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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. HIGH: Volume of a cylinder?
1
V=pr²h (This is just the area multiplied by the height)
Bh
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.

2. HIGH: What is the factored version of x² + 2xy + y² ?
360 degrees
Multiply numerator times numerator and denominator times denominator.
Find a common denominator and make equivalent fractions. Then add or subtract.
(x+y)²

3. What are 'vertical angles'?
Find a common denominator and make equivalent fractions. Then add or subtract.
2
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.

4. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
V=s³

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

6. 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.
1.7
Between 0 and 1.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

7. Area of a square?
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%.
Order does matter for a permutation - but does not matter for a combination.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
S²

8. 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/x^n For example - 6-² = 1/6² = 1/36
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.
Order does matter for a permutation - but does not matter for a combination.

9. What number goes on the bottom of a probability fraction?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
The total # of possible outcomes.
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. 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

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

11. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
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%.
Find the total - or whole - first - and then set up a Ratio Box.

12. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
90 degrees each.
Groups - teams - or committees.

13. HIGH: x^-n is equal to
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/x^n For example - 6-² = 1/6² = 1/36
An integer is divisible by 2 if its units digit is divisible by 2.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

14. What is a 'Right' triangle?
(x+y)(x-y)
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 triangle in which one of the three interior angles is 90 degrees.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

15. Explain the special properties of zero.
25%
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.

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

17. HIGH: how do you calculate the surface area of a rectangular box?
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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 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.

18. For a bell curve - what three terms might be used to describe the number in the middle?
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.
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.
The average - mean - median - or mode.
80%

19. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
(x+y)²

20. HIGH: Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
x²-y²
A line is a 180-degree angle.

21. HIGH: How do you calculate the circumference of a circle?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
80%
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
2pr -or- pd

22. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
Invert the second fraction (reciprocal) and multiply
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.
4 angles are formed. Their sum is 360 degrees
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

23. Explain how to divide fractions.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

24. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

25. How do you calculate the probability of two events in a row? (Probability of A and B)
2r
Probability A * Probability B
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
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

26. HIGH: What is the order of math operations - and the mnemonic to remember it?
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
4 angles are formed. Their sum is 360 degrees
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Percentage Change = Difference/Original * 100

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

28. How do you solve a combination?

29. What do permutation problems often ask for?
80%
The total # of possible outcomes.
2r
Arrangements - orders - schedules - or lists.

30. v4 =
2
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 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

31. HIGH: Rough est. of v1 =
Groups - teams - or committees.
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
1.4

32. HIGH: What is the median?
x² -2xy + y²
The # falling in the center of an ordered data set
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
60%

33. HIGH: Rough est. of v3 =
2
The average - mean - median - or mode.
180 degrees.
1.7

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

35. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
The average - mean - median - or mode.
6
2

36. Area of a parallelogram?
3:4:5 5:12:13
180 degrees.
1
Bh

37. The three exterior angles of a triangle add up to...
360 degrees
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.
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.
Multiply numerator times numerator and denominator times denominator.

38. What is the factored version of x² -2xy + y² ?
The total # of possible outcomes.
(x-y)²
4 angles are formed. Their sum is 360 degrees
6

39. Explain how to solve for 7/¼
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
A line is a 180-degree angle.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

40. HIGH: Simplify this: v75/v27
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'.
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.
Favorable Outcomes/Total Possible Outcomes
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%.

41. The three interior angles of a triangle add up to...
3:4:5 5:12:13
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.
180 degrees
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.

42. Solve this: v6 * -v6 = ?
A triangle in which one of the three interior angles is 90 degrees.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
6
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.

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

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

45. How do you divide fractions?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
1/1
Invert the second fraction (reciprocal) and multiply
Not reading the problems carefully enough!

46. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
Invert the second fraction (reciprocal) and multiply
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
S*v2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

47. Explain how to calculate an average (arithmetic mean)
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Arrangements - orders - schedules - or lists.
V=s³
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

48. HIGH: What is the unfactored version of (x-y)² ?
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 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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
x² -2xy + y²

49. How is a range expressed with inequalities?
Example: 1 < x < 10
A=pr²
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
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

50. HIGH: What are the percentages for standard deviation?
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.
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
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
(0 -0)