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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. Convert to a percentage: 4/5
1.7
80%
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.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

2. HIGH: What is the unfactored version of (x+y)² ?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
x² + 2xy + y²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

3. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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. 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
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.

4. How is a range expressed with inequalities?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
An integer is divisible by 2 if its units digit is divisible by 2.
A 90-degree angle.
Example: 1 < x < 10

5. If something is possible but not certain - what is the numeric range of probability of it happening?
Invert the second fraction (reciprocal) and multiply
Groups - teams - or committees.
Between 0 and 1.
(0 -0)

6. HIGH: What is the median?
The # falling in the center of an ordered data set
(0 -0)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Probability A + Probability B

7. What is the factored version of x² -2xy + y² ?
Groups - teams - or committees.
1/x^n For example - 6-² = 1/6² = 1/36
S*v2
(x-y)²

8. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
Multiply numerator times numerator and denominator times denominator.
1. Given event A: A + notA = 1.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

9. What is the 'Third side' rule for triangles?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

10. What degree angle is a line?
Not necessarily. This is a trick question - because x could be either positive or negative.
A line is a 180-degree angle.
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

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

12. What'S the most important thing to remember about charts you'll see on the GRE?
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 - 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.
4 angles are formed. Their sum is 360 degrees
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

13. HIGH: What is the Pythagorean theorem?

14. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/x^n For example - 6-² = 1/6² = 1/36
60%
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.

15. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
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.
Arrangements - orders - schedules - or lists.
80%

16. What is the formula to determine probability?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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 should you do BEFORE you start to solve a GRE math problem?

18. 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
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.

19. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
S²
x² + 2xy + y²

20. Define the mode of a set of numbers.
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
x² + 2xy + y²
Find the total - or whole - first - and then set up a Ratio Box.

21. HIGH: How do you multiply and divide square roots?
4 angles are formed. Their sum is 360 degrees
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The # falling in the center of an ordered 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.

22. An integer is divisible by 3 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
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.
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

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

24. Explain the special properties of zero.
3:4:5 5:12:13
360 degrees
Find the total - or whole - first - and then set up a Ratio Box.
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.

25. HIGH: What is the order of math operations - and the mnemonic to remember it?
360 degrees
An integer is divisible by 2 if its units digit is divisible by 2.
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
Order does matter for a permutation - but does not matter for a combination.

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
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
x² + 2xy + y²
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

27. What do combination problems usually ask for?
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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
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.

28. How do you solve a permutation?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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
360 degrees

29. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or 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.
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Probability A + Probability B

30. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
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
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.
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

31. If x² = 144 - does v144 = x?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
Not reading the problems carefully enough!

32. HIGH: Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
80%
S²

33. Convert to a percentage: 3/5
Find a common denominator and make equivalent fractions. Then add or subtract.
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
60%

34. How do you add or subtract fractions?
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
Find a common denominator and make equivalent fractions. Then add or subtract.
A 90-degree angle.
S*v2

35. List two odd behaviors of exponents
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
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.

36. What is a 'Right' triangle?
Order does matter for a permutation - but does not matter for a combination.
(x-y)²
A triangle in which one of the three interior angles is 90 degrees.
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.

37. v4 =
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
The # falling in the center of an ordered data set
2
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

38. How many degrees does a circle contain?
90 degrees each.
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.
40%
360 degrees

39. Does order matter for a permutation? How about for a combination?
360 degrees
Order does matter for a permutation - but does not matter for a combination.
Groups - teams - or committees.
1

40. The three interior angles of a triangle add up to...
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
An integer is divisible by 5 if its units digit is either 0 or 5.
180 degrees
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

41. On the GRE - should you ever assume that diagrams are truthful?
The value that appears most often in a data set.
1
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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

42. What is the equation for a group problem?
1.7
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.
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
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.

43. HIGH: What is the side ratio for a 30:60:90 triangle?
6
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/1
2

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

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

46. How do you divide fractions?
Find a common denominator and make equivalent fractions. Then add or subtract.
Percentage Change = Difference/Original * 100
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Invert the second fraction (reciprocal) and multiply

47. What kind of triangle is this: has two sides of equal length - and 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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Probability A * Probability B
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.

48. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A 90-degree angle.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
90 degrees each.

49. HIGH: Volume of a cube?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
V=s³
1.4
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

50. In a coordinate system - what is the origin?
(0 -0)
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2