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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. HIGH: what is the side ratio for a Right Isosceles triangle?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
An integer is divisible by 2 if its units digit is divisible by 2.

2. Explain the special properties of zero.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
Example: 1 < x < 10
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.

3. HIGH: What is the side ratio for a 30:60:90 triangle?
60%
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

4. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Not necessarily. This is a trick question - because x could be either positive or negative.
1. Given event A: A + notA = 1.
x² -2xy + y²
A radius

5. Does order matter for a permutation? How about for a combination?
360 degrees
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Order does matter for a permutation - but does not matter for a combination.
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.

6. What do combination problems usually ask for?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
25%
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.
Groups - teams - or committees.

7. What do permutation problems often ask for?
6
1/1
Arrangements - orders - schedules - or lists.
40%

8. How do you solve a combination?

9. An integer is divisible by 9 if...
S*v2
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(0 -0)
An integer is divisible by 9 if the sum of its digits is divisible by 9.

10. Explain how to use a 'Rate Pie'
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.
Not reading the problems carefully enough!
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
x² -2xy + y²

11. What'S the most important thing to remember about charts you'll see on the GRE?
Arrangements - orders - schedules - or lists.
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.
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.

12. What is the sum of any 'big' angle and any 'Small' angle?
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'.
A triangle in which one of the three interior angles is 90 degrees.
180 degrees.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

13. For a bell curve - what three terms might be used to describe the number in the middle?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
V=s³
The average - mean - median - or mode.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

14. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
1/1
'Big' angles and 'Small' angles.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

15. HIGH: Rough est. of v1 =
1
180 degrees.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
60%

16. HIGH: What is the factored version of x² + 2xy + y² ?
1.7
(0 -0)
(x+y)²
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.

17. What is the key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
A line is a 180-degree angle.
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.
'Big' angles and 'Small' angles.

18. HIGH: how do you calculate the surface area of a rectangular box?
1.4
x²-y²
S*v2
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.

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

20. HIGH: What is 'absolute value' - and how is it represented?

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

22. What are 'vertical angles'?
2pr -or- pd
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.

23. HIGH: What is a '30:60:90' triangle?
2pr -or- pd
Probability A + Probability B
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.
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. HIGH: Rough est. of v3 =
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.
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.
1.7
Example: 1 < x < 10

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

26. HIGH: What is the unfactored version of (x-y)² ?
x² -2xy + y²
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.
2
1/1

27. Explain the difference between handling a permutation versus a combination.
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.
The average - mean - median - or mode.
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

28. 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
2
A line is a 180-degree angle.
Arrangements - orders - schedules - or lists.

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

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

31. Diameter of a circle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
A 90-degree angle.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
2r

32. HIGH: What is the formula for the diagonal of any square?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.
Favorable Outcomes/Total Possible Outcomes
S*v2

33. HIGH: What is the order of math operations - and the mnemonic to remember it?
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
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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
2

34. HIGH: What is the mode?
The value that appears most often in a data set.
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.
40%
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

35. Convert to a percentage: 4/5
Probability A * Probability B
S²
80%
360 degrees

36. An integer is divisible by 5 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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
An integer is divisible by 5 if its units digit is either 0 or 5.

37. HIGH: Volume of a cube?
V=s³
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Arrangements - orders - schedules - or lists.
6

38. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
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%.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
6

39. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.

40. HIGH: Volume of a cylinder?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
V=pr²h (This is just the area multiplied by the height)
(x+y)²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

41. On the GRE - should you ever assume that diagrams are truthful?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
S²
A 90-degree angle.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

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

43. HIGH: Area of a circle
(x-y)²
A=pr²
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

44. Solve this: v6 * -v6 = ?
Example: 1 < x < 10
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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
6

45. HIGH: Area of a triangle?
An integer is divisible by 5 if its units digit is either 0 or 5.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

46. List two odd behaviors of exponents
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.
1.7
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

47. What is the factored version of x² -2xy + y² ?
(x-y)²
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Probability A * Probability B
Groups - teams - or committees.

48. 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.
Order does matter for a permutation - but does not matter for a combination.
180 degrees
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

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

50. HIGH: What is the median?
Not necessarily. This is a trick question - because x could be either positive or negative.
The # falling in the center of an ordered data set
The average - mean - median - or mode.
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%.