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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. How do you calculate the probability of two events in a row? (Probability of A and B)
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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)+
Probability A * Probability B

2. For a bell curve - what three terms might be used to describe the number in the middle?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Not necessarily. This is a trick question - because x could be either positive or negative.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The average - mean - median - or mode.

3. How do you divide fractions?
Example: 1 < x < 10
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Invert the second fraction (reciprocal) and multiply
A radius

4. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
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
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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

5. Define a factorial of a number - and how it is written.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
(0 -0)
x² + 2xy + y²

6. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
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
Find a common denominator and make equivalent fractions. Then add or subtract.

7. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2
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.
90 degrees each.

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

9. 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.
A triangle in which one of the three interior angles is 90 degrees.
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% |

10. What is the key to dealing with ratio questions?
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%
Bh
Find the total - or whole - first - and then set up a Ratio Box.

11. HIGH: List the two most common side ratios for right triangles
180 degrees.
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.
3:4:5 5:12:13
S*v2

12. In a coordinate system - identify the quadrants and describe their location.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Favorable Outcomes/Total Possible Outcomes
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.

13. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
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.
1.4
1. Given event A: A + notA = 1.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

14. What is an 'equilateral' triangle?
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
A radius
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

15. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(x-y)²
A triangle in which one of the three interior angles is 90 degrees.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

16. Convert to a percentage: 1/4
(x+y)(x-y)
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
25%
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.

17. An integer is divisible by 5 if...
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
An integer is divisible by 5 if its units digit is either 0 or 5.
Probability A + Probability B
The total # of possible outcomes.

18. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
Not reading the problems carefully enough!
Not necessarily. This is a trick question - because x could be either positive or negative.
4 angles are formed. Their sum is 360 degrees
'Big' angles and 'Small' angles.

19. HIGH: Volume of a cylinder?
Invert the second fraction (reciprocal) and multiply
x²-y²
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)+
V=pr²h (This is just the area multiplied by the height)

20. Convert to a percentage: 2/5
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.
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.
40%

21. HIGH: Rough est. of v1 =
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.
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)+
80%

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

23. Explain how to use a 'Rate Pie'
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.
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
40%
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. On the GRE - should you ever assume that diagrams are truthful?
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
4 angles are formed. Their sum is 360 degrees
90 degrees each.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

25. What is the equation for a group problem?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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
Bh
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

26. An integer is divisible by 4 if...

27. How do you calculate the percentage of change?
Groups - teams - or committees.
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.

28. How do you add or subtract fractions?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
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.

29. Define the range of a set of numbers.
360 degrees
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.
90 degrees each.
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.

30. What is the sum of any 'big' angle and any 'Small' angle?
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.
60%
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

31. How many degrees does a circle contain?
Not reading the problems carefully enough!
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.
360 degrees
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'.

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

33. 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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
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.

34. List all the prime numbers that are less than 30:
Between 0 and 1.
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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)+

35. Does order matter for a permutation? How about for a combination?
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
The total # of possible outcomes.
Order does matter for a permutation - but does not matter for a combination.
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.

36. HIGH: What are the percentages for standard deviation?
The # falling in the center of an ordered data set
Find the total - or whole - first - and then set up a Ratio Box.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
A triangle in which one of the three interior angles is 90 degrees.

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

38. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
1/1
A triangle in which one of the three interior angles is 90 degrees.

39. HIGH: Describe how to deal with 2 sets of parentheses.
The average - mean - median - or mode.
Between 0 and 1.
Arrangements - orders - schedules - or lists.
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)+

40. Explain the difference between handling a permutation versus a combination.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
2
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.
180 degrees.

41. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
Probability A + Probability B
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

42. How is a range expressed with inequalities?
A radius
(x-y)²
Example: 1 < x < 10
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

43. HIGH: How do you multiply and divide square roots?
4 angles are formed. Their sum is 360 degrees
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

44. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
Multiply numerator times numerator and denominator times denominator.
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'.
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%.

45. What is the factored version of x² -2xy + y² ?
1
(x-y)²
A line is a 180-degree angle.
(a+b)(a-b)

46. 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.
'Big' angles and 'Small' angles.
3:4:5 5:12:13
1

47. Simplify this: v32
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Multiply numerator times numerator and denominator times denominator.
360 degrees
6

48. Area of a parallelogram?
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.
Bh
(0 -0)
V=s³

49. What are 'vertical angles'?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
360 degrees
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

50. HIGH: What is the formula for the diagonal of any square?
S*v2
V=pr²h (This is just the area multiplied by the height)
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.
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.