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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
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A radius

2. HIGH: What is the factored version of x² + 2xy + y² ?
40%
(x+y)²
A=pr²
Between 0 and 1.

3. What number goes on the bottom of a probability fraction?
1.7
The total # of possible outcomes.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.

4. What is a 'Right' triangle?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
A triangle in which one of the three interior angles is 90 degrees.
1
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

5. Area of a square?
S²
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.
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

6. Probability Formula
The average - mean - median - or mode.
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
Favorable Outcomes/Total Possible Outcomes
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

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

8. HIGH: List the two most common side ratios for right triangles
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
3:4:5 5:12:13
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

9. On the GRE - should you ever assume that diagrams are truthful?
180 degrees.
Not necessarily. This is a trick question - because x could be either positive or negative.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

10. HIGH: x^-n is equal to
An integer is divisible by 2 if its units digit is divisible by 2.
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% |
1/x^n For example - 6-² = 1/6² = 1/36

11. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
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
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%.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

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

13. An integer is divisible by 6 if...

14. What do permutation problems often ask for?
Favorable Outcomes/Total Possible Outcomes
Arrangements - orders - schedules - or lists.
Not necessarily. This is a trick question - because x could be either positive or negative.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

15. What do combination problems usually ask for?
Multiply numerator times numerator and denominator times denominator.
(x+y)(x-y)
Groups - teams - or committees.
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

16. v4 =
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. 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.
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.

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

18. 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.
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.
V=s³
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.

19. 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+b)(a-b)
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

20. How do you multiply fractions?
x²-y²
1
Multiply numerator times numerator and denominator times denominator.
An integer is divisible by 2 if its units digit is divisible by 2.

21. HIGH: What is the equation of a line?

22. Explain how to calculate an average (arithmetic mean)
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.
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
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

23. What is the equation for a group problem?
A line is a 180-degree angle.
Probability A * Probability B
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
Not necessarily. This is a trick question - because x could be either positive or negative.

24. How many degrees does a circle contain?
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.
360 degrees
A triangle in which one of the three interior angles is 90 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.

25. What is an 'equilateral' triangle?
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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'.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

26. HIGH: What is a '30:60:90' triangle?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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

27. HIGH: Describe how to deal with 2 sets of parentheses.
1/1
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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)+

28. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A triangle in which one of the three interior angles is 90 degrees.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

29. HIGH: What is the unfactored version of (x+y)² ?
A triangle in which one of the three interior angles is 90 degrees.
(x+y)(x-y)
x² + 2xy + y²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

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

31. 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.
A=pr²
Find the total - or whole - first - and then set up a Ratio Box.
1/x^n For example - 6-² = 1/6² = 1/36

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

33. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
A radius
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Between 0 and 1.

34. HIGH: How do you multiply powers with the same base?
The # falling in the center of an ordered data set
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.
x² -2xy + y²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

35. Does order matter for a permutation? How about for a combination?
Probability A * Probability B
A triangle in which one of the three interior angles is 90 degrees.
(0 -0)
Order does matter for a permutation - but does not matter for a combination.

36. HIGH: What is the formula for the diagonal of any square?
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
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'.
S*v2
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

37. 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.
The value that appears most often in a data set.
Find the total - or whole - first - and then set up a Ratio Box.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

38. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
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.
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.
Order does matter for a permutation - but does not matter for a combination.

39. Simplify this: v32
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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
An integer is divisible by 5 if its units digit is either 0 or 5.

40. The three interior angles of a triangle add up to...
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
180 degrees
90 degrees each.
(0 -0)

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

42. HIGH: What must be true before a quadratic equation can be solved?

43. Solve this: v6 * -v6 = ?
2r
6
Find the total - or whole - first - and then set up a Ratio Box.
S*v2

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

45. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

46. HIGH: Area of a circle
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
A=pr²
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

47. What causes 80% of errors on the math section of the GRE?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
40%
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.
Not reading the problems carefully enough!

48. What is the sum of any 'big' angle and any 'Small' angle?
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.
'Big' angles and 'Small' angles.
S*v2
180 degrees.

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

50. Convert to a percentage: 3/5
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.
Favorable Outcomes/Total Possible Outcomes
60%
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