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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. Define 'proportionate' values
The set of points which are all the same distance (the radius) from a certain point (the center).
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Pir^2h
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

2. How do you multiply and divide square roots?
(x+y)²
2Length + 2width [or (length + width) x 2]
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
x² + 2xy + y²

3. What is the circumference of a circle?
The average - mean - median - or mode.
2(pi)r
Lw
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

4. a²+2ab+b²
T1 * r^(n-1)/(r-1)
(a+b)²
(pi)r^2(h)
The average - mean - median - or mode.

5. What is the average speed?
1/2bh
The four big angles are equal and the four small angles are equal
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
Total distance/total time

6. 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.
1/3pir^2*h
(n degrees/360) * (pi)r^2
(a-b)(a+b)

7. 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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8. List two odd behaviors of exponents
A+b
The distance from one point on the circle to another point on the circle.
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.
Pir^2h

9. What is the unfactored version of (x-y)² ?
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'.
(n/2) * (t1+tn)
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.
x² -2xy + y²

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

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11. Volume of pyramid
?r²
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.
1/3Bh
½(b1 +b2) x h [or (b1 +b2) x h÷2]

12. What is the area of a sector?
(a-b)(a+b)
2pi*r
(n degrees/360) * (pi)r^2
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

13. Perimeter of polygon
Sum of the lengths of the sides
S^2
1/2bh
(x-y)²

14. Area of Square
(a-b)(a+b)
1.7
2(pi)r(r+h)
S^2

15. What is the factored version of x² -2xy + y² ?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Sum of terms/number of terms
(x-y)²
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.

16. In a coordinate system - identify the quadrants and describe their location.
Less
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
(n degrees/360) * (pi)r^2

17. When you reverse FOIL - the term that needs to multiply out is the _____
A=bh
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Last term
T1 * r^(n-1)

18. What is the probability?
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'.
Number of desired outcomes/number of total outcomes
S² - where s = length of a side
(x-y)²

19. Define the mode of a set of numbers.
N x M
Number of desired outcomes/number of total outcomes
Sum of terms/number of terms
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. 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.
Total distance/total time
b±[vb²-4ac]/2a
2pi*r

21. Area of a square
Percentage Change = Difference/Original * 100
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.
S² - where s = length of a side
2Length + 2width [or (length + width) x 2]

22. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
1/2bh
Sum of terms/number of terms
S*v2

23. What are the side ratios for a 30:60:90 triangle?
x°/360 times (2 pi r) - where x is the degrees in the angle
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
½(base x height) [or (base x height)÷2]

24. Area of a triangle
½(base x height) [or (base x height)÷2]
1. Given event A: A + notA = 1.
4s (where s = length of a side)
The total # of possible outcomes.

25. Volume of sphere
4pir^2
4/3pir^3
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
S² - where s = length of a side

26. What is the prime factorization of 200?
The four big angles are equal and the four small angles are equal
Probability A + Probability B
2x2x2x5x5
1

27. What is the factored version of x² + 2xy + y² ?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(x+y)²
(n-2)180
4/3pir^3

28. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
(a+b)²
Probability A + Probability B
(a-b)(a+b)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

29. What is the area of a cylinder?
b±[vb²-4ac]/2a
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.
Middle term
2(pi)r(r+h)

30. How do you find the slope?
y2-y1/x2-x1
(0 -0)
(y2-y1)/(x2-x1)
x² + 2xy + y²

31. Perimeter of rectangle
2l+2w
(a+b)²
?d OR 2?r
Sum of terms/number of terms

32. In a coordinate system - what is the origin?
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.
(n/2) * (t1+tn)
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.
(0 -0)

33. Circumference Formula
Part of a circle connecting two points on the circle.
C =?d
Order does matter for a permutation - but does not matter for a combination.
Sum of terms/number of terms

34. x^a * x^b = x^__
A+b
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Between 0 and 1.
(x1+x2)/2 - (y1+y2)/2

35. What do permutation problems often ask for?
(n/2) * (t1+tn)
Arrangements - orders - schedules - or lists.
T1 * r^(n-1)
4s (where s = length of a side)

36. Diameter
N x M
The distance across the circle through the center of the circle.The diameter is twice the radius.
Pi*r^2
A segment connecting the center of a circle to any point on the circle

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

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38. Arc
S² - where s = length of a side
Part of a circle connecting two points on the circle.
1/2bh
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

39. Chord
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.
Sum of terms/number of terms
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The distance from one point on the circle to another point on the circle.

40. Area of Trapezoid
Pi*d
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/2 h (b1 + b2)
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

41. If something is possible but not certain - what is the numeric range of probability of it happening?
2lw+2lh+2wh
Between 0 and 1.
Probability A + Probability B
(a-b)(a²+ab+b²)

42. Area of a trapezoid
(n degrees/360) * 2(pi)r
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Probability A * Probability B
½(b1 +b2) x h [or (b1 +b2) x h÷2]

43. Circle
The set of points which are all the same distance (the radius) from a certain point (the center).
?r²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
x² + 2xy + y²

44. What is the area of a triangle?
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Bh
1/2bh

45. Rough est. of v1 =
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.
1
(a+b)(a-b)
4s (where s = length of a side)

46. How do you multiply powers with the same base?
4s
T1 + (n-1)d
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.

47. The length of one side of any triangle is ____ than the sum of the other two sides.
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.
Total distance/total time
Less
?d OR 2?r

48. 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.
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
1/3Bh
The distance across the circle through the center of the circle.The diameter is twice the radius.

49. How do you find the nth term of an arithmetic sequence?
S*v2
T1 + (n-1)d
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.
A=?r2

50. a²-2ab+b²
Number of desired outcomes/number of total outcomes
Opens down
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.
(a-b)²