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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. What number goes on the bottom of a probability fraction?
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.
25%
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

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

3. What is the 'distributive law'?
2r
(0 -0)
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.

4. Area of a parallelogram?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
Bh

5. In a coordinate system - identify the quadrants and describe their location.
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Multiply numerator times numerator and denominator times denominator.

6. 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
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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'.

7. List two odd behaviors of exponents
A=pr²
Favorable Outcomes/Total Possible Outcomes
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.
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.

8. What is the formula to determine probability?
2r
The total # of possible outcomes.
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

9. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
1/1
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.

10. HIGH: What is the Pythagorean theorem?

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

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

13. HIGH: To divide powers with the same base...
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

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

15. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
S*v2
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.

16. 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.
Between 0 and 1.
S*v2
The value that appears most often in a data set.

17. Diameter of a circle?
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2r

18. Solve this: v6 * -v6 = ?
Order does matter for a permutation - but does not matter for a combination.
6
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'.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

19. Explain how to use a 'Rate Pie'
An integer is divisible by 5 if its units digit is either 0 or 5.
V=pr²h (This is just the area multiplied by the height)
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
Not necessarily. This is a trick question - because x could be either positive or negative.

20. Probability Formula
Probability A * Probability B
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.
Favorable Outcomes/Total Possible Outcomes
A line is a 180-degree angle.

21. What is a 'Right' angle?
A 90-degree angle.
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.
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
Favorable Outcomes/Total Possible Outcomes

22. Explain how to use an 'Average Pie'
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
A=pr²
6

23. 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.
Groups - teams - or committees.
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
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

24. On the GRE - should you ever assume that diagrams are truthful?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
'Big' angles and 'Small' angles.

25. How do you solve a permutation?
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(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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

26. Explain the difference between handling a permutation versus a combination.
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 triangle in which one of the three interior angles is 90 degrees.
1/x^n For example - 6-² = 1/6² = 1/36
1.7

27. HIGH: How do you multiply and divide square roots?
A 90-degree angle.
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.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

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

29. What degree angle is a line?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
360 degrees
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)+
A line is a 180-degree angle.

30. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
'Big' angles and 'Small' angles.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

31. How do you divide fractions?
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.
Invert the second fraction (reciprocal) and multiply
The total # of possible outcomes.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

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

33. What is the key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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. Given event A: A + notA = 1.

34. HIGH: Describe how to deal with 2 sets of parentheses.
90 degrees each.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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)+
Favorable Outcomes/Total Possible Outcomes

35. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
An integer is divisible by 2 if its units digit is divisible by 2.
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

36. If something is possible but not certain - what is the numeric range of probability of it happening?
Find a common denominator and make equivalent fractions. Then add or subtract.
Between 0 and 1.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.

37. How do you add or subtract fractions?
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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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
Find a common denominator and make equivalent fractions. Then add or subtract.

38. HIGH: What is a '30:60:90' triangle?
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
Invert the second fraction (reciprocal) and multiply
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.

39. a² - b² is equal to
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(a+b)(a-b)

40. HIGH: What is the order of math operations - and the mnemonic to remember it?
(x+y)²
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
25%
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.

41. HIGH: What are the percentages for standard deviation?
Order does matter for a permutation - but does not matter for a combination.
2pr -or- pd
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

42. HIGH: Volume of a cube?
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
1.7
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
V=s³

43. How many degrees does a circle contain?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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% |
x²-y²

44. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
A 90-degree angle.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

45. What is the 'Third side' rule for triangles?
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 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
360 degrees

46. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
40%
S*v2
Between 0 and 1.

47. How do you calculate the probability of two events in a row? (Probability of A and B)
Between 0 and 1.
40%
Probability A * Probability B
2

48. What causes 80% of errors on the math section of the GRE?
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.
Multiply numerator times numerator and denominator times denominator.
Not reading the problems carefully enough!
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.

49. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
The value that appears most often in a data set.
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.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

50. The three interior angles of a triangle add up to...
180 degrees
180 degrees.
4 angles are formed. Their sum is 360 degrees
A radius