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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. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
S²

2. Convert to a percentage: 1/4
Multiply numerator times numerator and denominator times denominator.
25%
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

3. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
S²
360 degrees
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. 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

4. How do you calculate the probability of two events in a row? (Probability of A and B)
2pr -or- pd
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.
Probability A * Probability B
80%

5. HIGH: What is a 'Right isosceles' triangle?
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.
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
25%
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

6. Define 'proportionate' values
A line is a 180-degree angle.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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
6

7. a² - b² is equal to
(a+b)(a-b)
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.
Invert the second fraction (reciprocal) and multiply
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.

8. Area of a square?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Favorable Outcomes/Total 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.
S²

9. What is the 'distributive law'?
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.
(x+y)²
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
6

10. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
(x+y)(x-y)
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

11. How do you solve a permutation?
(x-y)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
A=pr²
Percentage Change = Difference/Original * 100

12. HIGH: List the two most common side ratios for right triangles
S*v2
1.7
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
3:4:5 5:12:13

13. HIGH: What are the percentages for standard deviation?
360 degrees
1.4
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Favorable Outcomes/Total Possible Outcomes

14. HIGH: Area of a triangle?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
A line is a 180-degree angle.
Probability A + Probability B

15. HIGH: how do you calculate the surface area of a rectangular box?
The average - mean - median - or mode.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.

16. An integer is divisible by 5 if...
Order does matter for a permutation - but does not matter for a combination.
2
An integer is divisible by 5 if its units digit is either 0 or 5.
Find the total - or whole - first - and then set up a Ratio Box.

17. An integer is divisible by 9 if...
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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
1/1
1. Given event A: A + notA = 1.

18. HIGH: Define the formula for calculating slope.
1. Given event A: A + notA = 1.
The total # of possible outcomes.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

19. 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
6
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.
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

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

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

22. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
x² -2xy + y²
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.
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%.

23. Area of a parallelogram?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Bh
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
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

24. What are the side ratios for a 30:60:90 triangle?
V=s³
A 90-degree angle.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

25. Define the mode of a set of numbers.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
'Big' angles and 'Small' angles.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

26. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 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.
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

27. What is a 'Right' triangle?
(x-y)²
360 degrees
A triangle in which one of the three interior angles is 90 degrees.
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%.

28. For a bell curve - what three terms might be used to describe the number in the middle?
Not reading the problems carefully enough!
The average - mean - median - or mode.
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

29. Probability Formula
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.
A 90-degree angle.
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.
Favorable Outcomes/Total Possible Outcomes

30. List two odd behaviors of exponents
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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
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.

31. HIGH: What is the side ratio for a 30:60:90 triangle?
1.7
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

32. How do you calculate the percentage of change?
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
Percentage Change = Difference/Original * 100
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Multiply numerator times numerator and denominator times denominator.

33. How many degrees does a circle contain?
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.
Percentage Change = Difference/Original * 100
360 degrees
S²

34. In a coordinate system - what is the origin?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(0 -0)
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.
A 90-degree angle.

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

36. Solve this: v6 * -v6 = ?
6
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
V=s³
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.

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

38. What is the factored version of x² -2xy + y² ?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Order does matter for a permutation - but does not matter for a combination.
(x-y)²

39. HIGH: What is the Pythagorean theorem?

40. HIGH: Rough est. of v1 =
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
Favorable Outcomes/Total Possible Outcomes
1

41. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
180 degrees
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
60%
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.

42. What kind of triangle is this: has two sides of equal length - and a 90 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)+
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

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

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

45. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
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.
(x+y)²
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

46. HIGH: What is the median?
The # falling in the center of an ordered data set
Order does matter for a permutation - but does not matter for a combination.
1.4
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'.

47. If something is possible but not certain - what is the numeric range of probability of it happening?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Between 0 and 1.

48. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

49. HIGH: Volume of a cylinder?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
(x+y)(x-y)
V=pr²h (This is just the area multiplied by the height)

50. Diameter of a circle?
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.
Not reading the problems carefully enough!
2r
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.