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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. Volume of sphere
4/3pir^3
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
1/3Bh

2. What is the probability?
Number of desired outcomes/number of total outcomes
A=?r2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
y = k/x

3. What is the length of an arc?
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.
(n degrees/360) * 2(pi)r
1/3Bh
(a+b)(a²-ab+b²)

4. Area of Square
2lw+2lh+2wh
4s (where s = length of a side)
S^2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

5. What is the sum of the inside angles of an n-sided polygon?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(a+b)²
N x M
(n-2)180

6. Diameter
N x M
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.
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.

7. Area of a sector
2(pi)r(r+h)
Ac+ad+bc+bd
Sqr( x2 -x1) + (y2- y1)
x°/360 times (?r²) - where x is the degrees in the angle

8. Area of Circle
The distance across the circle through the center of the circle.The diameter is twice the radius.
1/1
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.
Pi*r^2

9. a² - b² is equal to
Probability A * Probability B
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(a+b)(a-b)

10. How do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
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.
Equal
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

11. How do you calculate the probability of two events in a row? (Probability of A and B)
Sum of the lengths of the sides
Probability A * Probability B
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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'.

12. What do combination problems usually ask for?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Groups - teams - or committees.
1/2 h (b1 + b2)
2(pi)r(r+h)

13. What is the surface area of a cylinder?
2(pi)r(r+h)
Probability A * Probability B
2l+2w
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.

14. What is the area of a cylinder?
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.
2(pi)r(r+h)
Lwh
Bh

15. What is the 'distributive law'?
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Middle term

16. Area of Rectangle
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.
1/x^a
Lw
(a+b)(a²-ab+b²)

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

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

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19. Perimeter of a square
Number of desired outcomes/number of total outcomes
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.
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
4s (where s = length of a side)

20. What is the side ratio for a Right Isosceles triangle?
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.
Lwh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1.4

21. Rough est. of v3 =
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1.7
The distance across the circle through the center of the circle.The diameter is twice the radius.

22. What is the factored version of x² -2xy + y² ?
y = kx
(x-y)²
Order does matter for a permutation - but does not matter for a combination.
Ac+ad+bc+bd

23. Area of Trapezoid
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2x2x2x5x5
1/2 h (b1 + b2)
(a+b)²

24. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
(n degrees/360) * (pi)r^2
2 pi r
N x M
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

25. When you reverse FOIL - the term that needs to add out is the _____
x² -2xy + y²
T1 * r^(n-1)/(r-1)
An ange whose vertex is the center of the circle
Middle term

26. a²-b²
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.
2pir^2 + 2pir*h
(a-b)(a+b)
x°/360 times (?r²) - where x is the degrees in the angle

27. Lines reflected over the x or y axis have ____ slopes.
2 pi r
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
4s (where s = length of a side)
Negative

28. Point-Slope form
The four big angles are equal and the four small angles are equal
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
?r²
y-y1=m(x-x1)

29. 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
(0 -0)
1
A+b

30. What is the unfactored version of x²-y² ?
(x+y)(x-y)
(a+b)²
1.7
A segment connecting the center of a circle to any point on the circle

31. List two odd behaviors of exponents
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
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.
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.
Negative

32. What is the point-slope form?
(y-y1)=m(x-x1)
b±[vb²-4ac]/2a
x² -2xy + y²
y-y1=m(x-x1)

33. What is inversely proportional?
That they often have not just one answer - but two. For example - solving x² -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
b±[vb²-4ac]/2a
y = k/x
Ac+ad+bc+bd

34. Rough est. of v1 =
A+b
½(base x height) [or (base x height)÷2]
1. Given event A: A + notA = 1.
1

35. 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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36. 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.
(x+y)²
The average - mean - median - or mode.
S² - where s = length of a side

37. 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.
A=?r2
y = k/x
Part of a circle connecting two points on the circle.

38. Define the mode of a set of numbers.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2(pi)r(r+h)
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.
(n/2) * (t1+tn)

39. How do you solve a permutation?
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.
y-y1=m(x-x1)
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
A=bh

40. Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Pir^2h
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.

41. Circumference Formula
N x M
C =?d
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.
(x+y)(x-y)

42. What is a 'Right isosceles' triangle?
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.
(a+b)(a²-ab+b²)
1/1
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.

43. Does order matter for a permutation? How about for a combination?
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Order does matter for a permutation - but does not matter for a combination.
(x-y)²

44. Surface Area of Cylinder
(x-y)²
Ac+ad+bc+bd
T1 * r^(n-1)/(r-1)
2pir^2 + 2pir*h

45. Perimeter of a rectangle
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.
2Length + 2width [or (length + width) x 2]
(0 -0)
(n-2)180

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

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47. (a+b)(c+d)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Ac+ad+bc+bd
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.
2(pi)r

48. How do you find the nth term of a geometric sequence?
2(lw+wh+lh)
T1 * r^(n-1)
An ange whose vertex is the center of the circle
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

49. How do you find the sum of an arithmetic sequence?
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.
(n/2) * (t1+tn)
Probability A + Probability B
1/2bh

50. How do you calculate the percentage of change?
The total # of possible outcomes.
A²-b²
Percentage Change = Difference/Original * 100
2pir^2 + 2pir*h