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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. a²-b²
(a-b)²
(a-b)(a+b)
Lw
Lwh

2. Area of Trapezoid
x²-y²
2pi*r
(a-b)²
1/2 h (b1 + b2)

3. When a line crosses two parallel lines - ________.
The four big angles are equal and the four small angles are equal
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
(n degrees/360) * 2(pi)r

4. Rough est. of v1 =
½(base x height) [or (base x height)÷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.
1
Part of a circle connecting two points on the circle.

5. Radius (Radii)
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.
Between 0 and 1.
Probability A * Probability B
A segment connecting the center of a circle to any point on the circle

6. What is the side ratio for a Right Isosceles triangle?
1/3Bh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Last term
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.

7. (a+b)(c+d)
Ac+ad+bc+bd
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.
Bh
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.

8. What is the formula for the diagonal of any square?
S*v2
Bh
2 pi r
(pi)r^2(h)

9. Perimeter of a rectangle
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
2Length + 2width [or (length + width) x 2]
2pir^2 + 2pir*h
An ange whose vertex is the center of the circle

10. What is the area of a solid rectangle?
y2-y1/x2-x1
2(lw+wh+lh)
Middle term
y-y1=m(x-x1)

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

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12. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
T1 * r^(n-1)/(r-1)
Middle term
(a-b)²

13. Volume of sphere
Opens up
b±[vb²-4ac]/2a
4/3pir^3
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

14. Area of Parallelogram
(pi)r^2
(n degrees/360) * (pi)r^2
2Length + 2width [or (length + width) x 2]
Bh

15. What is the 'Third side' rule for triangles?
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
T1 * r^(n-1)/(r-1)
2(pi)r(r+h)

16. a³-b³
T1 * r^(n-1)/(r-1)
Equal
(a-b)(a²+ab+b²)
A²-b²

17. What is the factored version of x² -2xy + y² ?
1.4
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Pi*r^2
(x-y)²

18. What is a 'Right isosceles' triangle?
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.
2(pi)r(r+h)
Pi*d
(pi)r^2(h)

19. How do you find the sum of a geometric sequence?
?r²
T1 * r^(n-1)/(r-1)
S² - where s = length of a side
1.4

20. What are the side ratios for a 30:60:90 triangle?
Pi*r^2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x 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
2pir^2 + 2pir*h

21. 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.
y2-y1/x2-x1
Number of desired outcomes/number of total outcomes
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.

22. Central Angle
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 segment connecting the center of a circle to any point on the circle
4s (where s = length of a side)
An ange whose vertex is the center of the circle

23. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
The total # of possible outcomes.
Sum of the lengths of the sides
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.

24. Area of a trapezoid
The average - mean - median - or mode.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
1/2bh
1/3Bh

25. What is directly proportional?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
y = kx
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

26. What is the unfactored version of x²-y² ?
(x+y)(x-y)
1
1/2bh
The distance from one point on the circle to another point on the circle.

27. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
(a+b)(a²-ab+b²)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2(pi)r(r+h)

28. (a+b)(a-b)=
2l+2w
A²-b²
Order does matter for a permutation - but does not matter for a combination.
2 pi r

29. Explain the special properties of zero.
The distance from one point on the circle to another point on the circle.
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.
C =?d
1.7

30. length of a sector
1/2 h (b1 + b2)
Probability A + Probability B
1. Given event A: A + notA = 1.
x°/360 times (2 pi r) - where x is the degrees in the angle

31. How do you find the midpoint?
Bh
2pi*r
(x1+x2)/2 - (y1+y2)/2
4s (where s = length of a side)

32. What is the area of a sector?
y2-y1/x2-x1
(n degrees/360) * (pi)r^2
(a+b)²
(x+y)(x-y)

33. Slope
Sum of terms/number of terms
(y2-y1)/(x2-x1)
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.
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.

34. Lines reflected over the x or y axis have ____ slopes.
(n degrees/360) * 2(pi)r
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.
Probability A + Probability B
Negative

35. For a bell curve - what three terms might be used to describe the number in the middle?
Percentage Change = Difference/Original * 100
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The average - mean - median - or mode.
Lwh

36. What is inversely proportional?
y = k/x
2l+2w
The distance from one point on the circle to another point on the circle.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

37. Area of Circles
A=?r2
1/3pir^2*h
?r²
½(base x height) [or (base x height)÷2]

38. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
2lw+2lh+2wh
(x+y)(x-y)
Pir^2h

39. What is the circumference of a circle?
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.
b±[vb²-4ac]/2a
2(pi)r
1.4

40. In intersecting lines - opposite angles are _____.
Equal
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.
(x1+x2)/2 - (y1+y2)/2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

41. Volume of pyramid
2pi*r
1/3Bh
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.
Sum of the lengths of the sides

42. In a coordinate system - what is the origin?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
T1 * r^(n-1)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(0 -0)

43. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
2lw+2lh+2wh
Equal
The four big angles are equal and the four small angles are equal
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.

44. a²+2ab+b²
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'.
(a+b)²
1/2bh
1/3Bh

45. Arc
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
(n degrees/360) * (pi)r^2
Part of a circle connecting two points on the circle.

46. Point-Slope form
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Lwh

47. Volume of prism
Pi*r^2
(a+b)²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Bh

48. What is the 'distributive law'?
T1 * r^(n-1)/(r-1)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
A=bh

49. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
(n degrees/360) * (pi)r^2
1/2 h (b1 + b2)
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.

50. Define the 'Third side' rule for triangles

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