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GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 mode?
Percentage Change = Difference/Original * 100
The value that appears most often in a data set.
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.
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.

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

3. How is a range expressed with inequalities?
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.
2
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Example: 1 < x < 10

4. HIGH: What is the median?
A 90-degree angle.
The # falling in the center of an ordered data set
1.4
The value that appears most often in a data set.

5. What are 'vertical angles'?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

6. How do you solve a permutation?
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
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
3:4:5 5:12:13
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.

7. On the GRE - should you ever assume that diagrams are truthful?
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.

8. a² - b² is equal to
(a+b)(a-b)
The # falling in the center of an ordered data set
S*v2
V=s³

9. HIGH: Area of a triangle?
The # falling in the center of an ordered data set
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

10. HIGH: Rough est. of v2 =
Arrangements - orders - schedules - or lists.
V=pr²h (This is just the area multiplied by the height)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1.4

11. What do combination problems usually ask for?
(x+y)(x-y)
1.4
S*v2
Groups - teams - or committees.

12. In a coordinate system - what is the origin?
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(0 -0)
S²

13. Area of a square?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
2
S²
Order does matter for a permutation - but does not matter for a combination.

14. The three exterior angles of a triangle add up to...
360 degrees
V=s³
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
2r

15. Explain how to divide fractions.
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Groups - teams - or committees.

16. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The value that appears most often in a data set.
180 degrees.
A triangle in which one of the three interior angles is 90 degrees.

17. Solve this: v6 * -v6 = ?
4 angles are formed. Their sum is 360 degrees
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
6
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

18. In a coordinate system - identify the quadrants and describe their location.
The average - mean - median - or mode.
1. Given event A: A + notA = 1.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(x-y)²

19. HIGH: What is the unfactored version of (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
x² + 2xy + y²
80%
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)+

20. How do you solve a combination?

21. An integer is divisible by 5 if...
A triangle in which one of the three interior angles is 90 degrees.
An integer is divisible by 5 if its units digit is either 0 or 5.
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).

22. v4 =
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
360 degrees
S*v2
2

23. Explain how to use an 'Average Pie'
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
S*v2
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.
2r

24. HIGH: what is the side ratio for a Right Isosceles 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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
A 90-degree angle.

25. HIGH: What is the factored version of x² + 2xy + y² ?
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
(x+y)²
60%

26. HIGH: x^-n is equal to
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/x^n For example - 6-² = 1/6² = 1/36
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 5 if its units digit is either 0 or 5.

27. What is the key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
Bh
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.
The value that appears most often in a data set.

28. Define 'proportionate' values
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
1/x^n For example - 6-² = 1/6² = 1/36
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A 90-degree angle.

29. Define a factorial of a number - and how it is written.
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.
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. 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
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.

30. For a bell curve - what three terms might be used to describe the number in the middle?
x²-y²
(x+y)(x-y)
The average - mean - median - or mode.
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

31. An integer is divisible by 3 if...
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.
2pr -or- pd
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Percentage Change = Difference/Original * 100

32. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
90 degrees each.
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.
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.

33. 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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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

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

35. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
An integer is divisible by 2 if its units digit is divisible by 2.
3:4:5 5:12:13
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

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

37. HIGH: Describe how to deal with 2 sets of parentheses.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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)+
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
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

38. How many degrees does a circle contain?
A line is a 180-degree angle.
360 degrees
80%
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.

39. How do you add or subtract fractions?
Find a common denominator and make equivalent fractions. Then add or subtract.
6
Favorable Outcomes/Total 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

40. What is an 'equilateral' triangle?
Find a common denominator and make equivalent fractions. Then add or subtract.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2pr -or- pd
The average - mean - median - or mode.

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

42. HIGH: What is the equation of a line?

43. What is the factored version of x² -2xy + y² ?
(x-y)²
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
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.

44. HIGH: How do you calculate the circumference of a circle?
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
2pr -or- pd
The total # of possible outcomes.
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.

45. What are the side ratios for a 30:60:90 triangle?
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.
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
V=pr²h (This is just the area multiplied by the height)

46. Explain how to calculate an average (arithmetic mean)
(x+y)²
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
Between 0 and 1.

47. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
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.
x²-y²
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

48. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
1.4
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

49. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.

50. List all the prime numbers that are less than 30:
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'.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.