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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. How do you calculate the probability of two events in a row? (Probability of A and B)
(y-y1)=m(x-x1)
A+b
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Probability A * Probability B

2. When you reverse FOIL - the term that needs to add out is the _____
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.
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.
Middle term
2x2x2x5x5

3. a²-b²
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.
Middle term
(a-b)(a+b)
1/2 h (b1 + b2)

4. Rough est. of v2 =
The distance across the circle through the center of the circle.The diameter is twice the radius.
1.4
b±[vb²-4ac]/2a
Sum of terms/number of terms

5. How do you find the sum of a geometric sequence?
(x+y)²
The total # of possible outcomes.
T1 * r^(n-1)/(r-1)
Total distance/total time

6. Volume of sphere
1. Given event A: A + notA = 1.
The distance across the circle through the center of the circle.The diameter is twice the radius.
4/3pir^3
Equal

7. Radius (Radii)
S*v2
4/3pir^3
2pi*r
A segment connecting the center of a circle to any point on the circle

8. a²-2ab+b²
(x+y)²
(a-b)²
The average - mean - median - or mode.
2(pi)r(r+h)

9. Area of Triangle
T1 + (n-1)d
Opens down
1/2bh
2x2x2x5x5

10. Point-Slope form
y2-y1/x2-x1
2Length + 2width [or (length + width) x 2]
y-y1=m(x-x1)
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.

11. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
N x M
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2lw+2lh+2wh
1/2bh

12. How do you find the nth term of an arithmetic sequence?
S*v2
T1 + (n-1)d
Bh
Sqr( x2 -x1) + (y2- y1)

13. Area of a triangle
½(base x height) [or (base x height)÷2]
(a+b)²
Sqr( x2 -x1) + (y2- y1)
Part of a circle connecting two points on the circle.

14. What is the volume of a cylinder?
x² + 2xy + y²
(a-b)(a²+ab+b²)
(pi)r^2(h)
y-y1=m(x-x1)

15. Central Angle
S^2
An ange whose vertex is the center of the circle
(a-b)(a+b)
T1 * r^(n-1)/(r-1)

16. Surface Area of Cylinder
A+b
1/1
A=bh
2pir^2 + 2pir*h

17. What is a '30:60:90' triangle?
1/2 h (b1 + 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
N x M
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.

18. Slope
(y2-y1)/(x2-x1)
2x2x2x5x5
1
S*v2

19. 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.
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.
?d OR 2?r
x² + 2xy + y²

20. Volume of Cone
1/3pir^2*h
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Negative
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.

21. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Opens down
(y-y1)=m(x-x1)

22. a²+2ab+b²
(a+b)²
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 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
(y2-y1)/(x2-x1)

23. Area of Parallelogram
A+b
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
Bh

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

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25. What is the side ratio for a 30:60:90 triangle?
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.
½(b1 +b2) x h [or (b1 +b2) x h÷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.

26. How do you multiply powers with the same base?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Between 0 and 1.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

27. How do you find the slope?
The four big angles are equal and the four small angles are equal
Bh
y2-y1/x2-x1
2pi*r

28. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
Groups - teams - or committees.
S*v2
A segment connecting the center of a circle to any point on the circle

29. Define the range of a set of numbers.
Not necessarily. This is a trick question - because x could be either positive or negative.
A+b
(a-b)(a²+ab+b²)
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. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
y = kx
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
(n-2)180

31. What is the side ratio for a Right Isosceles triangle?
(y-y1)=m(x-x1)
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.
T1 * r^(n-1)/(r-1)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

32. How do you find the nth term of a geometric sequence?
(x+y)(x-y)
Bh
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.
T1 * r^(n-1)

33. perimeter of square
2 pi r
4s
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.
1/2bh

34. What is the average speed?
Pir^2h
Total distance/total time
b±[vb²-4ac]/2a
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.

35. What is the area of a cylinder?
1
Number of desired outcomes/number of total outcomes
2(pi)r(r+h)
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.

36. Area of Circle
2pi*r
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
y2-y1/x2-x1
Pi*r^2

37. List two odd behaviors of exponents
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
(a+b)²
Probability A * Probability B

38. Area of a trapezoid
(0 -0)
Opens up
2x2x2x5x5
½(b1 +b2) x h [or (b1 +b2) x h÷2]

39. Lines reflected over the x or y axis have ____ slopes.
Negative
1. Given event A: A + notA = 1.
Order does matter for a permutation - but does not matter for a combination.
Ac+ad+bc+bd

40. How do you multiply and divide square roots?
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-b)(a+b)
4s
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

41. The length of one side of any triangle is ____ than the sum of the other two sides.
Not necessarily. This is a trick question - because x could be either positive or negative.
(a+b)²
(a+b)(a²-ab+b²)
Less

42. What is the distance formula?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Opens up
4s
Sqr( x2 -x1) + (y2- y1)

43. What do permutation problems often ask for?
A+b
(a-b)(a+b)
S² - where s = length of a side
Arrangements - orders - schedules - or lists.

44. Circumference Formula
An ange whose vertex is the center of the circle
2l+2w
Lwh
C =?d

45. What is directly proportional?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
y = kx
x°/360 times (2 pi r) - where x is the degrees in the angle

46. Volume of Cylinder
Pir^2h
Last term
(a+b)²
y2-y1/x2-x1

47. Area of Circles
2lw+2lh+2wh
Arrangements - orders - schedules - or lists.
4s
A=?r2

48. How do you calculate the surface area of a rectangular box?
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.
2pir^2 + 2pir*h
2x2x2x5x5
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'.

49. length of a sector
(pi)r^2(h)
x°/360 times (2 pi r) - where x is the degrees in the angle
1/3Bh
x°/360 times (?r²) - where x is the degrees in the angle

50. In a coordinate system - what is the origin?
Pir^2h
(0 -0)
4pir^2
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.