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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. Convert to a percentage: 2/5
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.
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.
40%
Multiply numerator times numerator and denominator times denominator.

2. What is an 'equilateral' triangle?
(0 -0)
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
90 degrees each.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

3. a² - b² is equal to
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
(a+b)(a-b)
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

4. 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.
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 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
3:4:5 5:12:13

5. HIGH: Volume of a cube?
'Big' angles and 'Small' angles.
V=s³
60%
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%.

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

7. Explain how to use an 'Average Pie'
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

8. What is the sum of any 'big' angle and any 'Small' angle?
A line is a 180-degree angle.
2pr -or- pd
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
180 degrees.

9. How do you solve a combination?

10. Convert to a percentage: 3/5
60%
360 degrees
6
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

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

12. HIGH: Define the formula for calculating slope.
(a+b)(a-b)
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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

13. HIGH: Simplify this: v75/v27
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.
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%.
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.
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.

14. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Order does matter for a permutation - but does not matter for a combination.
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
A=pr²

15. Diameter of a circle?
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.
(x-y)²
2r
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

16. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Probability A + Probability B
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.

17. HIGH: x^-n is equal to
Order does matter for a permutation - but does not matter for a combination.
The value that appears most often in a data set.
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.
1/x^n For example - 6-² = 1/6² = 1/36

18. Explain the special properties of zero.
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
S*v2
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.

19. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
'Big' angles and 'Small' angles.

20. Area of a square?
1
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'.
S²
S*v2

21. HIGH: how do you calculate the surface area of a rectangular box?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

22. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Multiply numerator times numerator and denominator times denominator.
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
360 degrees
1. Given event A: A + notA = 1.

23. HIGH: Rough est. of v1 =
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
90 degrees each.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
1

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

25. How many degrees does a circle contain?
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.
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'.
360 degrees

26. What is the factored version of x² -2xy + y² ?
(x-y)²
Not necessarily. This is a trick question - because x could be either positive or negative.
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%.
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

27. Solve this: v6 * -v6 = ?
Percentage Change = Difference/Original * 100
Probability A * Probability B
6
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

28. How is a range expressed with inequalities?
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
Example: 1 < x < 10
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.
The total # of possible outcomes.

29. HIGH: What is the Pythagorean theorem?

30. How do you multiply fractions?
A radius
40%
Multiply numerator times numerator and denominator times denominator.
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.

31. 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
An integer is divisible by 5 if its units digit is either 0 or 5.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1. Given event A: A + notA = 1.

32. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
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)+
The total # of possible outcomes.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

33. In a coordinate system - identify the quadrants and describe their location.
2r
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

34. What is the name of a line that extends from the center of a circle to the edge of a circle?
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.
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.
A radius
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.

35. HIGH: Area of a triangle?
(0 -0)
(x+y)²
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Probability A * Probability B

36. What is the 'distributive law'?
2
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.
1/x^n For example - 6-² = 1/6² = 1/36
90 degrees each.

37. In a coordinate system - what is the origin?
(0 -0)
Probability A + Probability B
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
An integer is divisible by 2 if its units digit is divisible by 2.

38. Define the mode of a set of numbers.
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'.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Arrangements - orders - schedules - or lists.
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.

39. Convert to a percentage: 1/4
x² -2xy + y²
25%
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)+
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

40. If something is certain to happen - how is the probability of this event expressed mathematically?
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)+
1/1
x²-y²
1

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

42. HIGH: Define the 'Third side' rule for triangles

43. Convert to a percentage: 4/5
V=pr²h (This is just the area multiplied by the height)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
80%

44. An integer is divisible by 9 if...
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
An integer is divisible by 9 if the sum of its digits is divisible by 9.

45. 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.
x² -2xy + y²
An integer is divisible by 2 if its units digit is divisible by 2.
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.

46. What is the equation for a group problem?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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

47. Area of a parallelogram?
Bh
2pr -or- pd
(x+y)²
180 degrees

48. If x² = 144 - does v144 = x?
Bh
The average - mean - median - or mode.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.

49. How do you divide 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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Invert the second fraction (reciprocal) and multiply
1/x^n For example - 6-² = 1/6² = 1/36

50. 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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Percentage Change = Difference/Original * 100
The # falling in the center of an ordered data set