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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. Sector
(a+b)²
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.
The set of points which are all the same distance (the radius) from a certain point (the center).
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.

2. Diameter
Probability A * Probability B
The distance across the circle through the center of the circle.The diameter is twice the radius.
1/2bh
2lw+2lh+2wh

3. a³-b³
1/2 h (b1 + b2)
Sum of terms/number of terms
(a-b)(a²+ab+b²)
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

4. a² - b² is equal to
Probability A + Probability B
(a+b)(a-b)
1/x^a
2pi*r

5. What is the area of a triangle?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A+b
1/2bh
(x1+x2)/2 - (y1+y2)/2

6. What is the surface area of a cylinder?
x²-y²
1/2bh
Lwh
2(pi)r(r+h)

7. Lines reflected over the x or y axis have ____ slopes.
Negative
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.
A²-b²
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

8. What is the area of a cylinder?
Arrangements - orders - schedules - or lists.
2(pi)r(r+h)
4s (where s = length of a side)
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.

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

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10. Explain the special properties of zero.
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
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.
y = k/x
(a+b)(a-b)

11. What is a '30:60:90' triangle?
?d OR 2?r
Lwh
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
y-y1=m(x-x1)

12. What is the unfactored version of x²-y² ?
(x+y)(x-y)
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.
1/2bh
Probability A + Probability B

13. Slope
4s (where s = length of a side)
An ange whose vertex is the center of the circle
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.
(y2-y1)/(x2-x1)

14. The length of one side of any triangle is ____ than the sum of the other two sides.
A=?r2
y2-y1/x2-x1
Less
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.

15. If x² = 144 - does v144 = x?
2x2x2x5x5
Not necessarily. This is a trick question - because x could be either positive or negative.
A²-b²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

16. (a+b)(a-b)=
Lw
A²-b²
Between 0 and 1.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

17. In a parabola - if the first term is negative - the parabola ________.
1/3Bh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Not necessarily. This is a trick question - because x could be either positive or negative.
Opens down

18. Circumference of cirlce using diameter
Arrangements - orders - schedules - or lists.
Pi*d
(a-b)(a²+ab+b²)
Pir^2h

19. What is directly proportional?
y = kx
x°/360 times (?r²) - where x is the degrees in the angle
2Length + 2width [or (length + width) x 2]
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

20. What is the side ratio for a 30:60:90 triangle?
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.
4pir^2
2x2x2x5x5
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

21. Rough est. of v1 =
2(pi)r(r+h)
Groups - teams - or committees.
Arrangements - orders - schedules - or lists.
1

22. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
1/1
(a+b)(a²-ab+b²)
1/2 h (b1 + b2)

23. If something is possible but not certain - what is the numeric range of probability of it happening?
(n degrees/360) * 2(pi)r
Probability A + Probability B
Between 0 and 1.
Groups - teams - or committees.

24. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
?d OR 2?r
2 pi r
1. Given event A: A + notA = 1.

25. What is the 'Third side' rule for triangles?
2(pi)r(r+h)
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.
2x2x2x5x5
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.

26. To divide powers with the same base...
A=bh
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

27. In intersecting lines - opposite angles are _____.
1
1.4
(n degrees/360) * 2(pi)r
Equal

28. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
C =?d
(y-y1)=m(x-x1)
1. Given event A: A + notA = 1.
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.

29. What is the length of an arc?
(n degrees/360) * 2(pi)r
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Percentage Change = Difference/Original * 100
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.

30. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
Probability A * Probability B
A=?r2
S*v2

31. Perimeter of polygon
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.
(x-y)²
Sum of the lengths of the sides
Number of desired outcomes/number of total outcomes

32. Area of Circles
A=?r2
Middle term
T1 * r^(n-1)/(r-1)
x°/360 times (2 pi r) - where x is the degrees in the angle

33. How do you find the sum of an arithmetic sequence?
2(lw+wh+lh)
4s
(n-2)180
(n/2) * (t1+tn)

34. Area of Square
S^2
y2-y1/x2-x1
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.
1. Given event A: A + notA = 1.

35. How do you find the slope?
Arrangements - orders - schedules - or lists.
Middle term
y2-y1/x2-x1
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.

36. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
(a-b)²
Negative
An ange whose vertex is the center of the circle

37. x^a * x^b = x^__
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.
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.
Last term
A+b

38. Area of Parallelogram
2 pi r
The distance from one point on the circle to another point on the circle.
Bh
2l+2w

39. What is the average speed?
A+b
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.
(x+y)(x-y)
Total distance/total time

40. Surface Area of Cylinder
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.
Percentage Change = Difference/Original * 100
The total # of possible outcomes.
2pir^2 + 2pir*h

41. perimeter of square
4s
Negative
1.4
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.

42. What is the average?
1/2bh
Sum of terms/number of terms
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
?r²

43. Rough est. of v3 =
1.7
2Length + 2width [or (length + width) x 2]
Pir^2h
Pi*r^2

44. a²-b²
Bh
(a-b)(a+b)
(n-2)180
Order does matter for a permutation - but does not matter for a combination.

45. Volume of Cylinder
Number of desired outcomes/number of total outcomes
S^2
½(base x height) [or (base x height)÷2]
Pir^2h

46. Define a factorial of a number - and how it is written.
(y2-y1)/(x2-x1)
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 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.
4s (where s = length of a side)

47. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
Bh
Probability A + Probability B
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.

48. What is an 'equilateral' triangle?
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.
(pi)r^2(h)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

49. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
½(base x height) [or (base x height)÷2]
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2pir^2 + 2pir*h

50. Rough est. of v2 =
The set of points which are all the same distance (the radius) from a certain point (the center).
2 pi r
1.4
4/3pir^3

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GRE Math 2

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