GRE Math 2

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. What is inversely proportional?
2(pi)r(r+h)
y = k/x
A segment connecting the center of a circle to any point on the circle
S*v2


2. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
(a+b)(a-b)
2 pi r
4s
N x M


3. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
(a-b)(a+b)
Pi*r^2
1. Given event A: A + notA = 1.


4. Perimeter of rectangle
2l+2w
y = kx
y2-y1/x2-x1
(x+y)(x-y)


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

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6. What is the area of a triangle?
(n/2) * (t1+tn)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/2bh
4/3pir^3


7. What is the unfactored version of (x+y)² ?
x² + 2xy + y²
1.7
(pi)r^2(h)
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.


8. Area of Circle
Probability A + Probability B
Pi*r^2
Lwh
(a-b)²


9. What is the area of a sector?
A²-b²
C =?d
(n degrees/360) * (pi)r^2
(pi)r^2


10. Volume of prism
x°/360 times (?r²) - where x is the degrees in the angle
Ac+ad+bc+bd
S*v2
Bh


11. a² - b² is equal to
Less
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
(a+b)(a-b)


12. Volume of Cone
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
1/3pir^2*h
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.


13. Area of a circle
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
Total distance/total time
?r²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


14. Area of Trapezoid
Part of a circle connecting two points on the circle.
1/2 h (b1 + b2)
(n-2)180
Probability A * Probability B


15. perimeter of square
4s
Lwh
Bh
A segment connecting the center of a circle to any point on the circle


16. Define the 'Third side' rule for triangles

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17. How do you calculate a diagonal inside a 3-dimensional rectangular box?
(a-b)(a+b)
The set of points which are all the same distance (the radius) from a certain point (the center).
(pi)r^2(h)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


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

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19. Quadratic Formula
b±[vb²-4ac]/2a
Part of a circle connecting two points on the circle.
2(pi)r
1/2 h (b1 + b2)


20. How do you calculate the surface area of a rectangular box?
2(pi)r
Opens down
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.


21. What number goes on the bottom of a probability fraction?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The total # of possible outcomes.
Total distance/total time
b±[vb²-4ac]/2a


22. What is directly proportional?
y = kx
A segment connecting the center of a circle to any point on the circle
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.


23. How do you find the sum of a geometric sequence?
Less
(x+y)(x-y)
T1 * r^(n-1)/(r-1)
S^2


24. How do you find the sum of an arithmetic sequence?
(n/2) * (t1+tn)
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.
The average - mean - median - or mode.
(y2-y1)/(x2-x1)


25. Define a factorial of a number - and how it is written.
Total distance/total time
An ange whose vertex is the center of the circle
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.


26. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
S^2
The distance from one point on the circle to another point on the circle.
The average - mean - median - or mode.


27. x^a * x^b = x^__
4s (where s = length of a side)
1.7
A+b
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.


28. In a parabola - if the first term is negative - the parabola ________.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The distance from one point on the circle to another point on the circle.
Opens down
x² -2xy + y²


29. Rough est. of v2 =
1.4
(x1+x2)/2 - (y1+y2)/2
b±[vb²-4ac]/2a
(0 -0)


30. What is the volume of a solid rectangle?
The distance across the circle through the center of the circle.The diameter is twice the radius.
Lwh
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.
1.4


31. What is the prime factorization of 200?
Probability A * Probability B
1/1
2x2x2x5x5
Opens down


32. What is the probability?
2lw+2lh+2wh
Ac+ad+bc+bd
Number of desired outcomes/number of total outcomes
(y2-y1)/(x2-x1)


33. Circumference of a circle
?d OR 2?r
Order does matter for a permutation - but does not matter for a combination.
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.
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


34. a²-b²
(a-b)(a+b)
(0 -0)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Part of a circle connecting two points on the circle.


35. What is the area of a cylinder?
2Length + 2width [or (length + width) x 2]
2(pi)r(r+h)
?r²
(x-y)²


36. x^-a =
1/x^a
(pi)r^2(h)
Pi*d
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.


37. Circumference Formula
1/2bh
C =?d
b±[vb²-4ac]/2a
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.


38. What is the equation of a line?

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39. Lines reflected over the x or y axis have ____ slopes.
A²-b²
C =?d
Negative
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.


40. What is an 'equilateral' triangle?
Total distance/total time
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2lw+2lh+2wh
(x+y)(x-y)


41. What is the side ratio for a 30:60:90 triangle?
b±[vb²-4ac]/2a
4s (where s = length of a side)
x²-y²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


42. 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.
A+b
Opens down
Lw


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

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44. Area of a square
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.
S² - where s = length of a side
T1 + (n-1)d
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


45. Volume of sphere
N x M
4/3pir^3
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.
Order does matter for a permutation - but does not matter for a combination.


46. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
Bh
Lwh
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.


47. Volume of pyramid
1/3Bh
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
Lw
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


48. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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)
1/2 h (b1 + b2)
1. Given event A: A + notA = 1.


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

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50. Sector
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.
S^2
(n/2) * (t1+tn)
2(pi)r(r+h)