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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. Explain the difference between a digit and a number.

2. 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.
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
Order does matter for a permutation - but does not matter for a combination.
Lwh

3. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

4. Area of Square
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.
x°/360 times (?r²) - where x is the degrees in the angle
S^2
Groups - teams - or committees.

5. Circumference Formula
C =?d
Equal
1/1
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

6. Volume of sphere
(n degrees/360) * 2(pi)r
y2-y1/x2-x1
Groups - teams - or committees.
4/3pir^3

7. To divide powers with the same base...
1/x^a
y-y1=m(x-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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

8. What is the probability?
N x M
1/1
Number of desired outcomes/number of total outcomes
1/3Bh

9. What is the average?
Sum of terms/number of terms
(a-b)(a+b)
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.
Percentage Change = Difference/Original * 100

10. What is the area of a sector?
S^2
(n-2)180
y = k/x
(n degrees/360) * (pi)r^2

11. What are the side ratios for a 30:60:90 triangle?
Negative
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

12. Area of a circle
?r²
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
(n/2) * (t1+tn)
Last term

13. Rough est. of v2 =
x² + 2xy + y²
The distance across the circle through the center of the circle.The diameter is twice the radius.
S² - where s = length of a side
1.4

14. Volume of Cone
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.
1/3pir^2*h
Percentage Change = Difference/Original * 100
(n-2)180

15. Central Angle
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.
An ange whose vertex is the center of the circle
A²-b²
Number of desired outcomes/number of total outcomes

16. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
C =?d
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.
x² -2xy + y²
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. Radius (Radii)
Total distance/total time
A segment connecting the center of a circle to any point on the circle
S*v2
Opens up

18. What is the factored version of (x+y)(x-y) ?
b±[vb²-4ac]/2a
x²-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
2 pi r

19. Area of a triangle
1/3Bh
½(base x height) [or (base x height)÷2]
2Length + 2width [or (length + width) x 2]
A+b

20. Circumference of cirlce using diameter
(a+b)²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Pi*d
Sum of terms/number of terms

21. Volume of pyramid
2Length + 2width [or (length + width) x 2]
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/3Bh

22. (a+b)(c+d)
A+b
y = k/x
Ac+ad+bc+bd
N x M

23. (a+b)(a-b)=
Percentage Change = Difference/Original * 100
A²-b²
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

24. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
1/2bh
(a+b)(a-b)
x°/360 times (2 pi r) - where x is the degrees in the angle

25. Rough est. of v3 =
1.7
2lw+2lh+2wh
The distance across the circle through the center of the circle.The diameter is twice the radius.
(n degrees/360) * (pi)r^2

26. Diameter
A=bh
1/2bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The distance across the circle through the center of the circle.The diameter is twice the radius.

27. Area of rectangle - square - parallelogram
Number of desired outcomes/number of total outcomes
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(y-y1)=m(x-x1)
A=bh

28. Quadratic Formula
Lw
b±[vb²-4ac]/2a
4s
2pir^2 + 2pir*h

29. How do you multiply powers with the same base?
(y-y1)=m(x-x1)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1/x^a
2 pi r

30. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Negative
(x1+x2)/2 - (y1+y2)/2
1. Given event A: A + notA = 1.
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.

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

32. What do combination problems usually ask for?
Order does matter for a permutation - but does not matter for a combination.
(a-b)(a+b)
N x M
Groups - teams - or committees.

33. List two odd behaviors of exponents
2l+2w
2(pi)r(r+h)
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.
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.

34. Volume of Cylinder
A+b
2pir^2 + 2pir*h
Pir^2h
(a+b)²

35. Perimeter (circumference) of a circle
2 pi r
(x+y)²
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'.
The average - mean - median - or mode.

36. If x² = 144 - does v144 = x?
T1 * r^(n-1)/(r-1)
Groups - teams - or committees.
The set of points which are all the same distance (the radius) from a certain point (the center).
Not necessarily. This is a trick question - because x could be either positive or negative.

37. For a bell curve - what three terms might be used to describe the number in the middle?
2pir^2 + 2pir*h
The average - mean - median - or mode.
1/2bh
1.7

38. How do you find the sum of an arithmetic sequence?
x²-y²
Number of desired outcomes/number of total outcomes
(n/2) * (t1+tn)
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.

39. length of a sector
Number of desired outcomes/number of total outcomes
x°/360 times (2 pi r) - where x is the degrees in the angle
(y2-y1)/(x2-x1)
y = k/x

40. What is the side ratio for a 30:60:90 triangle?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Opens up
(pi)r^2(h)

41. a³+b³
(a+b)(a²-ab+b²)
Order does matter for a permutation - but does not matter for a combination.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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

42. If something is certain to happen - how is the probability of this event expressed mathematically?
y2-y1/x2-x1
1. Given event A: A + notA = 1.
S² - where s = length of a side
1/1

43. Volume of prism
An ange whose vertex is the center of the circle
Bh
The distance across the circle through the center of the circle.The diameter is twice the radius.
A segment connecting the center of a circle to any point on the circle

44. Circumference of a circle
x²-y²
?d OR 2?r
(x-y)²
x² + 2xy + y²

45. Area of a square
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.
S*v2
S² - where s = length of a side
Arrangements - orders - schedules - or lists.

46. What is the factored version of x² + 2xy + y² ?
(x+y)(x-y)
4/3pir^3
(x+y)²
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.

47. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
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.
Between 0 and 1.
(a+b)²

48. Define the mode of a set of numbers.
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.
Opens down
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
Pi*d

49. Sector
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.
1/3pir^2*h
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
½(b1 +b2) x h [or (b1 +b2) x h÷2]

50. a²-b²
2l+2w
Less
(a-b)(a+b)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.