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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. What degree angle is a line?
80%
1/x^n For example - 6-² = 1/6² = 1/36
A line is a 180-degree angle.
(x-y)²

2. HIGH: Area of a circle
A=pr²
(x+y)²
2pr -or- pd
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.

3. An integer is divisible by 5 if...
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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
An integer is divisible by 5 if its units digit is either 0 or 5.
Order does matter for a permutation - but does not matter for a combination.

4. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

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

6. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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)+
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
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

7. How do you add or subtract fractions?
1. Given event A: A + notA = 1.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Find a common denominator and make equivalent fractions. Then add or subtract.
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

8. What causes 80% of errors on the math section of the GRE?
180 degrees
A 90-degree angle.
'Big' angles and 'Small' angles.
Not reading the problems carefully enough!

9. HIGH: Rough est. of v3 =
3:4:5 5:12:13
1.7
1. Given event A: A + notA = 1.
V=s³

10. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

11. Explain how to calculate an average (arithmetic mean)
1. Given event A: A + notA = 1.
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

12. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1
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

13. Solve this: v6 * -v6 = ?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
6
Bh

14. For a bell curve - what three terms might be used to describe the number in the middle?
40%
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 average - mean - median - or mode.
(0 -0)

15. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
6
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 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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

16. An integer is divisible by 3 if...
Favorable Outcomes/Total Possible Outcomes
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
1.7

17. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
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.

18. If something is possible but not certain - what is the numeric range of probability of it happening?
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
Between 0 and 1.
360 degrees

19. HIGH: What is a 'Right isosceles' triangle?
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
Find the total - or whole - first - and then set up a Ratio Box.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.

20. An integer is divisible by 8 if...

21. Explain how to solve for 7/¼
The average - mean - median - or mode.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Find the total - or whole - first - and then set up a Ratio Box.
Order does matter for a permutation - but does not matter for a combination.

22. How do you divide fractions?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The total # of possible outcomes.
Invert the second fraction (reciprocal) and multiply

23. How do you solve a permutation?
360 degrees
2pr -or- pd
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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

24. Does order matter for a permutation? How about for a combination?
A line is a 180-degree angle.
Order does matter for a permutation - but does not matter for a combination.
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

25. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
1. Given event A: A + notA = 1.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

26. What are 'vertical angles'?
1
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.
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.

27. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
1.4

28. 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.
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.
2r
80%

29. Probability Formula
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.
2pr -or- pd
Favorable Outcomes/Total Possible Outcomes
25%

30. What is the 'distributive law'?
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.
(x-y)²
(x+y)²
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

31. What are the side ratios for a 30:60:90 triangle?
Invert the second fraction (reciprocal) and multiply
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2pr -or- pd
3:4:5 5:12:13

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

33. Explain how to use an 'Average Pie'
2r
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
An integer is divisible by 5 if its units digit is either 0 or 5.
2pr -or- pd

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

35. Explain the difference between handling a permutation versus a combination.
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.
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.
x² -2xy + y²

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

37. Diameter of a circle?
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.
90 degrees each.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
2r

38. What do permutation problems often ask for?
Groups - teams - or committees.
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.
Arrangements - orders - schedules - or lists.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

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

40. HIGH: x^-n is equal to
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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/x^n For example - 6-² = 1/6² = 1/36
(x+y)(x-y)

41. An integer is divisible by 9 if...
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
An integer is divisible by 9 if the sum of its digits is divisible by 9.
A=pr²

42. How many degrees does a circle contain?
360 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'.
1.7
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.

43. HIGH: What is the Pythagorean theorem?

44. HIGH: How much of your times table should you know - for the GRE?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
40%

45. What is the sum of any 'big' angle and any 'Small' angle?
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
180 degrees.
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.
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

46. HIGH: Simplify this: v75/v27
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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

47. 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.
1.7
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

48. a² - b² is equal to
The total # of possible outcomes.
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)(a-b)
Probability A * Probability B

49. The three exterior angles of a triangle add up to...
Invert the second fraction (reciprocal) and multiply
360 degrees
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.
S*v2

50. What is the 'Third side' rule for triangles?
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'.
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.
x² -2xy + y²
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28