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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 calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
(x-y)²
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
1.7
Probability A + Probability B

2. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
360 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
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

3. HIGH: what is the side ratio for a Right Isosceles triangle?
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.
60%
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1.7

4. For a bell curve - what three terms might be used to describe the number in the middle?
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 median is the middle value of a set of numbers. For an odd number of values - it'S simply the middle number. For an even number of values - take the average of the center two values.
The average - mean - median - or mode.
Bh

5. Explain how to solve for 7/¼
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.
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.

6. Explain how to use a 'Rate Pie'
360 degrees
6
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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

7. An integer is divisible by 3 if...
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 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.
V=pr²h (This is just the area multiplied by the height)
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

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

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9. What is the sum of any 'big' angle and any 'Small' angle?
Bh
180 degrees.
Favorable Outcomes/Total Possible Outcomes
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.

10. HIGH: Area of a circle
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
Between 0 and 1.
1.4
A=pr²

11. In a coordinate system - what is the origin?
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.
(x+y)(x-y)
(0 -0)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

12. What'S the most important thing to remember about charts you'll see on the GRE?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
1/x^n For example - 6-² = 1/6² = 1/36
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.
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.

13. What is the key to dealing with ratio questions?
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
Find the total - or whole - first - and then set up a Ratio Box.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Find a common denominator and make equivalent fractions. Then add or subtract.

14. HIGH: Rough est. of v1 =
1
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.

15. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?

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16. Convert to a percentage: 3/5
1
60%
An integer is divisible by 2 if its units digit is divisible by 2.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

17. Explain the difference between handling a permutation versus a combination.
Not reading the problems carefully enough!
Probability A + Probability 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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

18. What degree angle is a line?
(0 -0)
The # falling in the center of an ordered data set
A line is a 180-degree angle.
x² + 2xy + y²

19. How many degrees does a circle contain?
360 degrees
1.7
Not necessarily. This is a trick question - because x could be either positive or negative.
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.

20. An integer is divisible by 2 if...
Between 0 and 1.
An integer is divisible by 2 if its units digit is divisible by 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
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)+

21. HIGH: What is the formula for the diagonal of any square?
A median is the middle value of a set of numbers. For an odd number of values - it'S simply the middle number. For an even number of values - take the average of the center two values.
1/x^n For example - 6-² = 1/6² = 1/36
Find a common denominator and make equivalent fractions. Then add or subtract.
S*v2

22. HIGH: How do you calculate the circumference of a circle?
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.
2pr -or- pd
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

23. Explain how to divide fractions.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
1/1

24. HIGH: Area of a triangle?
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
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

25. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
'Big' angles and 'Small' angles.
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.
(x+y)(x-y)
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.

26. Explain how to calculate an average (arithmetic mean)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
(0 -0)
25%
'Big' angles and 'Small' angles.

27. HIGH: Simplify this: v75/v27
(x+y)²
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

28. HIGH: x^-n is equal to
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
Multiply numerator times numerator and denominator times denominator.
1/x^n For example - 6-² = 1/6² = 1/36
Between 0 and 1.

29. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Bh
Invert the second fraction (reciprocal) and multiply
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

30. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
A 90-degree angle.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

31. An integer is divisible by 9 if...
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Probability A * Probability B
An integer is divisible by 9 if the sum of its digits is divisible by 9.

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

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33. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
An integer is divisible by 5 if its units digit is either 0 or 5.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

34. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
S*v2
Example: 1 < x < 10
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

35. What is the factored version of x² -2xy + y² ?
Percentage Change = Difference/Original * 100
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.
(x-y)²
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%.

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

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37. HIGH: What is the factored version of (x+y)(x-y) ?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
1.7
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.
x²-y²

38. HIGH: List the two most common side ratios for right triangles
S²
1. Given event A: A + notA = 1.
3:4:5 5:12:13
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.

39. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
Between 0 and 1.
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
3:4:5 5:12:13

40. Diameter of a circle?
x² + 2xy + y²
2r
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.
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.

41. Simplify this: v32
Find the total - or whole - first - and then set up a Ratio Box.
1. Given event A: A + notA = 1.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

42. HIGH: Describe how to deal with 2 sets of parentheses.
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.
3:4:5 5:12:13
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)+
360 degrees

43. What causes 80% of errors on the math section of the GRE?
1. Given event A: A + notA = 1.
Not reading the problems carefully enough!
1.4
x² + 2xy + y²

44. What are 'vertical angles'?
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.
1
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

45. How do you add or subtract fractions?
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
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.
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.
Find a common denominator and make equivalent fractions. Then add or subtract.

46. HIGH: What are the percentages for standard deviation?
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
1.7
Not reading the problems carefully enough!

47. List two odd behaviors of exponents
x² -2xy + y²
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 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
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.

48. The probability of an event happening and the probability of an event NOT happening must add up to what number?
180 degrees
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'.
1. Given event A: A + notA = 1.
90 degrees each.

49. a² - b² is equal to
(a+b)(a-b)
Between 0 and 1.
An integer is divisible by 5 if its units digit is either 0 or 5.
180 degrees.

50. How is a range expressed with inequalities?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Example: 1 < x < 10
The value that appears most often in a data set.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.