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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: how do you calculate a diagonal inside a 3-dimensional rectangular box?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1/1
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.

2. What causes 80% of errors on the math section of the GRE?
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.
Not reading the problems carefully enough!
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 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.

3. HIGH: What is the mode?
The value that appears most often in a data set.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Groups - teams - or committees.
A radius

4. How do you multiply fractions?
2r
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Multiply numerator times numerator and denominator times denominator.

5. On the GRE - should you ever assume that diagrams are truthful?
2r
x² + 2xy + y²
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

6. What number goes on the bottom of a probability fraction?
A line is a 180-degree angle.
180 degrees.
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
The total # of possible outcomes.

7. Explain how to divide fractions.
4 angles are formed. Their sum is 360 degrees
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.
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

8. How do you calculate the probability of two events in a row? (Probability of A and B)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Probability A * Probability B

9. How is a range expressed with inequalities?
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.
(0 -0)
x² -2xy + y²
Example: 1 < x < 10

10. Simplify this: v32
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
V=pr²h (This is just the area multiplied by the height)
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
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?
Between 0 and 1.
90 degrees each.
An integer is divisible by 5 if its units digit is either 0 or 5.
Probability A * Probability B

12. Convert to a percentage: 1/4
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
25%
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
(x+y)(x-y)

13. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
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.
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.

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

15. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Percentage Change = Difference/Original * 100
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)+

16. Define the mode of a set of numbers.
2r
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.
60%
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)+

17. If something is certain to happen - how is the probability of this event expressed mathematically?
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'.
1/1
(x-y)²
A line is a 180-degree angle.

18. HIGH: What is the factored version of (x+y)(x-y) ?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
2pr -or- pd
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
x²-y²

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

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

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

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

23. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
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.
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

24. Probability Formula
180 degrees
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Favorable Outcomes/Total Possible Outcomes
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

25. What is the formula to determine probability?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
(x+y)(x-y)
1/x^n For example - 6-² = 1/6² = 1/36
x²-y²

26. For a bell curve - what three terms might be used to describe the number in the middle?
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.
The average - mean - median - or mode.
1.7
S*v2

27. What do permutation problems often ask for?
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.
Arrangements - orders - schedules - or lists.
25%
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%.

28. Define the range of a set of numbers.
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

29. HIGH: what is the side ratio for a Right Isosceles triangle?
(0 -0)
2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(a+b)(a-b)

30. HIGH: What are the percentages for standard deviation?
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 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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

31. What is the 'Third side' rule for triangles?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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. Given event A: A + notA = 1.
Find the total - or whole - first - and then set up a Ratio Box.

32. HIGH: What is the Pythagorean theorem?

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

34. Convert to a percentage: 2/5
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.
40%
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
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.

35. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
x² + 2xy + y²
Favorable Outcomes/Total Possible Outcomes

36. Explain how to use a 'Rate Pie'
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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
360 degrees
The average - mean - median - or mode.

37. HIGH: What is the formula for the diagonal of any square?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/1
360 degrees
S*v2

38. HIGH: What is the order of math operations - and the mnemonic to remember it?
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.
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
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

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

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

41. List two odd behaviors of exponents
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.
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.
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.
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

42. Convert to a percentage: 4/5
Probability A + Probability B
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.
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
80%

43. In a coordinate system - identify the quadrants and describe their location.
A triangle in which one of the three interior angles is 90 degrees.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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%.

44. HIGH: How do you calculate the circumference of a circle?
(x+y)²
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
x² -2xy + y²
2pr -or- pd

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

46. Convert to a percentage: 3/5
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.
60%
1.7
The # falling in the center of an ordered data set

47. Explain the special properties of zero.
Not necessarily. This is a trick question - because x could be either positive or negative.
(0 -0)
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

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

49. How do you add or subtract fractions?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Find a common denominator and make equivalent fractions. Then add or subtract.
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
Multiply numerator times numerator and denominator times denominator.

50. What is the factored version of x² -2xy + y² ?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
A triangle in which one of the three interior angles is 90 degrees.
60%
(x-y)²