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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. How do you divide fractions?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Invert the second fraction (reciprocal) and multiply
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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.

2. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
The value that appears most often in a data set.
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

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

4. HIGH: Define the formula for calculating slope.
1
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

5. HIGH: What is the factored version of (x+y)(x-y) ?
A=pr²
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
x²-y²

6. HIGH: What is the unfactored version of (x+y)² ?
Not necessarily. This is a trick question - because x could be either positive or negative.
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'.
Order does matter for a permutation - but does not matter for a combination.
x² + 2xy + y²

7. Diameter of a circle?
Invert the second fraction (reciprocal) and multiply
2r
An integer is divisible by 9 if the sum of its digits is divisible by 9.
S²

8. HIGH: Rough est. of v1 =
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
180 degrees
1
Arrangements - orders - schedules - or lists.

9. Convert to a percentage: 1/4
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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
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Invert the second fraction (reciprocal) and multiply

10. If something is certain to happen - how is the probability of this event expressed mathematically?
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
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
1/1
Favorable Outcomes/Total Possible Outcomes

11. What is an 'equilateral' triangle?
The value that appears most often in a data set.
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. Given event A: A + notA = 1.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

12. HIGH: What is a '30:60:90' triangle?
Probability A * Probability B
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.
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.
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

13. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
(x+y)²
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.
Probability A + Probability B
Example: 1 < x < 10

14. An integer is divisible by 2 if...
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Not necessarily. This is a trick question - because x could be either positive or negative.
An integer is divisible by 2 if its units digit is divisible by 2.
Probability A + Probability B

15. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
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
V=pr²h (This is just the area multiplied by the height)
It will be a great advantage on test day to have your times table memorized from 1 through 15.

16. What is the equation for a group problem?
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
V=s³
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.
180 degrees.

17. What is the 'distributive law'?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
S²
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.
1.7

18. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A triangle in which one of the three interior angles is 90 degrees.

19. How do you add or subtract fractions?
Probability A * Probability B
The average - mean - median - or mode.
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.
Find a common denominator and make equivalent fractions. Then add or subtract.

20. HIGH: what is the side ratio for a Right Isosceles triangle?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.

21. Define the range of a set of numbers.
A=pr²
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.
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.
An integer is divisible by 5 if its units digit is either 0 or 5.

22. Explain how to use a 'Rate Pie'
A radius
Multiply numerator times numerator and denominator times denominator.
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
(x-y)²

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

24. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Between 0 and 1.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

25. What are the side ratios for a 30:60:90 triangle?
90 degrees each.
A line is a 180-degree angle.
6
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

26. Explain how to calculate an average (arithmetic mean)
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.
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.
Find the total - or whole - first - and then set up a Ratio Box.

27. How do you multiply fractions?
S²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Multiply numerator times numerator and denominator times denominator.

28. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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. Given event A: A + notA = 1.
Groups - teams - or committees.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

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

30. What is the factored version of x² -2xy + y² ?
(x-y)²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
V=pr²h (This is just the area multiplied by the height)
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

31. Define 'proportionate' values
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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
60%

32. What causes 80% of errors on the math section of the GRE?
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
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.
Not reading the problems carefully enough!

33. Does order matter for a permutation? How about for a combination?
90 degrees each.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
V=s³
Order does matter for a permutation - but does not matter for a combination.

34. List two odd behaviors of exponents
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.
4 angles are formed. Their sum is 360 degrees
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

35. What number goes on the bottom of a probability fraction?
A=pr²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The total # of possible outcomes.
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.

36. HIGH: What is the factored version of x² + 2xy + y² ?
3:4:5 5:12:13
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
(x+y)²
A 90-degree angle.

37. How do you solve a combination?

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

39. HIGH: Simplify this: v75/v27
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(x+y)²
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

40. 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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
60%
The total # of possible outcomes.

41. HIGH: What is the median?
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)+
The # falling in the center of an ordered data set
An integer is divisible by 5 if its units digit is either 0 or 5.
3:4:5 5:12:13

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

43. 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.
Not necessarily. This is a trick question - because x could be either positive or negative.
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'.
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.

44. HIGH: What is the formula for the diagonal of any square?
1/x^n For example - 6-² = 1/6² = 1/36
S*v2
Favorable Outcomes/Total Possible Outcomes
Probability A + Probability B

45. What is the key to dealing with ratio questions?
The # falling in the center of an ordered data set
60%
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Find the total - or whole - first - and then set up a Ratio Box.

46. What do combination problems usually ask for?
V=s³
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.
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.
Groups - teams - or committees.

47. Solve this: v6 * -v6 = ?
1
6
The value that appears most often in a data set.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

48. HIGH: Volume of a cube?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
V=s³
x²-y²
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.

49. 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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Order does matter for a permutation - but does not matter for a combination.
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

50. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
S²
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.
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