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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 'proportionate' values
1/x^n For example - 6-² = 1/6² = 1/36
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

2. How do you solve a combination?

3. HIGH: What is the unfactored version of (x-y)² ?
Groups - teams - or committees.
Between 0 and 1.
'Big' angles and 'Small' angles.
x² -2xy + y²

4. What do combination problems usually ask for?
Groups - teams - or committees.
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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

5. Convert to a percentage: 3/5
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
60%
Order does matter for a permutation - but does not matter for a combination.
(x+y)²

6. What number goes on the bottom of a probability fraction?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
The total # of possible outcomes.
180 degrees.

7. HIGH: What is the unfactored version of x²-y² ?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
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.
(x+y)(x-y)

8. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
1. Given event A: A + notA = 1.
The value that appears most often in a data set.
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'.

9. HIGH: What is the side ratio for a 30:60:90 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.
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

10. HIGH: To divide powers with the same 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.
x² + 2xy + y²
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

11. Area of a square?
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
S²
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.
(x+y)²

12. HIGH: What is a '30:60:90' triangle?
40%
The total # of possible outcomes.
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
2pr -or- pd

13. Convert to a percentage: 2/5
40%
Percentage Change = Difference/Original * 100
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.
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.

14. For a bell curve - what three terms might be used to describe the number in the middle?
40%
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

15. Convert to a percentage: 4/5
1/x^n For example - 6-² = 1/6² = 1/36
1.7
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
80%

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

17. List all the prime numbers that are less than 30:
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(x+y)(x-y)

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

19. What is the equation for a group problem?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
(x+y)²
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
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.

20. What is the 'Third side' rule for triangles?
2
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.
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.

21. How do you multiply fractions?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Multiply numerator times numerator and denominator times denominator.

22. Explain how to use a 'Rate Pie'
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Not reading the problems carefully enough!

23. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
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
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Multiply numerator times numerator and denominator times denominator.
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.

24. HIGH: Area of a triangle?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Favorable Outcomes/Total Possible Outcomes
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.

25. HIGH: What is the order of math operations - and the mnemonic to remember it?
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.
Favorable Outcomes/Total Possible Outcomes
4 angles are formed. Their sum is 360 degrees
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

26. Define the range of a set of numbers.
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.
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.
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.
x²-y²

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

28. An integer is divisible by 2 if...
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.
Probability A + Probability B
An integer is divisible by 2 if its units digit is divisible by 2.
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

29. HIGH: How much of your times table should you know - for the GRE?
An integer is divisible by 5 if its units digit is either 0 or 5.
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

30. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
4 angles are formed. Their sum is 360 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.
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.

31. HIGH: Rough est. of v3 =
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
90 degrees each.
1.7
x² -2xy + y²

32. HIGH: Volume of a cube?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
V=s³
2r
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'.

33. Explain how to divide fractions.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
A 90-degree angle.

34. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
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.
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
90 degrees each.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

35. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
6
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.
1/x^n For example - 6-² = 1/6² = 1/36
Order does matter for a permutation - but does not matter for a combination.

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

37. Explain how to solve for 7/¼
A radius
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

38. What is the factored version of x² -2xy + y² ?
V=s³
(x-y)²
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Order does matter for a permutation - but does not matter for a combination.

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

40. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

41. What are 'vertical angles'?
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
A=pr²
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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

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

43. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Groups - teams - or committees.
1. Given event A: A + notA = 1.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

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

45. The three exterior angles of a triangle add up to...
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
6
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
360 degrees

46. HIGH: What is the Pythagorean theorem?

47. HIGH: What must be true before a quadratic equation can be solved?

48. What is the key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
x²-y²
Order does matter for a permutation - but does not matter for a combination.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

49. HIGH: What is the unfactored version of (x+y)² ?
360 degrees
80%
x² + 2xy + y²
180 degrees.

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