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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 degree angle is a line?
Percentage Change = Difference/Original * 100
1. Given event A: A + notA = 1.
V=pr²h (This is just the area multiplied by the height)
A line is a 180-degree angle.

2. HIGH: What is the factored version of (x+y)(x-y) ?
Groups - teams - or committees.
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.
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.
x²-y²

3. List all the prime numbers that are less than 30:
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

4. How do you divide fractions?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 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
Invert the second fraction (reciprocal) and multiply
360 degrees

5. Explain how to use an 'Average Pie'
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(x+y)²

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

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

8. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
'Big' angles and 'Small' angles.
Order does matter for a permutation - but does not matter for a combination.
1/x^n For example - 6-² = 1/6² = 1/36

9. Explain how to solve for 7/¼
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
It will be a great advantage on test day to have your times table memorized from 1 through 15.

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

11. 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.
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
A radius

12. Explain how to divide fractions.
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.
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(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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

13. HIGH: What is the median?
The # falling in the center of an ordered data set
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.

14. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Order does matter for a permutation - but does not matter for a combination.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
60%

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

16. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
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
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.
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.

17. a² - b² is equal to
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
(a+b)(a-b)
It will be a great advantage on test day to have your times table memorized from 1 through 15.

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

19. HIGH: How do you multiply powers with the same base?
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
360 degrees

20. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

21. v4 =
2
x²-y²
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

22. Does order matter for a permutation? How about for a combination?
Probability A * Probability B
40%
Order does matter for a permutation - but does not matter for a combination.
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

23. HIGH: Rough est. of v1 =
An integer is divisible by 9 if the sum of its digits is divisible by 9.
1
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
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.

24. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
Not necessarily. This is a trick question - because x could be either positive or negative.
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
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.

25. In a coordinate system - identify the quadrants and describe their location.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
360 degrees
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
180 degrees

26. HIGH: What is the mode?
Find a common denominator and make equivalent fractions. Then add or subtract.
60%
1/x^n For example - 6-² = 1/6² = 1/36
The value that appears most often in a data set.

27. Define the mode of a set of numbers.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
(x-y)²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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: Area of a triangle?
An integer is divisible by 5 if its units digit is either 0 or 5.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Percentage Change = Difference/Original * 100
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

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

30. How do you add or subtract fractions?
A=pr²
80%
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Find a common denominator and make equivalent fractions. Then add or subtract.

31. What are 'vertical angles'?
V=s³
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
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A triangle in which one of the three interior angles is 90 degrees.

32. What is the key to dealing with ratio questions?
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.
Find the total - or whole - first - and then set up a Ratio Box.
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.
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.

33. HIGH: What is the formula for the diagonal of any square?
S*v2
(x+y)²
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

34. Solve this: v6 * -v6 = ?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
6
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

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

36. The three exterior angles of a triangle add up to...
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
360 degrees
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

37. In a coordinate system - what is the origin?
(0 -0)
x² + 2xy + y²
Order does matter for a permutation - but does not matter for a combination.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

38. HIGH: Simplify this: v75/v27
(x+y)(x-y)
Arrangements - orders - schedules - or lists.
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

39. Explain the difference between handling a permutation versus a combination.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
Multiply numerator times numerator and denominator times denominator.
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. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
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 # falling in the center of an ordered data set
360 degrees

41. How do you solve a permutation?
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.
The total # of possible outcomes.
Multiply numerator times numerator and denominator times denominator.
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

42. How do you solve a combination?

43. HIGH: How much of your times table should you know - for the GRE?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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'.
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.
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.

44. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
S*v2
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

45. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?

46. HIGH: What is the unfactored version of (x-y)² ?
x² -2xy + y²
1
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.

47. An integer is divisible by 5 if...
80%
An integer is divisible by 5 if its units digit is either 0 or 5.
6
Example: 1 < x < 10

48. Area of a parallelogram?
x²-y²
Bh
The average - mean - median - or mode.
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.

49. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
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
V=s³
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
90 degrees each.

50. For a bell curve - what three terms might be used to describe the number in the middle?
S*v2
6
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The average - mean - median - or mode.