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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: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Not reading the problems carefully enough!
(0 -0)

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

3. What are the side ratios for a 30:60:90 triangle?
Example: 1 < x < 10
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.

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

5. HIGH: Rough est. of v1 =
Percentage Change = Difference/Original * 100
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 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.
1

6. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
2r
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
Between 0 and 1.

7. The three interior angles of a triangle add up to...
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.
60%
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
180 degrees

8. HIGH: List the two most common side ratios for right triangles
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 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
3:4:5 5:12:13
(x+y)(x-y)

9. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
180 degrees
360 degrees
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

10. HIGH: what is the side ratio for a Right Isosceles triangle?
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
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
90 degrees each.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

11. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

12. Area of a square?
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.
S²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
V=s³

13. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
Not necessarily. This is a trick question - because x could be either positive or negative.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
4 angles are formed. Their sum is 360 degrees
The average - mean - median - or mode.

14. An integer is divisible by 5 if...
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
60%
An integer is divisible by 5 if its units digit is either 0 or 5.
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%.

15. HIGH: What is the mode?
The value that appears most often in a data set.
An integer is divisible by 2 if its units digit is divisible by 2.
2r
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

16. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A radius
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

17. What is the 'Third side' rule for triangles?
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
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.
An integer is divisible by 2 if its units digit is divisible by 2.
360 degrees

18. HIGH: What is a '30:60:90' triangle?
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.
Groups - teams - or committees.
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
S*v2

19. HIGH: What is the factored version of (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.
x²-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.
(x+y)²

20. An integer is divisible by 3 if...
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.
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 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.
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.

21. HIGH: What is the factored version of 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.
1. Given event A: A + notA = 1.
(x+y)²
Order does matter for a permutation - but does not matter for a combination.

22. What'S the most important thing to remember about charts you'll see on the GRE?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
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.

23. HIGH: how do you calculate the surface area of a rectangular box?
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
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. HIGH: How much of your times table should you know - for the GRE?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
(0 -0)
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.
An integer is divisible by 2 if its units digit is divisible by 2.

25. What number goes on the bottom of a probability fraction?
90 degrees each.
V=s³
1/x^n For example - 6-² = 1/6² = 1/36
The total # of possible outcomes.

26. On the GRE - should you ever assume that diagrams are truthful?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
1.4
360 degrees
Percentage Change = Difference/Original * 100

27. What is the key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
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.
Not reading the problems carefully enough!
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

28. HIGH: Describe how to deal with 2 sets of parentheses.
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 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.
(0 -0)
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

29. What is an 'equilateral' triangle?
Example: 1 < x < 10
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Probability A + Probability B
(a+b)(a-b)

30. 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.
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
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
(x+y)(x-y)

31. HIGH: Area of a circle
A=pr²
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.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

32. The three exterior angles of a triangle add up to...
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
360 degrees
S*v2
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

33. HIGH: What is the Pythagorean theorem?

34. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Not necessarily. This is a trick question - because x could be either positive or negative.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

35. How do you solve a permutation?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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

36. HIGH: What are the percentages for standard deviation?
A radius
S²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

37. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
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
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.

38. HIGH: What is the unfactored version of x²-y² ?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
180 degrees.
(x+y)(x-y)

39. Convert to a percentage: 1/4
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.
25%
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

40. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
S²
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.
Not reading the problems carefully enough!
Not necessarily. This is a trick question - because x could be either positive or negative.

41. Explain how to use a 'Rate Pie'
The total # of possible outcomes.
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
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.
3:4:5 5:12:13

42. How many degrees does a circle contain?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
2
360 degrees
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

43. HIGH: Volume of a cylinder?
2r
V=pr²h (This is just the area multiplied by the height)
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.
x²-y²

44. What is the equation for a group problem?
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
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
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
360 degrees

45. HIGH: What is the order of math operations - and the mnemonic to remember it?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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
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.
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.

46. How do you add or subtract fractions?
Find a common denominator and make equivalent fractions. Then add or subtract.
V=s³
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
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.

47. v4 =
The average - mean - median - or mode.
Multiply numerator times numerator and denominator times denominator.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2

48. Simplify this: v32
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. 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
Invert the second fraction (reciprocal) and multiply
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

49. How do you solve a combination?

50. 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.
A radius
6
The total # of possible outcomes.