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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. Area of Triangle
1/2bh
(a-b)(a²+ab+b²)
(n/2) * (t1+tn)
(n-2)180

2. Area of a square
½(b1 +b2) x h [or (b1 +b2) x h÷2]
S² - where s = length of a side
?r²
y = k/x

3. What is the prime factorization of 200?
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.
1/2 h (b1 + b2)
1/3Bh
2x2x2x5x5

4. What'S the most important thing to remember about charts you'll see on the GRE?
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.
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.
1
2Length + 2width [or (length + width) x 2]

5. What is the 'Third side' rule for triangles?
2pir^2 + 2pir*h
1. Given event A: A + notA = 1.
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 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.

6. What is 'absolute value' - and how is it represented?

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7. a²-b²
(a-b)(a+b)
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.

8. Does order matter for a permutation? How about for a combination?
T1 * r^(n-1)
Order does matter for a permutation - but does not matter for a combination.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

9. Rough est. of v2 =
1.4
1/3Bh
1/2 h (b1 + b2)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

10. What is the formula for the diagonal of any square?
x² -2xy + y²
x°/360 times (2 pi r) - 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.
S*v2

11. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
S² - where s = length of a side
Last term
1/x^a
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.

12. What is the probability?
Number of desired outcomes/number of total outcomes
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A+b
2pir^2 + 2pir*h

13. What is the unfactored version of (x+y)² ?
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.
1.4
x² + 2xy + y²
2(pi)r(r+h)

14. How do you find the sum of an arithmetic sequence?
1/3pir^2*h
The total # of possible outcomes.
A=?r2
(n/2) * (t1+tn)

15. x^a * x^b = x^__
2lw+2lh+2wh
A+b
Negative
(0 -0)

16. To divide powers with the same base...
y2-y1/x2-x1
½(base x height) [or (base x height)÷2]
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
x°/360 times (2 pi r) - where x is the degrees in the angle

17. Volume of Cylinder
x°/360 times (?r²) - where x is the degrees in the angle
Pir^2h
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.
Probability A * Probability B

18. (a+b)(c+d)
2x2x2x5x5
A=bh
Not necessarily. This is a trick question - because x could be either positive or negative.
Ac+ad+bc+bd

19. (a+b)(a-b)=
Between 0 and 1.
A segment connecting the center of a circle to any point on the circle
A²-b²
The total # of possible outcomes.

20. a²+2ab+b²
The distance from one point on the circle to another point on the circle.
(y2-y1)/(x2-x1)
1/2bh
(a+b)²

21. 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.
?d OR 2?r
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

22. Rough est. of v1 =
2(pi)r(r+h)
A+b
(x+y)(x-y)
1

23. What is the unfactored version of x²-y² ?
(x+y)(x-y)
2(pi)r(r+h)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/3Bh

24. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
Part of a circle connecting two points on the circle.
(x-y)²
1

25. What is the length of an arc?
4s (where s = length of a side)
(n degrees/360) * 2(pi)r
Number of desired outcomes/number of total outcomes
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

26. Central Angle
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.
An ange whose vertex is the center of the circle
S² - where s = length of a side
(pi)r^2

27. Point-Slope form
2x2x2x5x5
½(b1 +b2) x h [or (b1 +b2) x h÷2]
?d OR 2?r
y-y1=m(x-x1)

28. What is directly proportional?
The average - mean - median - or mode.
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.
y = kx
A=bh

29. 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.
Sum of terms/number of terms
y = kx
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

30. Define the range of a set of numbers.
(x+y)(x-y)
2pi*r
2x2x2x5x5
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.

31. Circumference of a circle
4pir^2
(a+b)(a-b)
Probability A + Probability B
?d OR 2?r

32. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
1/2 h (b1 + b2)
y-y1=m(x-x1)
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

33. What is the average?
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.
N x M
Sum of terms/number of terms
Opens up

34. Volume of sphere
A segment connecting the center of a circle to any point on the circle
2pi*r
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.
4/3pir^3

35. If x² = 144 - does v144 = x?
Equal
2pi*r
1/3Bh
Not necessarily. This is a trick question - because x could be either positive or negative.

36. How do you find the slope?
Number of desired outcomes/number of total outcomes
(0 -0)
y2-y1/x2-x1
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

37. What is the 'distributive law'?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Opens up
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.
1.7

38. Perimeter of a square
Probability A + Probability B
4s (where s = length of a side)
2(pi)r(r+h)
T1 * r^(n-1)

39. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Negative
(a-b)(a+b)
Opens down

40. The length of one side of any triangle is ____ than the sum of the other two sides.
b±[vb²-4ac]/2a
Less
Probability A * Probability B
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.

41. a² - b² is equal to
2(pi)r(r+h)
(a+b)(a-b)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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

42. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
Sqr( x2 -x1) + (y2- y1)
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.
1/1

43. Perimeter of rectangle
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.
2pi*r
2l+2w
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.

44. x^-a =
1/x^a
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.
Equal
1/3pir^2*h

45. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
2(pi)r
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.
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.

46. What is inversely proportional?
y = k/x
A²-b²
2lw+2lh+2wh
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

47. Define the formula for calculating slope.
Sum of the lengths of the sides
Pir^2h
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
N x M

48. What is the surface area of a cylinder?
2(pi)r(r+h)
2 pi r
4/3pir^3
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.

49. In a coordinate system - what is the origin?
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
y = kx
Probability A + Probability B
(0 -0)

50. a³-b³
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(a-b)(a²+ab+b²)
1/2 h (b1 + b2)