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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 order of math operations - and the mnemonic to remember it?
Order does matter for a permutation - but does not matter for a combination.
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.
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

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

3. a² - b² is equal to
An integer is divisible by 2 if its units digit is divisible by 2.
A line is a 180-degree angle.
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.
(a+b)(a-b)

4. Convert to a percentage: 3/5
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
60%

5. How is a range expressed with inequalities?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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'.
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.

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

7. Explain how to use a 'Rate Pie'
2r
Favorable Outcomes/Total Possible Outcomes
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
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

8. Explain how to divide fractions.
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

9. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

10. How do you solve a permutation?
180 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
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

11. Convert to a percentage: 1/4
25%
A radius
x²-y²
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

12. HIGH: How do you multiply and divide square roots?
Find the total - or whole - first - and then set up a Ratio Box.
'Big' angles and 'Small' angles.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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

13. HIGH: What is a 'Right isosceles' 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)+
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
It will be a great advantage on test day to have your times table memorized from 1 through 15.

14. HIGH: x^-n is equal to
Find the total - or whole - first - and then set up a Ratio Box.
1/x^n For example - 6-² = 1/6² = 1/36
Example: 1 < x < 10
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

15. If something is certain to happen - how is the probability of this event expressed mathematically?
1. Given event A: A + notA = 1.
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
1/1
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

16. HIGH: Describe how to deal with 2 sets of parentheses.
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.
Order does matter for a permutation - but does not matter for a combination.
A line is a 180-degree angle.
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)+

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

18. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
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
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Bh

19. Solve this: v6 * -v6 = ?
6
1. Given event A: A + notA = 1.
The total # of possible outcomes.
Between 0 and 1.

20. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
4 angles are formed. Their sum is 360 degrees
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.

21. How do you add or subtract fractions?
Find the total - or whole - first - and then set up a Ratio Box.
Find a common denominator and make equivalent fractions. Then add or subtract.
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'.
360 degrees

22. Explain the difference between handling a permutation versus a combination.
The total # of possible outcomes.
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.
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

23. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

24. HIGH: How much of your times table should you know - for the GRE?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Favorable Outcomes/Total Possible Outcomes
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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. What is a 'Right' triangle?
S*v2
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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%.
A triangle in which one of the three interior angles is 90 degrees.

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

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

28. An integer is divisible by 5 if...
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
An integer is divisible by 5 if its units digit is either 0 or 5.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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

29. HIGH: Volume of a cube?
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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
V=s³

30. HIGH: Define the formula for calculating slope.
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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%.
Example: 1 < x < 10

31. What degree angle is a line?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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 line is a 180-degree angle.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

32. The three exterior angles of a triangle add up to...
360 degrees
1.4
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 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.

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

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

35. Convert to a percentage: 4/5
Bh
80%
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'.
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

36. Probability Formula
(x+y)(x-y)
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.
Favorable Outcomes/Total Possible Outcomes
Not reading the problems carefully enough!

37. HIGH: To divide powers with the same base...
Multiply numerator times numerator and denominator times denominator.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Invert the second fraction (reciprocal) and multiply
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

38. List two odd behaviors of exponents
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Probability A * Probability B
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.
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.

39. HIGH: Rough est. of v2 =
(a+b)(a-b)
1.4
Arrangements - orders - schedules - or lists.
40%

40. HIGH: What is the side ratio for a 30:60:90 triangle?
Groups - teams - or committees.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4 angles are formed. Their sum is 360 degrees
1/1

41. In a coordinate system - what is the origin?
(0 -0)
S²
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.

42. Explain how to solve for 7/¼
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
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. Given event A: A + notA = 1.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

43. Area of a parallelogram?
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.
2r
The average - mean - median - or mode.
Bh

44. What is the 'Third side' rule for triangles?
6
25%
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

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

46. What should you do BEFORE you start to solve a GRE math problem?

47. What is the equation for a group problem?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
S*v2
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
x² + 2xy + y²

48. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
1.4
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.
The total # of possible outcomes.

49. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 2.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
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.

50. How do you calculate the percentage of change?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Find a common denominator and make equivalent fractions. Then add or subtract.