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GRE Math 2

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 directly proportional?
(a-b)(a+b)
2x2x2x5x5
T1 + (n-1)d
y = kx

2. a²-b²
1/3Bh
Lwh
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.
(a-b)(a+b)

3. List two odd behaviors of exponents
Between 0 and 1.
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.
Pi*r^2
T1 * r^(n-1)/(r-1)

4. Circle
Bh
The set of points which are all the same distance (the radius) from a certain point (the center).
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.
2(pi)r

5. What is the area of a cylinder?
Probability A * Probability B
2(pi)r(r+h)
The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.
y-y1=m(x-x1)

6. If x² = 144 - does v144 = x?
(a-b)(a²+ab+b²)
The distance across the circle through the center of the circle.The diameter is twice the radius.
Last term
Not necessarily. This is a trick question - because x could be either positive or negative.

7. What is the prime factorization of 200?
2x2x2x5x5
2l+2w
Arrangements - orders - schedules - or lists.
2Length + 2width [or (length + width) x 2]

8. What number goes on the bottom of a probability fraction?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(y-y1)=m(x-x1)
The distance across the circle through the center of the circle.The diameter is twice the radius.
The total # of possible outcomes.

9. What is a '30:60:90' triangle?
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
The distance from one point on the circle to another point on the circle.
Pi*r^2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

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

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11. How do you solve a permutation?
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.
(a+b)²
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
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

12. (a+b)(a-b)=
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
A²-b²
2l+2w
x°/360 times (?r²) - where x is the degrees in the angle

13. Area of Triangle
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.
1/2bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
T1 + (n-1)d

14. Define the mode of a set of numbers.
x²-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.
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
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

15. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
(x+y)(x-y)
S^2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

16. What do permutation problems often ask for?
2pi*r
Arrangements - orders - schedules - or lists.
A+b
(x-y)²

17. Slope
Less
1/2bh
(y2-y1)/(x2-x1)
Number of desired outcomes/number of total outcomes

18. What is the 'Third side' rule for triangles?
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.
?d OR 2?r
(a-b)(a²+ab+b²)

19. Radius (Radii)
2(lw+wh+lh)
2 pi r
A segment connecting the center of a circle to any point on the circle
Arrangements - orders - schedules - or lists.

20. a³+b³
x°/360 times (2 pi r) - where x is the degrees in the angle
(pi)r^2(h)
Opens up
(a+b)(a²-ab+b²)

21. Area of a trapezoid
(n degrees/360) * 2(pi)r
2(pi)r
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(0 -0)

22. What is the length of an arc?
Not necessarily. This is a trick question - because x could be either positive or negative.
Bh
(n degrees/360) * 2(pi)r
The set of points which are all the same distance (the radius) from a certain point (the center).

23. Volume of pyramid
Probability A * Probability B
The set of points which are all the same distance (the radius) from a certain point (the center).
1/3Bh
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

24. (a+b)(c+d)
4pir^2
Less
1
Ac+ad+bc+bd

25. How do you find the sum of an arithmetic sequence?
Middle term
(n/2) * (t1+tn)
1.4
(x1+x2)/2 - (y1+y2)/2

26. What is the area of a sector?
2pir^2 + 2pir*h
Pi*r^2
The set of points which are all the same distance (the radius) from a certain point (the center).
(n degrees/360) * (pi)r^2

27. Volume of Cylinder
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.
Pir^2h
(x1+x2)/2 - (y1+y2)/2
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.

28. What is the average?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The total # of possible outcomes.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Sum of terms/number of terms

29. Surface Area of Sphere
Groups - teams - or committees.
2(pi)r(r+h)
4pir^2
2Length + 2width [or (length + width) x 2]

30. How do you multiply and divide square roots?
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
1/3Bh
T1 * r^(n-1)

31. Define a factorial of a number - and how it is written.
x°/360 times (2 pi r) - where x is the degrees in the angle
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.
(a+b)(a²-ab+b²)
1/3pir^2*h

32. Volume of Cone
Percentage Change = Difference/Original * 100
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
Middle term
1/3pir^2*h

33. Surface Area of Cylinder
2pir^2 + 2pir*h
Not necessarily. This is a trick question - because x could be either positive or negative.
x°/360 times (?r²) - where x is the degrees in the angle
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.

34. Area of Square
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+b)²
Probability A + Probability B
S^2

35. What is the probability?
Middle term
(a-b)²
Number of desired outcomes/number of total outcomes
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.

36. Volume of prism
Probability A + Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

37. What is an 'equilateral' triangle?
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
(x1+x2)/2 - (y1+y2)/2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
T1 + (n-1)d

38. How do you calculate the surface area of a rectangular box?
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.
N x M
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.
2 pi r

39. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
N x M
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.
x² + 2xy + y²

40. What is the point-slope form?
Sum of the lengths of the sides
1.4
Arrangements - orders - schedules - or lists.
(y-y1)=m(x-x1)

41. Chord
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.
The distance from one point on the circle to another point on the circle.
(x-y)²
(n-2)180

42. How do you calculate a diagonal inside a 3-dimensional rectangular box?
(a-b)(a²+ab+b²)
A segment connecting the center of a circle to any point on the circle
2pi*r
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

43. How do you find the slope?
y2-y1/x2-x1
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Last term
Part of a circle connecting two points on the circle.

44. For a bell curve - what three terms might be used to describe the number in the middle?
The distance from one point on the circle to another point on the circle.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The average - mean - median - or mode.
2(pi)r

45. When a line crosses two parallel lines - ________.
2(pi)r
The four big angles are equal and the four small angles are equal
A=bh
T1 + (n-1)d

46. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
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 -2xy + y²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

47. What is the area of a solid rectangle?
2(lw+wh+lh)
x°/360 times (?r²) - where x is the degrees in the angle
Last term
(a+b)(a-b)

48. What is the area of a triangle?
The set of points which are all the same distance (the radius) from a certain point (the center).
1/2bh
Negative
Number of desired outcomes/number of total outcomes

49. What do combination problems usually ask for?
Groups - teams - or committees.
b±[vb²-4ac]/2a
S^2
2(pi)r(r+h)

50. Circumference of a circle using radius
Equal
2pi*r
(n/2) * (t1+tn)
Middle term