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 are the side ratios for a 30:60:90 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.
Bh
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a-b)(a²+ab+b²)


2. What is the area of a cylinder?
The distance from one point on the circle to another point on the circle.
(y-y1)=m(x-x1)
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
2(pi)r(r+h)


3. (a+b)(a-b)=
A²-b²
(a-b)(a+b)
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
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'.


4. Does order matter for a permutation? How about for a combination?
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.
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.
Middle term


5. x^a * x^b = x^__
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.
A+b
The total # of possible outcomes.
T1 * r^(n-1)


6. What is the unfactored version of (x-y)² ?
x² + 2xy + y²
Percentage Change = Difference/Original * 100
x² -2xy + y²
x²-y²


7. What is the factored version of x² -2xy + y² ?
The distance across the circle through the center of the circle.The diameter is twice the radius.
(x-y)²
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


8. What is the area of a solid rectangle?
S² - where s = length of a side
2(lw+wh+lh)
Bh
1/2bh


9. In a parabola - if the first term is positive - the parabola ________.
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 up
x²-y²
(x+y)²


10. Volume of Cone
Pi*d
4pir^2
1/3pir^2*h
Pir^2h


11. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
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.
b±[vb²-4ac]/2a
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.


12. What is the prime factorization of 200?
2x2x2x5x5
N x M
(pi)r^2
(y2-y1)/(x2-x1)


13. In a coordinate system - what is the origin?
?d OR 2?r
(pi)r^2(h)
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
(0 -0)


14. Perimeter of a rectangle
(pi)r^2(h)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Number of desired outcomes/number of total outcomes
2Length + 2width [or (length + width) x 2]


15. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
S^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
Number of desired outcomes/number of total outcomes
Negative


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

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17. Volume of pyramid
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
1/3Bh


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

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19. (a+b)(c+d)
Pi*r^2
2pi*r
Ac+ad+bc+bd
Pi*d


20. Area of rectangle - square - parallelogram
Middle term
A=bh
S*v2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


21. When a line crosses two parallel lines - ________.
(n degrees/360) * (pi)r^2
The four big angles are equal and the four small angles are equal
S² - where s = length of a side
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.


22. What is the average?
Sum of terms/number of terms
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. 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
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.


23. What is the surface area of a cylinder?
2(pi)r(r+h)
Number of desired outcomes/number of total outcomes
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


24. Perimeter (circumference) of a circle
1/2 h (b1 + b2)
2l+2w
Pir^2h
2 pi r


25. Define 'proportionate' values
2Length + 2width [or (length + width) x 2]
(x1+x2)/2 - (y1+y2)/2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The set of points which are all the same distance (the radius) from a certain point (the center).


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

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27. Area of Rectangle
Arrangements - orders - schedules - or lists.
2l+2w
Lw
½(base x height) [or (base x height)÷2]


28. List two odd behaviors of exponents
1/2 h (b1 + b2)
2pir^2 + 2pir*h
x² + 2xy + y²
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.


29. How do you multiply and divide square roots?
A+b
Bh
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Between 0 and 1.


30. Perimeter of polygon
(x-y)²
½(base x height) [or (base x height)÷2]
Sum of the lengths of the sides
½(b1 +b2) x h [or (b1 +b2) x h÷2]


31. Volume of Cylinder
Order does matter for a permutation - but does not matter for a combination.
1/3pir^2*h
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


32. Area of Trapezoid
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
2(pi)r(r+h)
1/2 h (b1 + b2)
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.


33. Define the range of a set of numbers.
y-y1=m(x-x1)
A+b
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.
Sqr( x2 -x1) + (y2- y1)


34. Point-Slope form
2(pi)r(r+h)
y-y1=m(x-x1)
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.
?d OR 2?r


35. Surface Area of rectangular prism
(pi)r^2
The four big angles are equal and the four small angles are equal
(a+b)(a²-ab+b²)
2lw+2lh+2wh


36. Area of a trapezoid
2(pi)r
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(n/2) * (t1+tn)
x°/360 times (?r²) - where x is the degrees in the angle


37. Circumference of a circle
(pi)r^2(h)
Pi*d
The distance from one point on the circle to another point on the circle.
?d OR 2?r


38. How do you multiply powers with the same base?
(n/2) * (t1+tn)
A²-b²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Part of a circle connecting two points on the circle.


39. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Bh
Probability A + Probability B
Not necessarily. This is a trick question - because x could be either positive or negative.
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.


40. a²-b²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(a-b)(a+b)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(x1+x2)/2 - (y1+y2)/2


41. How do you calculate a diagonal inside a 3-dimensional rectangular box?
The total # of possible outcomes.
Last term
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
½(b1 +b2) x h [or (b1 +b2) x h÷2]


42. Define the 'Third side' rule for triangles

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43. How do you find the sum of an arithmetic sequence?
Number of desired outcomes/number of total outcomes
1/2bh
(n/2) * (t1+tn)
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'.


44. In a parabola - if the first term is negative - the parabola ________.
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.
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.
Lw
Opens down


45. 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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46. What is inversely proportional?
2pi*r
2(lw+wh+lh)
y = k/x
Groups - teams - or committees.


47. Circle
Pir^2h
The set of points which are all the same distance (the radius) from a certain point (the center).
Lw
x²-y²


48. What is the circumference of a circle?
4/3pir^3
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2(pi)r
1/1


49. If something is certain to happen - how is the probability of this event expressed mathematically?
y = kx
1/1
2lw+2lh+2wh
The total # of possible outcomes.


50. Sector
Opens down
(y2-y1)/(x2-x1)
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.
Part of a circle connecting two points on the circle.