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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. List two odd behaviors of exponents
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
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 6 if it'S divisible by BOTH 2 and 3.

2. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
'Big' angles and 'Small' angles.
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)+
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

3. HIGH: What is the factored version of (x+y)(x-y) ?
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.
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.
x²-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)+

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

5. a² - b² is equal to
(x+y)²
S²
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+b)(a-b)

6. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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%.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

7. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
An integer is divisible by 2 if its units digit is divisible by 2.
2pr -or- pd
90 degrees each.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

8. An integer is divisible by 2 if...
Not reading the problems carefully enough!
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
An integer is divisible by 2 if its units digit is divisible by 2.

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

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

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

12. Define the mode of a set of numbers.
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.
1
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.
Arrangements - orders - schedules - or lists.

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

14. 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.
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
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'.
Percentage Change = Difference/Original * 100

15. What degree angle is a line?
A line is a 180-degree angle.
360 degrees
1. Given event A: A + notA = 1.
1/x^n For example - 6-² = 1/6² = 1/36

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

17. v4 =
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. 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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

18. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
2r
25%
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

19. How is a range expressed with inequalities?
(x+y)²
Bh
(a+b)(a-b)
Example: 1 < x < 10

20. What is the name of a line that extends from the center of a circle to the edge of a circle?
A radius
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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
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.

21. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
40%
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

22. HIGH: What is the mode?
The # falling in the center of an ordered data set
The value that appears most often in a data set.
6
1

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

24. Explain how to calculate an average (arithmetic mean)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Order does matter for a permutation - but does not matter for a combination.
x² + 2xy + y²
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.

25. 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
4 angles are formed. Their sum is 360 degrees
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

26. Probability Formula
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%.
Favorable Outcomes/Total Possible Outcomes
(a+b)(a-b)
360 degrees

27. HIGH: What is a 'Right isosceles' triangle?
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 # falling in the center of an ordered data set
80%
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.

28. HIGH: How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

29. HIGH: Rough est. of v1 =
1
80%
x² + 2xy + y²
Example: 1 < x < 10

30. HIGH: What is the unfactored version of (x-y)² ?
4 angles are formed. Their sum is 360 degrees
x²-y²
x² -2xy + y²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

31. HIGH: What is the median?
6
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.
The # falling in the center of an ordered data set
S²

32. What'S the most important thing to remember about charts you'll see on the GRE?
x² + 2xy + y²
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.
Bh
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.

33. In a coordinate system - identify the quadrants and describe their location.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
S²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

34. HIGH: x^-n is equal to
Multiply numerator times numerator and denominator times denominator.
1/x^n For example - 6-² = 1/6² = 1/36
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
6

35. HIGH: Area of a circle
Groups - teams - or committees.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Order does matter for a permutation - but does not matter for a combination.
A=pr²

36. What is the equation for a group problem?
A circle'S perimeter is roughly 3x its diameter (the formula is 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
40%
A=pr²

37. What causes 80% of errors on the math section of the GRE?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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
Not reading the problems carefully enough!
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

38. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
Favorable Outcomes/Total Possible Outcomes
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

39. What is an 'equilateral' triangle?
90 degrees each.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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

40. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
Not reading the problems carefully enough!
2pr -or- pd
An integer is divisible by 9 if the sum of its digits is divisible by 9.

41. How do you solve a permutation?
x² + 2xy + y²
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
(x-y)²
25%

42. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
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.
Probability A + Probability B
2pr -or- pd

43. What is the formula to determine probability?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
40%
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

44. Explain how to use an 'Average Pie'
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
x² -2xy + y²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

45. HIGH: How do you calculate the circumference of a circle?
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.
2pr -or- pd
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 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.

46. Convert to a percentage: 2/5
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
40%
A line is a 180-degree angle.
Find the total - or whole - first - and then set up a Ratio Box.

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

48. How do you multiply fractions?
1.4
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.

49. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
The average - mean - median - or mode.
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. 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
Between 0 and 1.

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