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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 side ratio for a 30:60:90 triangle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
180 degrees
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.
4 angles are formed. Their sum is 360 degrees

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

3. HIGH: What is a '30:60:90' triangle?
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
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.
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

4. What is the 'distributive law'?
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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 6 if it'S divisible by BOTH 2 and 3.

5. HIGH: To divide powers with the same base...
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x 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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

6. Convert to a percentage: 4/5
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.
Order does matter for a permutation - but does not matter for a combination.
80%
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

7. Explain the special properties of zero.
An integer is divisible by 2 if its units digit is divisible by 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
1. Given event A: A + notA = 1.
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.

8. Simplify this: v32
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
x² + 2xy + y²
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

9. Define a factorial of a number - and how it is written.
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.
180 degrees.
x² -2xy + y²
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)+

10. 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
2r
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.
Order does matter for a permutation - but does not matter for a combination.

11. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
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
Order does matter for a permutation - but does not matter for a combination.
90 degrees each.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

12. HIGH: What is a 'Right isosceles' triangle?
1. Given event A: A + notA = 1.
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.
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.
(x+y)²

13. What'S the most important thing to remember about charts you'll see on the GRE?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
360 degrees
1
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.

14. Define the range of a set of numbers.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.

15. Solve this: v6 * -v6 = ?
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
1. Given event A: A + notA = 1.
6

16. If something is possible but not certain - what is the numeric range of probability of it happening?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
'Big' angles and 'Small' angles.
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.
Between 0 and 1.

17. What do permutation problems often 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.
A line is a 180-degree angle.
(x+y)²
Arrangements - orders - schedules - or lists.

18. Convert to a percentage: 1/4
25%
1.4
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%.
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

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

20. Diameter of a circle?
S*v2
2r
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.
Between 0 and 1.

21. An integer is divisible by 3 if...
60%
Multiply numerator times numerator and denominator times denominator.
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.
Percentage Change = Difference/Original * 100

22. How is a range expressed with inequalities?
1
Between 0 and 1.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Example: 1 < x < 10

23. In a coordinate system - identify the quadrants and describe their location.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Percentage Change = Difference/Original * 100
Order does matter for a permutation - but does not matter for a combination.

24. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Order does matter for a permutation - but does not matter for a combination.
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
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.
Probability A + Probability B

25. Does order matter for a permutation? How about for a combination?
x² -2xy + y²
Order does matter for a permutation - but does not matter for a combination.
(0 -0)
(x+y)²

26. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
1
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%.

27. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A line is a 180-degree angle.
Example: 1 < x < 10
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.

28. What is the key to dealing with ratio questions?
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
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)+
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.
Find the total - or whole - first - and then set up a Ratio Box.

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

30. Area of a parallelogram?
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
x² -2xy + y²
Bh
360 degrees

31. How do you calculate the percentage of change?
4 angles are formed. Their sum is 360 degrees
Percentage Change = Difference/Original * 100
Multiply numerator times numerator and denominator times denominator.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

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

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

34. HIGH: Area of a 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.
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

35. What is the factored version of x² -2xy + y² ?
(x-y)²
S*v2
2pr -or- pd
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

36. What is the name of a line that extends from the center of a circle to the edge of a circle?
A line is a 180-degree angle.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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.
A radius

37. What is the 'Third side' rule for triangles?
(x+y)(x-y)
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.
360 degrees
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.

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

39. 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.
A radius
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.
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.

40. HIGH: What are the percentages for standard deviation?
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
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
x² -2xy + y²
Between 0 and 1.

41. How do you solve a combination?

42. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
(0 -0)

43. What are 'vertical angles'?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
1. Given event A: A + notA = 1.
2

44. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
A triangle in which one of the three interior angles is 90 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'.
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

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

46. HIGH: How much of your times table should you know - for the GRE?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
It will be a great advantage on test day to have your times table memorized from 1 through 15.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
A 90-degree angle.

47. What is a 'Right' triangle?
(x+y)(x-y)
'Big' angles and 'Small' angles.
2r
A triangle in which one of the three interior angles is 90 degrees.

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

49. HIGH: What is the formula for the diagonal of any square?
1/x^n For example - 6-² = 1/6² = 1/36
6
Percentage Change = Difference/Original * 100
S*v2

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