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. Explain the special properties of zero.
Percentage Change = Difference/Original * 100
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-b)(a²+ab+b²)
S² - where s = length of a side


2. How do you calculate the surface area of a rectangular box?
Sum of terms/number of terms
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.
x°/360 times (2 pi r) - where x is the degrees in the angle


3. What is the unfactored version of (x-y)² ?
Less
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.
y2-y1/x2-x1
x² -2xy + y²


4. What is the area of a circle?
2pir^2 + 2pir*h
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(pi)r^2
(a-b)²


5. Surface Area of Cylinder
A segment connecting the center of a circle to any point on the circle
The distance from one point on the circle to another point on the circle.
2pir^2 + 2pir*h
1.4


6. Area of Circle
Pi*r^2
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.
The total # of possible outcomes.
1/2bh


7. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
1/x^a
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.
x°/360 times (?r²) - where x is the degrees in the angle
Equal


8. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
?r²
½(base x height) [or (base x height)÷2]
2(lw+wh+lh)


9. perimeter of square
4s
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.
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.
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.


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

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11. The length of one side of any triangle is ____ than the sum of the other two sides.
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.
Less
?r²
C =?d


12. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
(a+b)(a-b)
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
S*v2
T1 + (n-1)d


13. 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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14. How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A=bh
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.
2lw+2lh+2wh


15. In a parabola - if the first term is positive - the parabola ________.
Opens up
Pi*r^2
Between 0 and 1.
Sum of the lengths of the sides


16. Area of a trapezoid
1/2 h (b1 + b2)
?d OR 2?r
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(n degrees/360) * (pi)r^2


17. Volume of Cone
2pir^2 + 2pir*h
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/3pir^2*h
The distance from one point on the circle to another point on the circle.


18. What do combination problems usually ask for?
1.7
Groups - teams - or committees.
1. Given event A: A + notA = 1.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


19. What is the sum of the inside angles of an n-sided polygon?
2 pi r
Order does matter for a permutation - but does not matter for a combination.
(n-2)180
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.


20. What is the surface area of a cylinder?
2Length + 2width [or (length + width) x 2]
A²-b²
2(pi)r(r+h)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


21. a²-2ab+b²
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.
(x+y)(x-y)
T1 * r^(n-1)/(r-1)
(a-b)²


22. What is the side ratio for a Right Isosceles triangle?
x² + 2xy + y²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Equal
y2-y1/x2-x1


23. Define the 'Third side' rule for triangles

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24. When you reverse FOIL - the term that needs to multiply out is the _____
Not necessarily. This is a trick question - because x could be either positive or negative.
The four big angles are equal and the four small angles are equal
Last term
x°/360 times (?r²) - where x is the degrees in the angle


25. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2Length + 2width [or (length + width) x 2]


26. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
Sqr( x2 -x1) + (y2- y1)
x°/360 times (?r²) - where x is the degrees in the angle
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.


27. In a coordinate system - what is the origin?
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
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Arrangements - orders - schedules - or lists.
(0 -0)


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

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29. Circle
1.4
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
Sqr( x2 -x1) + (y2- y1)
The set of points which are all the same distance (the radius) from a certain point (the center).


30. What is the equation of a line?

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31. How do you calculate the probability of two events in a row? (Probability of A and B)
(x1+x2)/2 - (y1+y2)/2
Probability A * Probability B
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.
4s (where s = length of a side)


32. Circumference Formula
C =?d
Sum of terms/number of terms
Probability A + Probability B
Lw


33. Area of Trapezoid
Last term
S*v2
1/2 h (b1 + b2)
?d OR 2?r


34. What is the area of a sector?
(n degrees/360) * (pi)r^2
1/1
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+b)²


35. The probability of an event happening and the probability of an event NOT happening must add up to what number?
(n-2)180
1. Given event A: A + notA = 1.
?d OR 2?r
(pi)r^2


36. How do you calculate a diagonal inside a 3-dimensional rectangular box?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2(pi)r(r+h)
Pi*d


37. How do you solve a permutation?
Middle term
x² -2xy + y²
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
The distance from one point on the circle to another point on the circle.


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


39. a²+2ab+b²
(a-b)²
(a+b)²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
A+b


40. Rough est. of v1 =
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
N x M
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1


41. Area of Triangle
x²-y²
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.
1/2bh
1. Given event A: A + notA = 1.


42. Rough est. of v2 =
1.4
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Percentage Change = Difference/Original * 100
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.


43. What is the formula for the diagonal of any square?
(a-b)(a+b)
The set of points which are all the same distance (the radius) from a certain point (the center).
(a-b)(a²+ab+b²)
S*v2


44. Volume of prism
Bh
A²-b²
1
(x+y)(x-y)


45. When you reverse FOIL - the term that needs to add out is the _____
Last term
Pi*r^2
Middle term
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.


46. Perimeter of polygon
Bh
Sum of the lengths of the sides
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


47. Volume of pyramid
(a+b)²
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1/3Bh


48. x^-a =
½(b1 +b2) x h [or (b1 +b2) x h÷2]
4pir^2
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
1/x^a


49. What is the area of a solid rectangle?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2(lw+wh+lh)
The total # of possible outcomes.
Pi*r^2


50. Perimeter of a rectangle
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Negative
y = kx
2Length + 2width [or (length + width) x 2]