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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. What is the 'Third side' rule for triangles?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.
1. Given event A: A + notA = 1.

2. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
The total # of possible outcomes.
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%.

3. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
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.
A radius
Between 0 and 1.

4. Explain the special properties of zero.
Favorable Outcomes/Total Possible Outcomes
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.

5. Solve this: v6 * -v6 = ?
'Big' angles and 'Small' angles.
2r
6
V=s³

6. Diameter of a circle?
S²
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
2r
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.

7. HIGH: What is the order of math operations - and the mnemonic to remember 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.
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.
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
Invert the second fraction (reciprocal) and multiply

8. List two odd behaviors of exponents
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
360 degrees
A radius

9. The three interior angles of a triangle add up to...
180 degrees
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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
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.

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

11. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(x+y)²
A triangle in which one of the three interior angles is 90 degrees.
'Big' angles and 'Small' angles.

12. Explain how to divide fractions.
A line is a 180-degree angle.
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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

13. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
1.4
1. Given event A: A + notA = 1.

14. Explain how to calculate an average (arithmetic mean)
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 line is a 180-degree angle.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
It will be a great advantage on test day to have your times table memorized from 1 through 15.

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

16. HIGH: Area of a circle
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
(0 -0)
A=pr²
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.

17. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

18. Explain how to use an 'Average Pie'
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
1.4
1/x^n For example - 6-² = 1/6² = 1/36

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

20. In a coordinate system - identify the quadrants and describe their location.
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
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

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

22. HIGH: What is the factored version of x² + 2xy + y² ?
360 degrees
90 degrees each.
(x+y)²
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.

23. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
4 angles are formed. Their sum is 360 degrees
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.
(x-y)²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

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

25. How do you add or subtract fractions?
1.7
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Not necessarily. This is a trick question - because x could be either positive or negative.
Find a common denominator and make equivalent fractions. Then add or subtract.

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

27. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
4 angles are formed. Their sum is 360 degrees
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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
1.4

28. HIGH: Rough est. of v3 =
180 degrees.
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
x² -2xy + y²
1.7

29. If x² = 144 - does v144 = x?
1
Not necessarily. This is a trick question - because x could be either positive or negative.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Between 0 and 1.

30. HIGH: How do you multiply and divide square roots?
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.
Groups - teams - or committees.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Find the total - or whole - first - and then set up a Ratio Box.

31. What is a 'Right' angle?
'Big' angles and 'Small' angles.
80%
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 90-degree angle.

32. HIGH: What is the Pythagorean theorem?

33. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
(x+y)(x-y)
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.

34. What are the side ratios 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.
1.4
The value that appears most often in a data set.
180 degrees.

35. 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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Between 0 and 1.
(x+y)²

36. Explain the difference between handling a permutation versus a combination.
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.
1.4
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x 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.

37. How is a range expressed with inequalities?
Find the total - or whole - first - and then set up a Ratio Box.
1
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Example: 1 < x < 10

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

39. HIGH: What are the percentages for standard deviation?
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(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.
S²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

40. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
V=s³
Not necessarily. This is a trick question - because x could be either positive or negative.
Multiply numerator times numerator and denominator times denominator.
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.

41. What is the key to dealing with ratio questions?
1.4
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.
60%
Find the total - or whole - first - and then set up a Ratio Box.

42. For a bell curve - what three terms might be used to describe the number in the middle?
3:4:5 5:12:13
Between 0 and 1.
The average - mean - median - or mode.
180 degrees

43. HIGH: How do you calculate the circumference of a circle?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The value that appears most often in a data set.
2pr -or- pd
1

44. In a coordinate system - what is the origin?
(0 -0)
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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
The # falling in the center of an ordered data set

45. What is an 'equilateral' triangle?
1/x^n For example - 6-² = 1/6² = 1/36
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

46. a² - b² is equal to
A line is a 180-degree angle.
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+b)(a-b)
The # falling in the center of an ordered data set

47. HIGH: Simplify this: v75/v27
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.
Order does matter for a permutation - but does not matter for a combination.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.

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

49. List all the prime numbers that are less than 30:
A 90-degree angle.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Find the total - or whole - first - and then set up a Ratio Box.

50. HIGH: What is the factored version of (x+y)(x-y) ?
2r
Bh
x²-y²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.