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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 unfactored version of x²-y² ?
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
A line is a 180-degree angle.
(x+y)(x-y)

2. HIGH: How do you calculate the circumference of a circle?
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.
2pr -or- pd
(a+b)(a-b)
Percentage Change = Difference/Original * 100

3. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
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%.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
'Big' angles and 'Small' angles.

4. What'S the most important thing to remember about charts you'll see on the GRE?
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.
Groups - teams - or committees.
180 degrees.
1.7

5. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
1.7
V=pr²h (This is just the area multiplied by the height)
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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

6. Solve this: v6 * -v6 = ?
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.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
6
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

7. What is the factored version of x² -2xy + 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
(x-y)²
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.
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.

8. Explain how to divide fractions.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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%.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
(x+y)(x-y)

9. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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
Favorable Outcomes/Total Possible Outcomes
A triangle in which one of the three interior angles is 90 degrees.

10. If x² = 144 - does v144 = x?
Percentage Change = Difference/Original * 100
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2pr -or- pd
Not necessarily. This is a trick question - because x could be either positive or negative.

11. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
(a+b)(a-b)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.

12. HIGH: Rough est. of v3 =
1.7
Not necessarily. This is a trick question - because x could be either positive or negative.
ZONE-F numbers: Zero - One - Negatives - Extreme values - 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.

13. An integer is divisible by 9 if...
Multiply numerator times numerator and denominator times denominator.
The average - mean - median - or mode.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
An integer is divisible by 5 if its units digit is either 0 or 5.

14. List all the prime numbers that are less than 30:
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
1/x^n For example - 6-² = 1/6² = 1/36

15. HIGH: Simplify this: v75/v27
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.
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.
1.4
A radius

16. How do you solve a combination?

17. Area of a parallelogram?
Bh
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.
Invert the second fraction (reciprocal) and multiply
(0 -0)

18. Simplify this: v32
Invert the second fraction (reciprocal) and multiply
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
A line is a 180-degree angle.
2pr -or- pd

19. What is a 'Right' triangle?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
A triangle in which one of the three interior angles is 90 degrees.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

20. Define a factorial of a number - and how it is written.
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 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+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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

21. Define the mode of a set of numbers.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Bh

22. In a coordinate system - what is the origin?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
(0 -0)

23. HIGH: Describe how to deal with 2 sets of parentheses.
(0 -0)
(x+y)²
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.
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)+

24. What is the 'Third side' rule for triangles?
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)+
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.
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.
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.

25. HIGH: To divide powers with the same base...
V=pr²h (This is just the area multiplied by the height)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
1.4

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

27. HIGH: What is the formula for the diagonal of any square?
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.
S*v2
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
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.

28. HIGH: How much of your times table should you know - for the GRE?
2
S*v2
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

29. HIGH: Rough est. of v2 =
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2
1.4
1

30. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
A triangle in which one of the three interior angles is 90 degrees.
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
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.

31. How do you calculate the percentage of change?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Percentage Change = Difference/Original * 100
(0 -0)

32. HIGH: How do you multiply and divide square roots?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

33. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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
The total # of possible outcomes.
Not reading the problems carefully enough!

34. How do you add or subtract 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 # falling in the center of an ordered data set
Find a common denominator and make equivalent fractions. Then add or subtract.
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.

35. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
1.7
V=s³
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

36. Explain the special properties of zero.
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.
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)+
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.

37. HIGH: What is the side ratio for a 30:60:90 triangle?
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 # falling in the center of an ordered data set
Bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

38. Diameter of a circle?
360 degrees
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
2r
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

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

40. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
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
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

41. If something is possible but not certain - what is the numeric range of probability of it happening?
2pr -or- pd
Favorable Outcomes/Total Possible Outcomes
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Between 0 and 1.

42. HIGH: What is the unfactored version of (x+y)² ?
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.
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.
x² + 2xy + y²
Order does matter for a permutation - but does not matter for a combination.

43. What is an 'equilateral' triangle?
1/x^n For example - 6-² = 1/6² = 1/36
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
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(x-y)²

44. An integer is divisible by 3 if...
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
6
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.

45. Define 'proportionate' values
Order does matter for a permutation - but does not matter for a combination.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

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

47. Explain how to calculate an average (arithmetic mean)
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
(0 -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.

48. What degree angle is a line?
A line is a 180-degree angle.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Arrangements - orders - schedules - or lists.
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.

49. Explain how to solve for 7/¼
The # falling in the center of an ordered data set
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Between 0 and 1.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

50. The three exterior angles of a triangle add up to...
360 degrees
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The total # of possible outcomes.
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%.