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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 is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
S*v2
Not reading the problems carefully enough!
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

2. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
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.
(x+y)²
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.

3. HIGH: Describe how to deal with 2 sets of parentheses.
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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)+
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

4. Define a factorial of a number - and how it is written.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
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.

5. HIGH: Rough est. of v1 =
The # falling in the center of an ordered data set
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.
1

6. An integer is divisible by 3 if...
2r
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.
180 degrees
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

7. Explain the difference between handling a permutation versus a combination.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
Example: 1 < x < 10

8. What causes 80% of errors on the math section of the GRE?
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
25%
90 degrees each.
Not reading the problems carefully enough!

9. On the GRE - should you ever assume that diagrams are truthful?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Multiply numerator times numerator and denominator times denominator.

10. HIGH: Simplify this: v75/v27
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
1.7

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

12. What is an 'equilateral' triangle?
A radius
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
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.

13. How is a range expressed with inequalities?
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'.
Example: 1 < x < 10
The value that appears most often in a data set.
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%.

14. How do you add or subtract fractions?
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
Not reading the problems carefully enough!
x²-y²

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

16. What do combination problems usually ask for?
Groups - teams - or committees.
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
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

17. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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 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.

18. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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

19. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
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.
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.
V=s³

20. Explain how to divide fractions.
x²-y²
90 degrees each.
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

21. Convert to a percentage: 1/4
25%
A=pr²
The value that appears most often in a data set.
A triangle in which one of the three interior angles is 90 degrees.

22. HIGH: How much of your times table should you know - for the GRE?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
The total # of possible outcomes.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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)+

23. What is the formula to determine probability?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A triangle in which one of the three interior angles is 90 degrees.
The # falling in the center of an ordered data set
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

24. a² - b² is equal to
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
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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
(a+b)(a-b)

25. How do you solve a permutation?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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
Example: 1 < x < 10
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)+

26. HIGH: Rough est. of v2 =
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Example: 1 < x < 10
1.4

27. 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.
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.
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.

28. HIGH: What is the formula for the diagonal of any square?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
25%
It will be a great advantage on test day to have your times table memorized from 1 through 15.
S*v2

29. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
360 degrees

30. v4 =
360 degrees
2
The total # of possible outcomes.
Arrangements - orders - schedules - or lists.

31. An integer is divisible by 2 if...
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
V=s³
An integer is divisible by 2 if its units digit is divisible by 2.

32. Define the mode of a set of numbers.
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 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.
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.
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.

33. Convert to a percentage: 4/5
80%
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Invert the second fraction (reciprocal) and multiply
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.

34. Explain how to use an 'Average Pie'
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.
V=s³
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
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

35. What is a 'Right' angle?
A 90-degree angle.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2r
Not reading the problems carefully enough!

36. HIGH: What is the Pythagorean theorem?

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

38. In a coordinate system - identify the quadrants and describe their location.
Not necessarily. This is a trick question - because x could be either positive or negative.
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
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Bh

39. The three interior angles of a triangle add up to...
'Big' angles and 'Small' angles.
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
180 degrees

40. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
x²-y²
Probability A + Probability B
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.
25%

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

42. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
Order does matter for a permutation - but does not matter for a combination.
(x+y)(x-y)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

43. What do permutation problems often ask for?
Invert the second fraction (reciprocal) and multiply
2pr -or- pd
Arrangements - orders - schedules - or lists.
1.7

44. Diameter of a circle?
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.
2r
3:4:5 5:12:13
60%

45. Simplify this: v32
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
An integer is divisible by 2 if its units digit is divisible by 2.

46. What number goes on the bottom of a probability fraction?
1/x^n For example - 6-² = 1/6² = 1/36
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 total # of possible outcomes.
25%

47. HIGH: What is the 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
Not reading the problems carefully enough!
The value that appears most often in a data set.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

48. HIGH: What is the median?
The # falling in the center of an ordered data set
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.
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
Not reading the problems carefully enough!

49. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
V=pr²h (This is just the area multiplied by the height)
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

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