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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: How do you calculate the length of an arc?

2. How is a range expressed with inequalities?
360 degrees
Between 0 and 1.
Example: 1 < x < 10
Favorable Outcomes/Total Possible Outcomes

3. Convert to a percentage: 1/4
(a+b)(a-b)
25%
A 90-degree angle.
x²-y²

4. Define the mode of a set of numbers.
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
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.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

5. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Arrangements - orders - schedules - or lists.
2
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
1.7

6. What causes 80% of errors on the math section of the GRE?
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.
Bh
Not reading the problems carefully enough!
1/1

7. HIGH: What is the side ratio for a 30:60:90 triangle?
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
360 degrees
80%

8. What is a 'Right' angle?
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.

9. HIGH: Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

10. HIGH: Rough est. of v2 =
An integer is divisible by 5 if its units digit is either 0 or 5.
x² + 2xy + y²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
1.4

11. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
25%
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.

12. What is the 'Third side' rule for triangles?
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
A line is a 180-degree angle.

13. HIGH: Rough est. of v3 =
V=pr²h (This is just the area multiplied by the height)
1/x^n For example - 6-² = 1/6² = 1/36
90 degrees each.
1.7

14. HIGH: Describe how to deal with 2 sets of parentheses.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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)+
S²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

15. Convert to a percentage: 2/5
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
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
40%

16. HIGH: Volume of a cube?
Find the total - or whole - first - and then set up a Ratio Box.
V=s³
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

17. What is the formula to determine probability?
Find a common denominator and make equivalent fractions. Then add or subtract.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.

18. HIGH: What is the unfactored version of (x+y)² ?
The total # of possible outcomes.
x² + 2xy + y²
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.
Groups - teams - or committees.

19. On the GRE - should you ever assume that diagrams are truthful?
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.
Percentage Change = Difference/Original * 100
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

20. v4 =
1
V=pr²h (This is just the area multiplied by the height)
2
x² + 2xy + y²

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

22. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

23. Probability Formula
2pr -or- pd
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
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.

24. What degree angle is a line?
1/x^n For example - 6-² = 1/6² = 1/36
6
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 line is a 180-degree angle.

25. What should you do BEFORE you start to solve a GRE math problem?

26. List two odd behaviors of exponents
Probability A * Probability B
The value that appears most often in a data set.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.

27. If x² = 144 - does v144 = x?
4 angles are formed. Their sum is 360 degrees
Not necessarily. This is a trick question - because x could be either positive or negative.
1.4
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

28. HIGH: x^-n is equal to
Find a common denominator and make equivalent fractions. Then add or subtract.
60%
1/x^n For example - 6-² = 1/6² = 1/36
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

29. Does order matter for a permutation? How about for a combination?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Order does matter for a permutation - but does not matter for a combination.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
2r

30. What is a 'Right' triangle?
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.
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)+
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.
A triangle in which one of the three interior angles is 90 degrees.

31. What do combination problems usually ask for?
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.
Groups - teams - or committees.
x²-y²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

32. What are 'vertical angles'?
Multiply numerator times numerator and denominator times denominator.
A triangle in which one of the three interior angles is 90 degrees.
x² + 2xy + y²
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

33. Convert to a percentage: 3/5
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
60%
A radius
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

34. 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.
40%
2pr -or- pd
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.

35. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
Bh
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)+
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.

36. How do you divide fractions?
S²
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
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.
Invert the second fraction (reciprocal) and multiply

37. Area of a square?
Order does matter for a permutation - but does not matter for a combination.
Multiply numerator times numerator and denominator times denominator.
S²
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. HIGH: What is the median?
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.
Bh
The # falling in the center of an ordered data set
Not reading the problems carefully enough!

39. What is the factored version of x² -2xy + y² ?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(x-y)²

40. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
1.4
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Example: 1 < x < 10
Bh

41. HIGH: What is 'absolute value' - and how is it represented?

42. Convert to a percentage: 4/5
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.
80%
Percentage Change = Difference/Original * 100
The # falling in the center of an ordered data set

43. HIGH: What is a '30:60:90' triangle?
40%
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
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

44. HIGH: what is the side ratio for a Right Isosceles triangle?
Between 0 and 1.
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

45. How do you solve a permutation?
1. Given event A: A + notA = 1.
An integer is divisible by 5 if its units digit is either 0 or 5.
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
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.

46. How do you add or subtract fractions?
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
The total # of possible outcomes.
60%

47. Solve this: v6 * -v6 = ?
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.
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
6
Probability A * Probability B

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

49. What are the side ratios for a 30:60:90 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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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 6 if it'S divisible by BOTH 2 and 3.

50. How many degrees does a circle contain?
360 degrees
A triangle in which one of the three interior angles is 90 degrees.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Bh