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. Circumference of a circle
?d OR 2?r
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.
4s
2lw+2lh+2wh


2. When you reverse FOIL - the term that needs to add out is the _____
Last term
(x-y)²
Middle term
1/3Bh


3. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(n degrees/360) * 2(pi)r


4. How do you calculate the probability of two events in a row? (Probability of A and B)
A+b
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. 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
Probability A * Probability B


5. Circumference of cirlce using diameter
2(pi)r
Pi*d
(0 -0)
1.4


6. x^a * x^b = x^__
1
A+b
Sqr( x2 -x1) + (y2- y1)
S^2


7. Area of Rectangle
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.
Lw
The four big angles are equal and the four small angles are equal
The distance from one point on the circle to another point on the circle.


8. Area of a sector
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
x°/360 times (?r²) - where x is the degrees in the angle
A segment connecting the center of a circle to any point on the circle
Lw


9. Rough est. of v1 =
1
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Not necessarily. This is a trick question - because x could be either positive or negative.


10. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
½(base x height) [or (base x height)÷2]
Between 0 and 1.
The distance from one point on the circle to another point on the circle.


11. How do you multiply powers with the same base?
(x-y)²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2Length + 2width [or (length + width) x 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.


12. If something is possible but not certain - what is the numeric range of probability of it happening?
x²-y²
1/2bh
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.
Between 0 and 1.


13. a²-b²
Equal
A+b
(a-b)(a+b)
x°/360 times (2 pi r) - where x is the degrees in the angle


14. What is the probability?
Number of desired outcomes/number of total outcomes
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
y = k/x
(x-y)²


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

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16. 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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17. Perimeter of rectangle
(n degrees/360) * 2(pi)r
x² -2xy + y²
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.
2l+2w


18. If something is certain to happen - how is the probability of this event expressed mathematically?
4s (where s = length of a side)
1/1
2pir^2 + 2pir*h
2x2x2x5x5


19. Define a factorial of a number - and how it is written.
(a+b)(a-b)
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
(a-b)²
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.


20. (a+b)(c+d)
A=bh
Ac+ad+bc+bd
Order does matter for a permutation - but does not matter for a combination.
1/3Bh


21. What is the formula for the diagonal of any square?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A+b
S*v2
The average - mean - median - or mode.


22. What is the area of a solid rectangle?
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)
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
Less


23. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
y2-y1/x2-x1
N x M
1.7
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.


24. How do you find the sum of a geometric sequence?
2x2x2x5x5
Pi*r^2
y2-y1/x2-x1
T1 * r^(n-1)/(r-1)


25. What is the factored version of x² -2xy + y² ?
(x-y)²
2pir^2 + 2pir*h
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.
(y-y1)=m(x-x1)


26. a²+2ab+b²
(a+b)²
(n/2) * (t1+tn)
C =?d
Total distance/total time


27. Volume of sphere
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
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
4/3pir^3


28. (a+b)(a-b)=
An ange whose vertex is the center of the circle
A²-b²
2l+2w
(y-y1)=m(x-x1)


29. What is inversely proportional?
Probability A * Probability B
Arrangements - orders - schedules - or lists.
T1 * r^(n-1)/(r-1)
y = k/x


30. What is the 'Third side' rule for triangles?
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.
2pir^2 + 2pir*h
1/2bh
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.


31. Area of Circles
Pi*d
A=?r2
1/2bh
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


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

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33. 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.
x°/360 times (?r²) - where x is the degrees in the angle
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.
A=?r2


34. What is the equation of a line?

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35. What do combination problems usually ask for?
Groups - teams - or committees.
A+b
Probability A + Probability 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.


36. What is the factored version of (x+y)(x-y) ?
y2-y1/x2-x1
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x²-y²
1/x^a


37. Volume of prism
Bh
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
The distance from one point on the circle to another point on the circle.
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


38. What is the area of a cylinder?
(x-y)²
2(pi)r(r+h)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.


39. When a line crosses two parallel lines - ________.
(a-b)(a²+ab+b²)
Sqr( x2 -x1) + (y2- y1)
The four big angles are equal and the four small angles are equal
Percentage Change = Difference/Original * 100


40. Define the 'Third side' rule for triangles

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41. Point-Slope form
1. Given event A: A + notA = 1.
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'.
(x-y)²
y-y1=m(x-x1)


42. length of a sector
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.
Percentage Change = Difference/Original * 100
T1 * r^(n-1)
x°/360 times (2 pi r) - where x is the degrees in the angle


43. 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
T1 * r^(n-1)/(r-1)
N x M
2(pi)r(r+h)


44. Circle
2x2x2x5x5
Total distance/total time
y2-y1/x2-x1
The set of points which are all the same distance (the radius) from a certain point (the center).


45. What is the area of a triangle?
Bh
1/2bh
(pi)r^2
The distance from one point on the circle to another point on the circle.


46. What is the average speed?
Total distance/total time
2(pi)r(r+h)
Opens down
Probability A + Probability B


47. a²-2ab+b²
(a-b)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.
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.
Order does matter for a permutation - but does not matter for a combination.


48. Perimeter (circumference) of a circle
Sum of the lengths of the sides
2 pi r
Bh
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49. 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
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.
Total distance/total time
A²-b²


50. Diameter
Total distance/total time
1/x^a
(x1+x2)/2 - (y1+y2)/2
The distance across the circle through the center of the circle.The diameter is twice the radius.