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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. Area of a square?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
V=pr²h (This is just the area multiplied by the height)
S²
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.

2. What'S the most important thing to remember about charts you'll see on the GRE?
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.
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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)+

3. Simplify this: v32
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.
x²-y²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Find the total - or whole - first - and then set up a Ratio Box.

4. HIGH: how do you calculate the surface area of a rectangular box?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

5. Define a factorial of a number - and how it is written.
The total # of possible outcomes.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
(0 -0)
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.

6. HIGH: What is the unfactored version of (x-y)² ?
Bh
40%
S²
x² -2xy + y²

7. 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
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
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
The average - mean - median - or mode.

8. What do permutation problems often ask for?
(x+y)²
Arrangements - orders - schedules - or lists.
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.

9. List two odd behaviors of exponents
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.
25%
Example: 1 < x < 10
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

10. Convert to a percentage: 2/5
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.
40%
An integer is divisible by 2 if its units digit is divisible by 2.
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.

11. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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
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 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.

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

13. Area of a parallelogram?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
180 degrees
(x+y)(x-y)
Bh

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

15. What degree angle is a line?
A line is a 180-degree angle.
Probability A + Probability 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.
Invert the second fraction (reciprocal) and multiply

16. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

17. How do you solve a permutation?
S*v2
Bh
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
It will be a great advantage on test day to have your times table memorized from 1 through 15.

18. HIGH: What is the unfactored version of (x+y)² ?
360 degrees
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
x² + 2xy + y²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

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

20. HIGH: Rough est. of v2 =
Groups - teams - or committees.
1.4
(0 -0)
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

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

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. Explain the special properties of zero.
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.
Probability A * Probability B
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

24. HIGH: What is the Pythagorean theorem?

25. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
60%
3:4:5 5:12:13
1/x^n For example - 6-² = 1/6² = 1/36

26. v4 =
2
90 degrees each.
Bh
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

27. HIGH: Define the formula for calculating slope.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
25%
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

28. What number goes on the bottom of a probability fraction?
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
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
The total # of possible outcomes.

29. How do you divide fractions?
Invert the second fraction (reciprocal) and multiply
Between 0 and 1.
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
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

30. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
V=s³
(x+y)(x-y)
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

31. What is the 'Third side' rule for triangles?
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.
90 degrees each.
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 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.

32. HIGH: To divide powers with the same base...
Bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(0 -0)
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.

33. What is an 'equilateral' triangle?
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%.
Not necessarily. This is a trick question - because x could be either positive or negative.
1.4
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

34. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x²-y²
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.

35. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
1.7
The average - mean - median - or mode.
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.

36. Explain how to use an 'Average Pie'
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
4 angles are formed. Their sum is 360 degrees
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

37. HIGH: What is the median?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
The # falling in the center of an ordered data set
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.
6

38. The three exterior angles of a triangle add up to...
Find a common denominator and make equivalent fractions. Then add or subtract.
A line is a 180-degree angle.
360 degrees
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

39. List all the prime numbers that are less than 30:
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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%.
Arrangements - orders - schedules - or lists.
4 angles are formed. Their sum is 360 degrees

40. HIGH: How do you multiply and divide square roots?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Absolute value is a number'S distance away from zero on the number line. It is always positive - regardless of whether the number is positive or negative. It is represented with | |. For example - |-5| = 5 - and |5| = 5.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
S*v2

41. HIGH: Volume of a cube?
V=s³
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.
x² + 2xy + y²
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

42. HIGH: What is the side ratio for a 30:60:90 triangle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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'.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Probability A + Probability B

43. 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.
x² + 2xy + y²
V=pr²h (This is just the area multiplied by the height)
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

44. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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
(x+y)(x-y)

45. HIGH: Rough est. of v3 =
x² -2xy + y²
1.7
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

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

47. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.

48. Probability Formula
Not necessarily. This is a trick question - because x could be either positive or negative.
Favorable Outcomes/Total Possible Outcomes
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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)+

49. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
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.
1.4
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.
Probability A + Probability B

50. What causes 80% of errors on the math section of the GRE?
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
60%
Not reading the problems carefully enough!