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

2. What number goes on the bottom of a probability fraction?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The total # of possible outcomes.

3. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Not reading the problems carefully enough!
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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a+b)(a-b)

4. HIGH: What is the unfactored version of (x+y)² ?
(0 -0)
x² + 2xy + y²
V=s³
Between 0 and 1.

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

6. HIGH: List the two most common side ratios for right triangles
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.
A line is a 180-degree angle.
3:4:5 5:12:13
Bh

7. The three interior angles of a triangle add up to...
(x+y)(x-y)
180 degrees
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
90 degrees each.

8. 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.
x² + 2xy + y²
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

9. HIGH: Area of a triangle?
Groups - teams - or committees.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2r

10. HIGH: How do you multiply powers with the same base?
Multiply numerator times numerator and denominator times denominator.
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

11. What is an 'equilateral' triangle?
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.
Order does matter for a permutation - but does not matter for a combination.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

12. What is the 'Third side' rule for triangles?
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.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

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

14. How do you divide fractions?
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.
Invert the second fraction (reciprocal) and multiply
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.
2pr -or- pd

15. 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.
(x-y)²
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

16. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Find the total - or whole - first - and then set up a Ratio Box.
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.
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.

17. What are 'vertical angles'?
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.
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.
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%.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

18. Explain how to solve for 7/¼
60%
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
x² -2xy + y²

19. Solve this: v6 * -v6 = ?
3:4:5 5:12:13
6
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
Probability A + Probability B

20. An integer is divisible by 2 if...
The # falling in the center of an ordered data set
A line is a 180-degree angle.
An integer is divisible by 2 if its units digit is divisible by 2.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

21. What is the equation for a group problem?
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.
2r
1.7

22. HIGH: How do you calculate the circumference of a circle?
40%
(0 -0)
2pr -or- pd
2r

23. Does order matter for a permutation? How about for a combination?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
A=pr²
1.4
Order does matter for a permutation - but does not matter for a combination.

24. Define the mode of a set of numbers.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The total # of possible outcomes.

25. Convert to a percentage: 4/5
80%
Invert the second fraction (reciprocal) and multiply
2pr -or- pd
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

26. What do combination problems usually ask for?
Not necessarily. This is a trick question - because x could be either positive or negative.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Groups - teams - or committees.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

27. In a coordinate system - what is the origin?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(0 -0)
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 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.

28. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
180 degrees.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
V=s³
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

29. HIGH: How do you multiply and divide square roots?
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.
S²
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

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.
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'.
Between 0 and 1.
x² + 2xy + y²

31. What is the key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
An integer is divisible by 5 if its units digit is either 0 or 5.
(x+y)(x-y)

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

33. Convert to a percentage: 3/5
A line is a 180-degree angle.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
60%
x² -2xy + y²

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

35. Convert to a percentage: 2/5
90 degrees each.
40%
360 degrees
x² + 2xy + y²

36. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
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.
25%

37. Define a factorial of a number - and how it is written.
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 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.
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%.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

38. HIGH: Area of a circle
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
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
A=pr²

39. 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.
A 90-degree angle.
1/x^n For example - 6-² = 1/6² = 1/36
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

40. What is the name of a line that extends from the center of a circle to the edge of a circle?
180 degrees
Probability A + Probability B
A radius
A 90-degree angle.

41. List all the prime numbers that are less than 30:
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

42. 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.
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
Invert the second fraction (reciprocal) and multiply
The value that appears most often in a data set.

43. Explain how to calculate an average (arithmetic mean)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
80%
40%

44. HIGH: Volume of a cube?
6
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
(x+y)(x-y)
V=s³

45. HIGH: To divide powers with the same base...
1.4
360 degrees
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
S*v2

46. Explain how to divide fractions.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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)+
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

47. HIGH: how do you calculate the surface area of a rectangular box?
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.
Groups - teams - or committees.
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.

48. The three exterior angles of a triangle add up to...
360 degrees
1/x^n For example - 6-² = 1/6² = 1/36
An integer is divisible by 5 if its units digit is either 0 or 5.
Probability A * Probability B

49. How do you solve a combination?

50. What is the factored version of x² -2xy + y² ?
(x-y)²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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 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.