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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. If something is certain to happen - how is the probability of this event expressed mathematically?
1/3Bh
(a+b)(a²-ab+b²)
1/1
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

2. Arc
Part of a circle connecting two points on 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
1
Arrangements - orders - schedules - or lists.

3. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(y-y1)=m(x-x1)

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

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5. What is the length of an arc?
(n degrees/360) * 2(pi)r
The average - mean - median - or mode.
A+b
(a-b)(a²+ab+b²)

6. What is a '30:60:90' triangle?
A²-b²
(pi)r^2(h)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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

7. What is the 'Third side' rule for triangles?
T1 + (n-1)d
(x+y)²
Opens down
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.

8. Rough est. of v3 =
Ac+ad+bc+bd
1.7
S*v2
Sum of terms/number of terms

9. Rough est. of v1 =
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Bh

10. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Arrangements - orders - schedules - or lists.
1.4
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
2x2x2x5x5

11. What number goes on the bottom of a probability fraction?
(n degrees/360) * (pi)r^2
Probability A + Probability B
2 pi r
The total # of possible outcomes.

12. What is the area of a solid rectangle?
1/3Bh
x°/360 times (?r²) - where x is the degrees in the angle
2(lw+wh+lh)
Pi*d

13. Area of a trapezoid
1/3Bh
1/2bh
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Negative

14. In intersecting lines - opposite angles are _____.
Equal
The set of points which are all the same distance (the radius) from a certain point (the center).
(a+b)²
Arrangements - orders - schedules - or lists.

15. What do combination problems usually ask for?
Groups - teams - or committees.
S*v2
4/3pir^3
The distance across the circle through the center of the circle.The diameter is twice the radius.

16. Perimeter of polygon
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
A²-b²
Sum of the lengths of the sides

17. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
2(pi)r(r+h)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.

18. Surface Area of rectangular prism
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.
Number of desired outcomes/number of total outcomes
Part of a circle connecting two points on the circle.
2lw+2lh+2wh

19. What is the circumference of a circle?
2(pi)r
1.4
Negative
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'.

20. Circle
Opens up
Probability A * Probability B
The set of points which are all the same distance (the radius) from a certain point (the center).
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

21. When you reverse FOIL - the term that needs to add out is the _____
2 pi r
Middle term
1/x^a
The distance across the circle through the center of the circle.The diameter is twice the radius.

22. Area of a circle
?r²
2(lw+wh+lh)
?d OR 2?r
Not necessarily. This is a trick question - because x could be either positive or negative.

23. (a+b)(a-b)=
A²-b²
Last term
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(n/2) * (t1+tn)

24. What'S the most important thing to remember about charts you'll see on the GRE?
y2-y1/x2-x1
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.
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.
S² - where s = length of a side

25. a³+b³
x²-y²
4pir^2
(a+b)(a²-ab+b²)
(0 -0)

26. Define the mode of a set of numbers.
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.
A+b
Arrangements - orders - schedules - or lists.
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.

27. What is directly proportional?
y = kx
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.
(0 -0)
The four big angles are equal and the four small angles are equal

28. What is the area of a circle?
(pi)r^2
A²-b²
(x-y)²
x² -2xy + y²

29. Circumference of a circle
(a+b)²
The average - mean - median - or mode.
1/x^a
?d OR 2?r

30. What is the distance formula?
Bh
A=?r2
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.
Sqr( x2 -x1) + (y2- y1)

31. Explain the special properties of zero.
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.
1/1
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
Sum of the lengths of the sides

32. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
The four big angles are equal and the four small angles are equal
The distance from one point on the circle to another point on the circle.
Number of desired outcomes/number of total outcomes

33. Volume of Cone
y = k/x
Between 0 and 1.
1/3pir^2*h
(a+b)²

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

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35. In a parabola - if the first term is negative - the parabola ________.
Opens down
S*v2
N x M
2(lw+wh+lh)

36. Does order matter for a permutation? How about for a combination?
Pir^2h
1/2bh
Order does matter for a permutation - but does not matter for a combination.
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

37. How do you find the nth term of an arithmetic sequence?
2x2x2x5x5
A=?r2
1/2 h (b1 + b2)
T1 + (n-1)d

38. Area of a triangle
1
½(base x height) [or (base x height)÷2]
2(pi)r(r+h)
1. Given event A: A + notA = 1.

39. Explain the difference between a digit and a number.

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40. How do you find the midpoint?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Bh
An ange whose vertex is the center of the circle
(x1+x2)/2 - (y1+y2)/2

41. a³-b³
(a-b)(a²+ab+b²)
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
x°/360 times (?r²) - where x is the degrees in the angle
1/3pir^2*h

42. The length of one side of any triangle is ____ than the sum of the other two sides.
1/2 h (b1 + b2)
Less
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.
Arrangements - orders - schedules - or lists.

43. What is the equation of a line?

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44. Surface Area of Sphere
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
?r²
4pir^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.

45. What is the area of a cylinder?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2Length + 2width [or (length + width) x 2]
1.4
2(pi)r(r+h)

46. What is the volume of a cylinder?
(pi)r^2(h)
1/3Bh
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

47. a²-2ab+b²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2lw+2lh+2wh
1.7
(a-b)²

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

49. Point-Slope form
(0 -0)
x°/360 times (?r²) - where x is the degrees in the angle
y-y1=m(x-x1)
Groups - teams - or committees.

50. 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.
S^2
x²-y²
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.

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GRE Math 2

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