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GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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. Explain how to divide fractions.
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
The value that appears most often in a data set.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

2. HIGH: What are the percentages for standard deviation?
A line is a 180-degree angle.
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
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

3. Define 'proportionate' values
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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

4. HIGH: How do you calculate the circumference of a circle?
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.
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
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

5. Define a factorial of a number - and how it is written.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

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

7. HIGH: Describe how to deal with 2 sets of parentheses.
180 degrees.
A line is a 180-degree angle.
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)+
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.

8. HIGH: List the two most common side ratios for right triangles
2r
A radius
3:4:5 5:12:13
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.

9. Explain the difference between handling a permutation versus a combination.
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
The total # of possible outcomes.

10. What is the name of a line that extends from the center of a circle to the edge of a circle?
Invert the second fraction (reciprocal) and multiply
A radius
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.
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

11. HIGH: What is the unfactored version of (x-y)² ?
1
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.
x² -2xy + y²
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.

12. Area of a parallelogram?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
S²
Bh
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.

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

14. An integer is divisible by 3 if...
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.
40%
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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

15. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
V=s³
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

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

17. HIGH: What is the unfactored version of (x+y)² ?
4 angles are formed. Their sum is 360 degrees
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
x² + 2xy + y²

18. HIGH: Rough est. of v2 =
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1.4
Invert the second fraction (reciprocal) and multiply
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

19. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Arrangements - orders - schedules - or lists.
x²-y²

20. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
1.7
Example: 1 < x < 10
180 degrees

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

22. HIGH: What is the formula for the diagonal of any square?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
90 degrees each.
S*v2
Find the total - or whole - first - and then set up a Ratio Box.

23. What is the formula to determine probability?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Multiply numerator times numerator and denominator times denominator.
A 90-degree angle.
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

24. An integer is divisible by 2 if...
Arrangements - orders - schedules - or lists.
An integer is divisible by 2 if its units digit is divisible by 2.
The total # of possible outcomes.
A triangle in which one of the three interior angles is 90 degrees.

25. How do you divide fractions?
The average - mean - median - or mode.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Invert the second fraction (reciprocal) and multiply
The value that appears most often in a data set.

26. HIGH: What is a 'Right isosceles' triangle?
A radius
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.
A=pr²
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.

27. What is the 'distributive law'?
A radius
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
1/1
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.

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

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

30. The three interior angles of a triangle add up to...
80%
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(x-y)²
180 degrees

31. HIGH: What is the factored version of x² + 2xy + y² ?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
x² -2xy + y²
(x+y)²
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. The three exterior angles of a triangle add up to...
The total # of possible outcomes.
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.
180 degrees.
360 degrees

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

34. Convert to a percentage: 4/5
80%
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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

35. Convert to a percentage: 3/5
(x+y)(x-y)
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.
Invert the second fraction (reciprocal) and multiply
60%

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

37. List all the prime numbers that are less than 30:
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Find a common denominator and make equivalent fractions. Then add or subtract.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

38. What'S the most important thing to remember about charts you'll see on the GRE?
x²-y²
Invert the second fraction (reciprocal) and multiply
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.
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.

39. Solve this: v6 * -v6 = ?
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.
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
6
A 90-degree angle.

40. HIGH: Area of a triangle?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

41. If something is possible but not certain - what is the numeric range of probability of it happening?
A 90-degree angle.
Between 0 and 1.
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=pr²

42. HIGH: Volume of a cube?
V=s³
An integer is divisible by 2 if its units digit is divisible by 2.
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 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

43. HIGH: What is the 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.
The value that appears most often in a data set.
Percentage Change = Difference/Original * 100
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.

44. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
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.
Multiply numerator times numerator and denominator times denominator.
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'.

45. Explain how to calculate an average (arithmetic mean)
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
180 degrees
S²

46. HIGH: How do you multiply and divide square roots?
Invert the second fraction (reciprocal) and multiply
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
It will be a great advantage on test day to have your times table memorized from 1 through 15.
A line is a 180-degree angle.

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

48. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
Multiply numerator times numerator and denominator times denominator.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
An integer is divisible by 5 if its units digit is either 0 or 5.
4 angles are formed. Their sum is 360 degrees

49. What do permutation problems often ask for?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Arrangements - orders - schedules - or lists.
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)+

50. 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.
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.
Find a common denominator and make equivalent fractions. Then add or subtract.