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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 is an 'equilateral' triangle?
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
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
S*v2

2. What do permutation problems often ask for?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Invert the second fraction (reciprocal) and multiply
Arrangements - orders - schedules - or lists.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

3. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
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.
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
90 degrees each.

4. Area of a square?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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%.
S²
180 degrees

5. HIGH: How much of your times table should you know - for the GRE?
1. Given event A: A + notA = 1.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Percentage Change = Difference/Original * 100
It will be a great advantage on test day to have your times table memorized from 1 through 15.

6. 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.
x²-y²
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.

7. Solve this: v6 * -v6 = ?
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.
1/1
An integer is divisible by 9 if the sum of its digits is divisible by 9.
6

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

9. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
3:4:5 5:12:13
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

10. What do combination problems usually ask for?
Groups - teams - or committees.
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 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-y²

11. What degree angle is a line?
A=pr²
A line is a 180-degree angle.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Not reading the problems carefully enough!

12. HIGH: What is the unfactored version of (x-y)² ?
A line is a 180-degree angle.
40%
x² -2xy + y²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

13. Explain the difference between handling a permutation versus a combination.
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.
40%
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!

14. HIGH: What is a '30:60:90' triangle?
1
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
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
40%

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

16. HIGH: What is the mode?
Not necessarily. This is a trick question - because x could be either positive or negative.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.
The value that appears most often in a data set.

17. HIGH: Rough est. of v1 =
Invert the second fraction (reciprocal) and multiply
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.
The value that appears most often in a data set.
1

18. Define a factorial of a number - and how it is written.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/x^n For example - 6-² = 1/6² = 1/36
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.

19. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Probability A * Probability B
360 degrees
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
1. Given event A: A + notA = 1.

20. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Order does matter for a permutation - but does not matter for a combination.
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A triangle in which one of the three interior angles is 90 degrees.

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

22. HIGH: What must be true before a quadratic equation can be solved?

23. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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
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.
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

24. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The average - mean - median - or mode.
2r

25. What is the key to dealing with ratio questions?
180 degrees
x² -2xy + y²
Find the total - or whole - first - and then set up a Ratio Box.
90 degrees each.

26. List all the prime numbers that are less than 30:
1.7
40%
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Find the total - or whole - first - and then set up a Ratio Box.

27. Define the mode of a set of numbers.
A radius
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
(x+y)(x-y)
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. HIGH: How do you multiply and divide square roots?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1.4
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

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

30. Area of a parallelogram?
Bh
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 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.
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. HIGH: What is the order of math operations - and the mnemonic to remember it?
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
1.4
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.
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.

32. HIGH: Volume of a cube?
Groups - teams - or committees.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
V=s³

33. What is a 'Right' angle?
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.
A 90-degree angle.
40%
360 degrees

34. HIGH: How do you multiply powers with the same base?
Between 0 and 1.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
2

35. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
An integer is divisible by 5 if its units digit is either 0 or 5.
4 angles are formed. Their sum is 360 degrees
A=pr²
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

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

37. HIGH: What is a 'Right isosceles' triangle?
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.
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
The total # of possible outcomes.
Find a common denominator and make equivalent fractions. Then add or subtract.

38. Explain how to calculate an average (arithmetic mean)
1
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

39. What are the side ratios for a 30:60:90 triangle?
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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.

40. Convert to a percentage: 4/5
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
80%
2r
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.

41. How many degrees does a circle contain?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Find a common denominator and make equivalent fractions. Then add or subtract.
360 degrees
Multiply numerator times numerator and denominator times denominator.

42. What is the 'Third side' rule for triangles?
Between 0 and 1.
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

43. Probability Formula
Favorable Outcomes/Total Possible Outcomes
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(a+b)(a-b)
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.

44. HIGH: What is the side ratio for a 30:60:90 triangle?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

45. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
1/1
80%
Not reading the problems carefully enough!

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

47. HIGH: To divide powers with the same base...
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)+
The average - mean - median - or mode.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1. Given event A: A + notA = 1.

48. In a coordinate system - identify the quadrants and describe their location.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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+b)(a-b)

49. How do you 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.
Probability A * Probability B
Percentage Change = Difference/Original * 100
Invert the second fraction (reciprocal) and multiply

50. HIGH: What is the factored version of (x+y)(x-y) ?
The total # of possible outcomes.
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.
x²-y²
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28