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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.
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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. What is a '30:60:90' triangle?
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
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
4s

2. How do you solve a permutation?
The distance from one point on the circle to another point on the circle.
Opens up
4s (where s = length of a side)
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

3. What is the average speed?
(a+b)(a²-ab+b²)
Total distance/total time
2(pi)r
(a-b)(a+b)

4. Area of a sector
Opens down
(pi)r^2(h)
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.
x°/360 times (?r²) - where x is the degrees in the angle

5. What is a 'Right isosceles' triangle?
(x+y)(x-y)
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
(n degrees/360) * (pi)r^2

6. In a coordinate system - what is the origin?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(0 -0)
Probability A * Probability B
1/2bh

7. What is the area of a circle?
(n degrees/360) * (pi)r^2
(x+y)(x-y)
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.
(pi)r^2

8. 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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9. What do permutation problems often ask for?
2(pi)r(r+h)
(x+y)²
Arrangements - orders - schedules - or lists.
1/1

10. How do you calculate the surface area of a rectangular box?
N x M
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a-b)²
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.

11. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Number of desired outcomes/number of total outcomes
1. Given event A: A + notA = 1.
S² - where s = length of a side

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

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13. How do you calculate the percentage of change?
(n-2)180
Percentage Change = Difference/Original * 100
The distance from one point on the circle to another point on the circle.
S² - where s = length of a side

14. In a parabola - if the first term is negative - the parabola ________.
Opens down
T1 * r^(n-1)
(a-b)(a+b)
Probability A * Probability B

15. What is the sum of the inside angles of an n-sided polygon?
(x+y)(x-y)
The average - mean - median - or mode.
(n-2)180
2pi*r

16. When you reverse FOIL - the term that needs to add out is the _____
Middle term
Pi*d
x²-y²
T1 * r^(n-1)

17. Surface Area of Sphere
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.
4s (where s = length of a side)
4pir^2
(n degrees/360) * (pi)r^2

18. Volume of pyramid
(a+b)(a²-ab+b²)
Opens up
1/3Bh
1.4

19. What is the unfactored version of (x-y)² ?
2(lw+wh+lh)
x² -2xy + y²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Last term

20. How do you multiply powers with the same base?
Opens down
A+b
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
4/3pir^3

21. perimeter of square
4s
Order does matter for a permutation - but does not matter for a combination.
T1 * r^(n-1)/(r-1)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

22. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2(pi)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.
2pir^2 + 2pir*h

23. What is the distance formula?
1. Given event A: A + notA = 1.
Sqr( x2 -x1) + (y2- y1)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2l+2w

24. Perimeter (circumference) of a circle
A+b
A²-b²
2 pi r
2lw+2lh+2wh

25. (a+b)(c+d)
Ac+ad+bc+bd
Pi*d
N x M
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

26. What is the area of a triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Pi*r^2
1/2bh
Part of a circle connecting two points on the circle.

27. How do you find the slope?
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 distance across the circle through the center of the circle.The diameter is twice the radius.
2 pi r

28. a²+2ab+b²
y = kx
y2-y1/x2-x1
An ange whose vertex is the center of the circle
(a+b)²

29. x^a * x^b = x^__
A+b
2pi*r
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 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.

30. How do you find the sum of an arithmetic sequence?
Lw
(n/2) * (t1+tn)
Probability A * Probability B
The total # of possible outcomes.

31. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.
Bh

32. x^-a =
b±[vb²-4ac]/2a
Sum of the lengths of the sides
1/x^a
The distance from one point on the circle to another point on the circle.

33. In intersecting lines - opposite angles are _____.
Bh
(y-y1)=m(x-x1)
T1 + (n-1)d
Equal

34. What is the factored version of x² + 2xy + y² ?
(x+y)²
Order does matter for a permutation - but does not matter for a combination.
(a+b)(a-b)
N x M

35. Area of Rectangle
Lw
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2(lw+wh+lh)
½(base x height) [or (base x height)÷2]

36. What is the area of a sector?
2l+2w
(n degrees/360) * (pi)r^2
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.
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.

37. Surface Area of rectangular prism
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.
Total distance/total time
2lw+2lh+2wh
2pir^2 + 2pir*h

38. What is the equation of a line?

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39. Volume of sphere
?r²
4/3pir^3
1/1
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. a³-b³
1.7
S^2
(a-b)(a²+ab+b²)
The four big angles are equal and the four small angles are equal

41. What'S the most important thing to remember about charts you'll see on the GRE?
Negative
(a+b)(a²-ab+b²)
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.
2pi*r

42. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Negative
(a+b)(a²-ab+b²)
The total # of possible outcomes.

43. Point-Slope form
1. Given event A: A + notA = 1.
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.
y-y1=m(x-x1)
Total distance/total time

44. What is the circumference of a circle?
2(pi)r
2l+2w
(x+y)(x-y)
(a-b)²

45. What is the probability?
The distance across the circle through the center of the circle.The diameter is twice the radius.
Ac+ad+bc+bd
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.
Number of desired outcomes/number of total outcomes

46. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
½(base x height) [or (base x height)÷2]
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.
(x1+x2)/2 - (y1+y2)/2

47. Circumference of a circle using radius
2pi*r
x² -2xy + y²
Not necessarily. This is a trick question - because x could be either positive or negative.
1/x^a

48. What is the factored version of (x+y)(x-y) ?
(pi)r^2
b±[vb²-4ac]/2a
x²-y²
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

49. The length of one side of any triangle is ____ than the sum of the other two sides.
The four big angles are equal and the four small angles are equal
Less
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2pir^2 + 2pir*h

50. Circumference of cirlce using diameter
1.4
Pi*d
Negative
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

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GRE Math 2

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