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GRE Math 2

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 EITHER one event OR another event happening? (Probability of A or B)
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.
Probability A + Probability B
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Bh

2. Volume of Cylinder
Pir^2h
Probability A + Probability B
N x M
Middle term

3. Define 'proportionate' values
Arrangements - orders - schedules - or lists.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(n-2)180
(a+b)²

4. How do you calculate the probability of two events in a row? (Probability of A and B)
y-y1=m(x-x1)
(y2-y1)/(x2-x1)
Probability A * Probability B
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. Circle
1/2bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The set of points which are all the same distance (the radius) from a certain point (the center).
2pi*r

6. Perimeter of a square
(n degrees/360) * (pi)r^2
4/3pir^3
4s (where s = length of a side)
(n-2)180

7. Circumference of a circle
Middle term
2 pi r
?d OR 2?r
Sum of the lengths of the sides

8. (a+b)(a-b)=
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.
Last term
A²-b²
(n degrees/360) * 2(pi)r

9. Circumference Formula
½(b1 +b2) x h [or (b1 +b2) x h÷2]
C =?d
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.
Sum of terms/number of terms

10. a³-b³
C =?d
(a-b)(a²+ab+b²)
Percentage Change = Difference/Original * 100
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.

11. What is an 'equilateral' triangle?
(pi)r^2
Less
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Probability A + Probability B

12. In intersecting lines - opposite angles are _____.
Arrangements - orders - schedules - or lists.
The average - mean - median - or mode.
Equal
S^2

13. To divide powers with the same base...
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1
Pi*d

14. Rough est. of v1 =
1
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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=?r2

15. x^-a =
Probability A * Probability B
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
1/x^a
The distance across the circle through the center of the circle.The diameter is twice the radius.

16. What do permutation problems often ask for?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Arrangements - orders - schedules - or lists.
(x+y)²
2(pi)r(r+h)

17. Define the range of a set of numbers.
x² -2xy + y²
2Length + 2width [or (length + width) x 2]
Arrangements - orders - schedules - or lists.
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.

18. Define the mode of a set of numbers.
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
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.
Probability A * Probability B
An ange whose vertex is the center of the circle

19. What is a '30:60:90' triangle?
2lw+2lh+2wh
Last term
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
1.7

20. Slope
Probability A + Probability B
2lw+2lh+2wh
?r²
(y2-y1)/(x2-x1)

21. Lines reflected over the x or y axis have ____ slopes.
Negative
1/x^a
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.
(a+b)²

22. Diameter
A segment connecting the center of a circle to any point on the circle
C =?d
The distance across the circle through the center of the circle.The diameter is twice the radius.
The average - mean - median - or mode.

23. What are the side ratios for a 30:60:90 triangle?
(x+y)(x-y)
2(lw+wh+lh)
2pir^2 + 2pir*h
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

24. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
2x2x2x5x5
Between 0 and 1.
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.

25. Volume of sphere
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.
S*v2
½(b1 +b2) x h [or (b1 +b2) x h÷2]
4/3pir^3

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

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27. Arc
x²-y²
Part of a circle connecting two points on the circle.
(0 -0)
1/x^a

28. Surface Area of rectangular prism
C =?d
Bh
S² - where s = length of a side
2lw+2lh+2wh

29. What is the 'distributive law'?
(n degrees/360) * 2(pi)r
N x M
2l+2w
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.

30. Define the 'Third side' rule for triangles

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31. Perimeter of a rectangle
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.
2Length + 2width [or (length + width) x 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.
Negative

32. How do you find the sum of a geometric sequence?
(0 -0)
Sqr( x2 -x1) + (y2- y1)
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.
T1 * r^(n-1)/(r-1)

33. What must be true before a quadratic equation can be solved?

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34. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
Less
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.
T1 * r^(n-1)

35. What is the side ratio for a 30:60:90 triangle?
Last term
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

36. How do you find the nth term of a geometric sequence?
Pi*d
x² + 2xy + y²
The total # of possible outcomes.
T1 * r^(n-1)

37. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
4/3pir^3
The four big angles are equal and the four small angles are equal
Between 0 and 1.
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.

38. Area of Parallelogram
Bh
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 distance across the circle through the center of the circle.The diameter is twice the radius.
Arrangements - orders - schedules - or lists.

39. Area of Rectangle
1/3pir^2*h
Lw
x°/360 times (?r²) - where x is the degrees in the angle
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.

40. Perimeter of polygon
y-y1=m(x-x1)
(y-y1)=m(x-x1)
4/3pir^3
Sum of the lengths of the sides

41. How do you solve a permutation?
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
1.7
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The total # of possible outcomes.

42. What is the prime factorization of 200?
2x2x2x5x5
Pir^2h
A segment connecting the center of a circle to any point on the circle
Less

43. What is the unfactored version of (x+y)² ?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
An ange whose vertex is the center of the circle
x² + 2xy + y²
4s (where s = length of a side)

44. What is the area of a triangle?
C =?d
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(a-b)(a+b)
1/2bh

45. a²-b²
1/3Bh
The total # of possible outcomes.
(a-b)(a+b)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

46. If x² = 144 - does v144 = x?
Lwh
1/3Bh
Not necessarily. This is a trick question - because x could be either positive or negative.
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

47. If something is certain to happen - how is the probability of this event expressed mathematically?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/1
Sum of the lengths of the sides
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.

48. For a bell curve - what three terms might be used to describe the number in the middle?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The average - mean - median - or mode.
Sqr( x2 -x1) + (y2- y1)

49. In a parabola - if the first term is positive - the parabola ________.
C =?d
(a+b)(a²-ab+b²)
Opens up
Percentage Change = Difference/Original * 100

50. How do you find the sum of an arithmetic sequence?
(n/2) * (t1+tn)
Between 0 and 1.
Last term
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.

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GRE Math 2

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