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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. Define a factorial of a number - and how it is written.
V=pr²h (This is just the area multiplied by the height)
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.
S*v2
Favorable Outcomes/Total Possible Outcomes

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

3. 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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

4. An integer is divisible by 8 if...

5. What is the 'Third side' rule for triangles?
Not reading the problems carefully enough!
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
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.

6. Explain how to calculate an average (arithmetic mean)
x²-y²
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
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.

7. In a coordinate system - identify the quadrants and describe their location.
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.
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.
1.7
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

8. 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
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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
x²-y²

9. HIGH: What is the Pythagorean theorem?

10. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
Order does matter for a permutation - but does not matter for a combination.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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

11. List all the prime numbers that are less than 30:
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
(x+y)²

12. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Favorable Outcomes/Total Possible Outcomes
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

13. 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% |
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
Not necessarily. This is a trick question - because x could be either positive or negative.
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.

14. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
180 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.
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
Multiply numerator times numerator and denominator times denominator.

15. What is the name of a line that extends from the center of a circle to the edge of a circle?
Percentage Change = Difference/Original * 100
A=pr²
1.7
A radius

16. Define 'proportionate' values
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
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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

17. HIGH: List the two most common side ratios for right triangles
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Example: 1 < x < 10
3:4:5 5:12:13
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.

18. HIGH: Volume of a cube?
6
360 degrees
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
V=s³

19. The three interior angles of a triangle add up to...
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.
(a+b)(a-b)
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
180 degrees

20. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
Order does matter for a permutation - but does not matter for a combination.
4 angles are formed. Their sum is 360 degrees
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

21. HIGH: What is the median?
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
360 degrees
The # falling in the center of an ordered data set
180 degrees

22. Solve this: v6 * -v6 = ?
6
The total # of possible outcomes.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.

23. HIGH: What is a 'Right isosceles' triangle?
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.
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.
Example: 1 < x < 10

24. HIGH: How do you multiply powers with the same base?
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'.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Not reading the problems carefully enough!

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

26. What is the key to dealing with ratio questions?
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 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.
Find the total - or whole - first - and then set up a Ratio Box.
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.

27. HIGH: How much of your times table should you know - for the GRE?
x² + 2xy + y²
It will be a great advantage on test day to have your times table memorized from 1 through 15.
6
1

28. HIGH: What is a '30:60:90' triangle?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
25%
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

29. HIGH: Rough est. of v1 =
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
1
60%
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

30. What is a 'Right' angle?
A 90-degree angle.
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.
The # falling in the center of an ordered data set
Groups - teams - or committees.

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

32. HIGH: Describe how to deal with 2 sets of parentheses.
Not reading the problems carefully enough!
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)+
Between 0 and 1.
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

33. HIGH: Volume of a cylinder?
The value that appears most often in a data set.
V=pr²h (This is just the area multiplied by the height)
x² -2xy + y²
Not necessarily. This is a trick question - because x could be either positive or negative.

34. HIGH: What is the factored version of x² + 2xy + y² ?
Probability A + Probability B
(x+y)²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
40%

35. Convert to a percentage: 1/4
The total # of possible outcomes.
25%
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)+
Find a common denominator and make equivalent fractions. Then add or subtract.

36. Convert to a percentage: 2/5
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
40%

37. The three exterior angles of a triangle add up to...
A 90-degree angle.
360 degrees
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
The average - mean - median - or mode.

38. Explain how to divide fractions.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

39. HIGH: What is the side ratio for a 30:60:90 triangle?
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.
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.
Find a common denominator and make equivalent fractions. Then add or subtract.

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

41. a² - b² is equal to
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'.
(a+b)(a-b)
80%

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

43. What degree angle is a line?
Order does matter for a permutation - but does not matter for a combination.
2
25%
A line is a 180-degree angle.

44. Explain how to solve for 7/¼
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
V=pr²h (This is just the area multiplied by the height)
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.

45. What is an 'equilateral' triangle?
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)+
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
A=pr²
4 angles are formed. Their sum is 360 degrees

46. Explain how to use a 'Rate Pie'
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
Between 0 and 1.
Bh
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.

47. HIGH: Simplify this: v75/v27
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.
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.
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

48. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
Arrangements - orders - schedules - or lists.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.
A=pr²

49. What is the factored version of x² -2xy + y² ?
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
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.
2r

50. HIGH: To divide powers with the same base...
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Not necessarily. This is a trick question - because x could be either positive or negative.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.