination.
(x+y)²
Groups - teams - or committees.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

7. Convert to a percentage: 1/4
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.
25%
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.

8. 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% |
x² -2xy + y²
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.
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.

9. Diameter of a circle?
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.
2r
360 degrees
'Big' angles and 'Small' angles.

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

11. Convert to a percentage: 3/5
60%
Invert the second fraction (reciprocal) and multiply
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.

12. Convert to a percentage: 4/5
80%
Between 0 and 1.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

13. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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
1.4
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.

14. Convert to a percentage: 2/5
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.
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
40%
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

15. What are the side ratios for a 30:60:90 triangle?
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
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

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

17. HIGH: Area of a circle
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%.
Favorable Outcomes/Total 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% |
A=pr²

18. Define the mode of a set of numbers.
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.
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.
Not reading the problems carefully enough!
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.

19. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
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.
(x-y)²

20. Probability Formula
2pr -or- pd
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Favorable Outcomes/Total Possible Outcomes
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.

21. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
'Big' angles and 'Small' angles.
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.
(x-y)²

22. HIGH: Volume of a cube?
4 angles are formed. Their sum is 360 degrees
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.
V=s³
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

23. 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.
6
V=pr²h (This is just the area multiplied by the height)
A triangle in which one of the three interior angles is 90 degrees.

24. HIGH: What is the unfactored version of x²-y² ?
1/x^n For example - 6-² = 1/6² = 1/36
(x+y)(x-y)
3:4:5 5:12:13
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

25. v4 =
A triangle in which one of the three interior angles is 90 degrees.
360 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.
2

26. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
1
(x+y)(x-y)

27. Area of a square?
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. 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
S²
(x-y)²

28. An integer is divisible by 3 if...
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 equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

29. HIGH: Rough est. of v1 =
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.
1
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

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

31. HIGH: What is the mode?
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.
Order does matter for a permutation - but does not matter for a combination.
Between 0 and 1.
The value that appears most often in a data set.

32. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
Probability A * Probability B
x²-y²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

33. HIGH: What is the factored version of x² + 2xy + y² ?
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.
2
(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.

34. List two odd behaviors of exponents
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.
A 90-degree angle.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.

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

36. The three interior angles of a triangle add up to...
Find the total - or whole - first - and then set up a Ratio Box.
(x-y)²
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
180 degrees

37. What is the factored version of x² -2xy + y² ?
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
(x+y)²
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
(x-y)²

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

39. HIGH: x^-n is equal to
Probability A + Probability B
Groups - teams - or committees.
1/x^n For example - 6-² = 1/6² = 1/36
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.

40. How do you solve a permutation?
The # falling in the center of an ordered data set
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.
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

41. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 2.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1.4

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

43. What do permutation problems often ask for?
Find a common denominator and make equivalent fractions. Then add or subtract.
An integer is divisible by 5 if its units digit is either 0 or 5.
Arrangements - orders - schedules - or lists.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

44. HIGH: What is the unfactored version of (x-y)² ?
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.
x² -2xy + y²
2pr -or- pd
360 degrees

45. List all the prime numbers that are less than 30:
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
S²
A=pr²
Probability A + Probability B

46. 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.
6
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 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.

47. What are 'vertical angles'?
Bh
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.

48. What number goes on the bottom of a probability fraction?
x²-y²
The total # of possible outcomes.
40%
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

49. HIGH: What is the unfactored version of (x+y)² ?
A triangle in which one of the three interior angles is 90 degrees.
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.
Favorable Outcomes/Total Possible Outcomes
x² + 2xy + y²

50. HIGH: Simplify this: v75/v27
(a+b)(a-b)
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.
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.
V=s³