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GRE Math 2

Subjects : gre, math

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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 the equation of a line?

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2. In intersecting lines - opposite angles are _____.
2x2x2x5x5
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
1/3pir^2*h
Equal

3. When you reverse FOIL - the term that needs to multiply out is the _____
1.7
x² -2xy + y²
Last term
1. Given event A: A + notA = 1.

4. Define the range of a set of numbers.
Order does matter for a permutation - but does not matter for a combination.
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.
?r²
(y-y1)=m(x-x1)

5. Area of Parallelogram
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.
Bh
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
1/1

6. a²-b²
C =?d
Percentage Change = Difference/Original * 100
4s (where s = length of a side)
(a-b)(a+b)

7. What is the length of an arc?
(n degrees/360) * 2(pi)r
2(pi)r(r+h)
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.
2(pi)r

8. How do you find the midpoint?
Lw
1/2 h (b1 + b2)
Between 0 and 1.
(x1+x2)/2 - (y1+y2)/2

9. What is the area of a cylinder?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/2 h (b1 + b2)
2(pi)r(r+h)
y = k/x

10. What is the formula for the diagonal of any square?
S*v2
y2-y1/x2-x1
(a-b)(a²+ab+b²)
(x+y)(x-y)

11. What is directly proportional?
1/3pir^2*h
1.7
(n degrees/360) * 2(pi)r
y = kx

12. Volume of prism
Not necessarily. This is a trick question - because x could be either positive or negative.
Bh
Equal
1/3Bh

13. What is the volume of a solid rectangle?
x² + 2xy + y²
The total # of possible outcomes.
Lwh
An ange whose vertex is the center of the circle

14. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Last term
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(x1+x2)/2 - (y1+y2)/2
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

15. What is a 'Right isosceles' triangle?
A+b
x°/360 times (2 pi r) - where x is the degrees in the angle
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.

16. Lines reflected over the x or y axis have ____ slopes.
Negative
2pi*r
Pir^2h
1/1

17. Area of a circle
?r²
S² - where s = length of a side
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The total # of possible outcomes.

18. Area of Circle
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(n degrees/360) * 2(pi)r
Pi*r^2
Probability A * Probability B

19. What is inversely proportional?
(a-b)(a+b)
Pir^2h
y = k/x
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.

20. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
A segment connecting the center of a circle to any point on the circle
The total # of possible outcomes.
S² - where s = length of a side

21. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
x²-y²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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

22. Volume of Cone
4s (where s = length of a side)
S^2
1/3pir^2*h
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.

23. What is the area of a circle?
A+b
The total # of possible outcomes.
(pi)r^2
4s

24. Surface Area of rectangular prism
The distance from one point on the circle to another point on the circle.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
½(base x height) [or (base x height)÷2]
2lw+2lh+2wh

25. What is the average?
Sum of terms/number of terms
Less
2(pi)r(r+h)
(n-2)180

26. List two odd behaviors of exponents
Bh
T1 + (n-1)d
2(lw+wh+lh)
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.

27. 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.
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)
(a+b)²

28. a²-2ab+b²
(a-b)²
A=bh
1.4
Sqr( x2 -x1) + (y2- y1)

29. Volume of Cylinder
Pir^2h
(n degrees/360) * (pi)r^2
½(b1 +b2) x h [or (b1 +b2) x h÷2]
½(base x height) [or (base x height)÷2]

30. Area of Square
S^2
2pir^2 + 2pir*h
Between 0 and 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.

31. Central Angle
(pi)r^2
y-y1=m(x-x1)
An ange whose vertex is the center of the circle
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

32. Arc
Part of a circle connecting two points on the circle.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(x-y)²
x°/360 times (?r²) - where x is the degrees in the angle

33. What number goes on the bottom of a probability fraction?
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
Sum of terms/number of terms
The total # of possible outcomes.

34. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2(pi)r(r+h)
2(pi)r(r+h)
A segment connecting the center of a circle to any point on the circle

35. What is the area of a triangle?
Arrangements - orders - schedules - or lists.
Between 0 and 1.
?r²
1/2bh

36. Radius (Radii)
4s (where s = length of a side)
A segment connecting the center of a circle to any point on the circle
x² + 2xy + y²
2lw+2lh+2wh

37. What do combination problems usually ask for?
1.4
Pir^2h
Groups - teams - or committees.
Arrangements - orders - schedules - or lists.

38. How do you solve a permutation?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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
2l+2w
2(pi)r

39. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
(a+b)(a²-ab+b²)
2x2x2x5x5
The four big angles are equal and the four small angles are equal

40. Surface Area of Cylinder
The four big angles are equal and the four small angles are equal
(a+b)(a-b)
2pir^2 + 2pir*h
2(pi)r(r+h)

41. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
Negative
1/x^a
Lw

42. x^a * x^b = x^__
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.
2(pi)r(r+h)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
A+b

43. Area of a triangle
4s (where s = length of a side)
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.
½(base x height) [or (base x height)÷2]
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

44. Perimeter of a 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.
2Length + 2width [or (length + width) x 2]
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 = 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'.

45. Chord
Pi*r^2
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 from one point on the circle to another point on the circle.
Bh

46. What is a '30:60:90' triangle?
Groups - teams - or committees.
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.
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
2(lw+wh+lh)

47. Circumference of a circle using radius
Order does matter for a permutation - but does not matter for a combination.
(a-b)(a²+ab+b²)
Equal
2pi*r

48. What is an 'equilateral' triangle?
The distance from one point on the circle to another point on the circle.
1/1
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

49. How do you find the nth term of a geometric sequence?
1
y = k/x
(a+b)²
T1 * r^(n-1)

50. 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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GRE Math 2

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