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. Area of rectangle - square - parallelogram
A=bh
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Part of a circle connecting two points on the circle.
Not necessarily. This is a trick question - because x could be either positive or negative.


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

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3. Surface Area of Sphere
4pir^2
A²-b²
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.
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.


4. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
N x M
T1 * r^(n-1)
y = k/x
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


5. What is the factored version of x² + 2xy + y² ?
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
C =?d
(x+y)²
2pir^2 + 2pir*h


6. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
1
The total # of possible outcomes.
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
2(lw+wh+lh)


7. What is the area of a cylinder?
Lwh
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2(pi)r(r+h)
C =?d


8. What is the equation of a line?

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

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10. Volume of sphere
4/3pir^3
Last term
Percentage Change = Difference/Original * 100
A=?r2


11. Define 'proportionate' values
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Between 0 and 1.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.


12. What is the point-slope form?
(x+y)(x-y)
(n-2)180
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.
(y-y1)=m(x-x1)


13. 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
2pi*r
(0 -0)
½(b1 +b2) x h [or (b1 +b2) x h÷2]


14. Circle
(pi)r^2(h)
The set of points which are all the same distance (the radius) from a certain point (the center).
Total distance/total time
Lw


15. What number goes on the bottom of a probability fraction?
(x-y)²
The total # of possible outcomes.
4s (where s = length of a side)
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.


16. What is the distance formula?
y-y1=m(x-x1)
(x+y)²
Sqr( x2 -x1) + (y2- y1)
1.4


17. Rough est. of v2 =
(a-b)²
1.4
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
½(b1 +b2) x h [or (b1 +b2) x h÷2]


18. What is the volume of a cylinder?
1/3pir^2*h
x°/360 times (2 pi r) - where x is the degrees in the angle
(pi)r^2(h)
(a+b)(a²-ab+b²)


19. How do you multiply and divide square roots?
(x1+x2)/2 - (y1+y2)/2
Negative
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


20. Explain the special properties of zero.
1/3Bh
A²-b²
x°/360 times (2 pi r) - where x is the degrees in the angle
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.


21. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
4s (where s = length of a side)
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.
y2-y1/x2-x1
Number of desired outcomes/number of total outcomes


22. Area of Trapezoid
Arrangements - orders - schedules - or lists.
1/2 h (b1 + b2)
1/2bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


23. Volume of prism
?r²
A=bh
Bh
1/1


24. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
Pi*d
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/2bh


25. What is the area of a solid rectangle?
N x M
(x1+x2)/2 - (y1+y2)/2
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.
2(lw+wh+lh)


26. How do you find the slope?
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.
(n degrees/360) * 2(pi)r
Not necessarily. This is a trick question - because x could be either positive or negative.
y2-y1/x2-x1


27. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
Between 0 and 1.
2lw+2lh+2wh
y2-y1/x2-x1


28. What is inversely proportional?
Lwh
Pi*d
Pir^2h
y = k/x


29. 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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30. a²+2ab+b²
The distance across the circle through the center of the circle.The diameter is twice the radius.
(a+b)²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
x² + 2xy + y²


31. What is the 'Third side' rule for triangles?
N x M
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.
1.7
The distance across the circle through the center of the circle.The diameter is twice the radius.


32. What'S the most important thing to remember about charts you'll see on the GRE?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The average - mean - median - or 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.
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


33. In a parabola - if the first term is negative - the parabola ________.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
Opens down
4s


34. Circumference Formula
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 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.
C =?d
An ange whose vertex is the center of the circle


35. What is directly proportional?
y = kx
y2-y1/x2-x1
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.
x°/360 times (?r²) - where x is the degrees in the angle


36. Area of Rectangle
Lw
(pi)r^2
1/2bh
1/3Bh


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

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38. What is the probability?
x°/360 times (?r²) - where x is the degrees in the angle
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.
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
Number of desired outcomes/number of total outcomes


39. 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.
The average - mean - median - or mode.
2l+2w
The distance across the circle through the center of the circle.The diameter is twice the radius.


40. What is the factored version of x² -2xy + y² ?
(x-y)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.
4s (where s = length of a side)
2x2x2x5x5


41. How do you calculate a diagonal inside a 3-dimensional rectangular box?
2lw+2lh+2wh
(a-b)(a²+ab+b²)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


42. What is the factored version of (x+y)(x-y) ?
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
C =?d
x²-y²


43. Surface Area of rectangular prism
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2lw+2lh+2wh
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.


44. How do you find the nth term of a geometric sequence?
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.
T1 * r^(n-1)
1/1
Between 0 and 1.


45. Area of Circles
1
A=?r2
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


46. Rough est. of v3 =
½(b1 +b2) x h [or (b1 +b2) x h÷2]
The distance across the circle through the center of the circle.The diameter is twice the radius.
x²-y²
1.7


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

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48. Volume of Cone
A+b
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.
1/3pir^2*h
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.


49. What is the side ratio for a Right Isosceles triangle?
2x2x2x5x5
2(pi)r(r+h)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Equal


50. Define the mode of a set of numbers.
Lw
(pi)r^2
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 average - mean - median - or mode.