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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. How do you calculate the percentage of change?
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.
1/1
Percentage Change = Difference/Original * 100
V=pr²h (This is just the area multiplied by the height)

2. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1/1
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.
Order does matter for a permutation - but does not matter for a combination.

3. What are 'vertical angles'?
4 angles are formed. Their sum is 360 degrees
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Groups - teams - or committees.
1/1

4. HIGH: Volume of a cylinder?
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%
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.
V=pr²h (This is just the area multiplied by the height)

5. Explain how to solve for 7/¼
A=pr²
An integer is divisible by 5 if its units digit is either 0 or 5.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
4 angles are formed. Their sum is 360 degrees

6. Area of a parallelogram?
Arrangements - orders - schedules - or lists.
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.
Bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

7. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
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.
90 degrees each.
(x+y)²
2pr -or- pd

8. An integer is divisible by 2 if...
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 2 if its units digit is divisible by 2.
An integer is divisible by 5 if its units digit is either 0 or 5.

9. 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.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Example: 1 < x < 10

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

11. HIGH: What is the unfactored version of (x-y)² ?
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 radius
x² -2xy + y²
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

12. List all the prime numbers that are less than 30:
(x+y)²
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 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

13. What is the 'Third side' rule for triangles?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.
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
6

14. What is the formula to determine probability?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

15. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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
S*v2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1. Given event A: A + notA = 1.

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

17. How do you add or subtract fractions?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
Probability A * Probability B

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

19. What is the key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
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 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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.

20. HIGH: What is the side ratio for a 30:60:90 triangle?
Example: 1 < x < 10
Not necessarily. This is a trick question - because x could be either positive or negative.
1. Given event A: A + notA = 1.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

21. HIGH: Volume of a cube?
Multiply numerator times numerator and denominator times denominator.
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
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.
V=s³

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

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

24. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
360 degrees
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.
1.7
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

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

26. Convert to a percentage: 3/5
Percentage Change = Difference/Original * 100
60%
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Order does matter for a permutation - but does not matter for a combination.

27. What is the sum of any 'big' angle and any 'Small' angle?
Favorable Outcomes/Total Possible Outcomes
S*v2
1/1
180 degrees.

28. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
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)+
Probability A + Probability B
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.

29. What is a 'Right' triangle?
A triangle in which one of the three interior angles is 90 degrees.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.

30. HIGH: Area of a circle
A=pr²
3:4:5 5:12:13
2
x²-y²

31. HIGH: Rough est. of v2 =
x² -2xy + y²
90 degrees each.
V=s³
1.4

32. The three interior angles of a triangle add up to...
180 degrees
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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
Example: 1 < x < 10

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

34. What causes 80% of errors on the math section of the GRE?
(x+y)(x-y)
Not reading the problems carefully enough!
60%
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.

35. Convert to a percentage: 4/5
80%
2pr -or- pd
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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. HIGH: Area of a triangle?
180 degrees.
1
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
A 90-degree angle.

37. How do you solve a combination?

38. Explain how to use a 'Rate Pie'
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=pr²
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.
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

39. What is the factored version of x² -2xy + y² ?
1/x^n For example - 6-² = 1/6² = 1/36
2pr -or- pd
Order does matter for a permutation - but does not matter for a combination.
(x-y)²

40. How do you calculate the probability of two events in a row? (Probability of A and B)
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
(x+y)²
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Probability A * Probability B

41. List two odd behaviors of exponents
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
A 90-degree angle.

42. How precise do you need to be - using p on the GRE?

43. HIGH: how do you calculate the surface area of a rectangular box?
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.
2pr -or- pd
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 2 if its units digit is divisible by 2.

44. HIGH: Describe how to deal with 2 sets of parentheses.
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.
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.
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.
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)+

45. HIGH: What is the median?
Not reading the problems carefully enough!
The # falling in the center of an ordered data set
Example: 1 < x < 10
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.

46. In a coordinate system - identify the quadrants and describe their location.
A triangle in which one of the three interior angles is 90 degrees.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.

47. How do you solve a permutation?
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
x² -2xy + y²
The total # of possible outcomes.

48. Explain how to calculate an average (arithmetic mean)
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 total # of possible outcomes.
Not necessarily. This is a trick question - because x could be either positive or negative.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

49. An integer is divisible by 9 if...
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.
180 degrees
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.

50. HIGH: What is the formula for the diagonal of any square?
2r
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
S*v2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.