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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: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Invert the second fraction (reciprocal) and multiply
Bh
180 degrees

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

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

4. HIGH: What is the formula for the diagonal of any square?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
S*v2
Groups - teams - or committees.

5. HIGH: What is the Pythagorean theorem?

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

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

8. On the GRE - should you ever assume that diagrams are truthful?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.

9. What do permutation problems often ask for?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
(x+y)(x-y)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Arrangements - orders - schedules - or lists.

10. List all the prime numbers that are less than 30:
Not necessarily. This is a trick question - because x could be either positive or negative.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

11. HIGH: What is the mode?
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 the total - or whole - first - and then set up a Ratio Box.
A=pr²
The value that appears most often in a data set.

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

13. An integer is divisible by 3 if...
Find a common denominator and make equivalent fractions. Then add or subtract.
Favorable Outcomes/Total Possible Outcomes
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

14. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
V=s³
3:4:5 5:12:13
Order does matter for a permutation - but does not matter for a combination.

15. Diameter of a circle?
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.
1/1
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2r

16. Explain how to use an 'Average Pie'
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The value that appears most often in a data set.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

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

18. What is the 'distributive law'?
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
Not reading the problems carefully enough!

19. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
A line is a 180-degree angle.
Not reading the problems carefully enough!
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
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

20. Convert to a percentage: 1/4
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
25%
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
360 degrees

21. 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.
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.
360 degrees
An integer is divisible by 9 if the sum of its digits is divisible by 9.

22. HIGH: What is the unfactored version of (x-y)² ?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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
x² -2xy + y²

23. What number goes on the bottom of a probability fraction?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
The total # of possible outcomes.

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

25. HIGH: To divide powers with the same base...
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 radius
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

26. An integer is divisible by 2 if...
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
An integer is divisible by 2 if its units digit is divisible by 2.
A=pr²
180 degrees

27. v4 =
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
2
180 degrees.

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

29. Explain the special properties of zero.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Between 0 and 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.
(x+y)(x-y)

30. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
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.
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
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Not reading the problems carefully enough!

31. HIGH: What is the median?
The # falling in the center of an ordered data set
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.
Multiply numerator times numerator and denominator times denominator.
40%

32. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
An integer is divisible by 2 if its units digit is divisible by 2.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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'.

33. HIGH: Rough est. of v1 =
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% |
1
60%

34. HIGH: Simplify this: v75/v27
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
Not reading the problems carefully enough!
Groups - teams - or committees.

35. Explain the difference between handling a permutation versus a combination.
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
Between 0 and 1.
360 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.

36. Area of a square?
S²
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.

37. HIGH: x^-n is equal to
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/x^n For example - 6-² = 1/6² = 1/36
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
80%

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

39. What is the 'Third side' rule for triangles?
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.
Not reading the problems carefully enough!
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.
40%

40. In a coordinate system - identify the quadrants and describe their location.
'Big' angles and 'Small' angles.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Probability A * Probability B

41. Define the mode of a set of numbers.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
360 degrees
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.

42. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
180 degrees
4 angles are formed. Their sum is 360 degrees
x²-y²

43. Explain how to divide fractions.
(# 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
'Big' angles and 'Small' angles.
Find the total - or whole - first - and then set up a Ratio Box.

44. Define a factorial of a number - and how it is written.
180 degrees.
1/1
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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

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

46. Define the range of a set of numbers.
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.
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.
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.
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

47. How do you solve a combination?

48. HIGH: How much of your times table should you know - for the GRE?
S²
An integer is divisible by 5 if its units digit is either 0 or 5.
x² + 2xy + y²
It will be a great advantage on test day to have your times table memorized from 1 through 15.

49. An integer is divisible by 9 if...
A=pr²
The value that appears most often in a data set.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

50. HIGH: List the two most common side ratios for right triangles
A triangle in which one of the three interior angles is 90 degrees.
Arrangements - orders - schedules - or lists.
3:4:5 5:12:13
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%.