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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 divide fractions.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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'.

2. 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 circle'S perimeter is roughly 3x its diameter (the formula is pd).
It will be a great advantage on test day to have your times table memorized from 1 through 15.
60%

3. HIGH: Volume of a cylinder?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
V=pr²h (This is just the area multiplied by the height)
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

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

5. HIGH: Rough est. of v2 =
1.4
60%
360 degrees
2r

6. HIGH: How do you multiply and divide square roots?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
V=s³

7. Define the mode of a set of numbers.
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
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.
6
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

8. Convert to a percentage: 4/5
Example: 1 < x < 10
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'.
80%
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.

9. HIGH: What is the median?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
The # falling in the center of an ordered data set
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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

10. HIGH: Simplify this: v75/v27
Bh
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.

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

12. HIGH: Define the formula for calculating slope.
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 integer is divisible by 9 if the sum of its digits is divisible by 9.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

13. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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%.
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
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Invert the second fraction (reciprocal) and multiply

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

16. HIGH: What is the mode?
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.
1. Given event A: A + notA = 1.
The total # of possible outcomes.
The value that appears most often in a data set.

17. HIGH: Volume of a cube?
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'.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
V=s³
The # falling in the center of an ordered data set

18. 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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
1.4
60%

19. What is the name of a line that extends from the center of a circle to the edge of a circle?
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
A radius
(x-y)²
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

20. HIGH: Describe how to deal with 2 sets of parentheses.
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)+
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

21. Explain how to use an 'Average Pie'
6
40%
x²-y²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

22. Solve this: v6 * -v6 = ?
1. Given event A: A + notA = 1.
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.
6
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

23. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
80%

24. Define the range of a set of numbers.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
V=s³
x² -2xy + y²
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.

25. Convert to a percentage: 3/5
x² + 2xy + y²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
60%

26. What are the side ratios 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.
90 degrees each.
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.

27. Convert to a percentage: 2/5
40%
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
2pr -or- pd
An integer is divisible by 2 if its units digit is divisible by 2.

28. How do you divide fractions?
A triangle in which one of the three interior angles is 90 degrees.
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.
Invert the second fraction (reciprocal) and multiply
'Big' angles and 'Small' angles.

29. Define a factorial of a number - and how it is written.
Probability A * Probability B
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
1/x^n For example - 6-² = 1/6² = 1/36
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.

30. How many degrees does a circle contain?
Groups - teams - or committees.
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.
360 degrees
2pr -or- pd

31. The three exterior angles of a triangle add up to...
Example: 1 < x < 10
360 degrees
1/x^n For example - 6-² = 1/6² = 1/36
60%

32. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
The average - mean - median - or mode.
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

33. List two odd behaviors of exponents
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
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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.

34. HIGH: What is the equation of a line?

35. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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
90 degrees each.

36. What do permutation problems often ask for?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Bh
Arrangements - orders - schedules - or lists.
Order does matter for a permutation - but does not matter for a combination.

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

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

39. For a bell curve - what three terms might be used to describe the number in the middle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
180 degrees.
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.
The average - mean - median - or mode.

40. What do combination problems usually ask for?
1/x^n For example - 6-² = 1/6² = 1/36
Groups - teams - or committees.
Bh
Probability A * Probability B

41. What causes 80% of errors on the math section of the GRE?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Find a common denominator and make equivalent fractions. Then add or subtract.
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.

42. Define 'proportionate' values
3:4:5 5:12:13
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
90 degrees each.

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

44. Area of a square?
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 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.
S²
An integer is divisible by 5 if its units digit is either 0 or 5.

45. Probability Formula
The value that appears most often in a data set.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Favorable Outcomes/Total 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.

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

47. What is the key to dealing with ratio questions?
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.
90 degrees each.
The # falling in the center of an ordered data set
Find the total - or whole - first - and then set up a Ratio Box.

48. HIGH: What is the Pythagorean theorem?

49. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
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.
Find the total - or whole - first - and then set up a Ratio Box.
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

50. HIGH: What is the order of math operations - and the mnemonic to remember it?
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
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.
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
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.