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 the equation of a line?

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2. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
1/2 h (b1 + b2)
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.
Sum of terms/number of terms


3. Define a factorial of a number - and how it is written.
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.
2Length + 2width [or (length + width) x 2]
2 pi r
Groups - teams - or committees.


4. What is the probability?
The total # of possible outcomes.
Sum of the lengths of the sides
Not necessarily. This is a trick question - because x could be either positive or negative.
Number of desired outcomes/number of total outcomes


5. Circumference Formula
C =?d
y = k/x
Negative
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.


6. What is the side ratio for a 30:60:90 triangle?
(pi)r^2(h)
2(lw+wh+lh)
1/1
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


7. How do you calculate the surface area of a rectangular box?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
The set of points which are all the same distance (the radius) from a certain point (the center).
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.


8. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
4pir^2
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
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.


9. What is the average speed?
4pir^2
Total distance/total time
Less
(a-b)²


10. Volume of Cylinder
Ac+ad+bc+bd
Pir^2h
N x M
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


11. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
A=bh
(n/2) * (t1+tn)


12. How do you find the slope?
Bh
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.
S² - where s = length of a side
y2-y1/x2-x1


13. What is the volume of a cylinder?
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.
(pi)r^2(h)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
y2-y1/x2-x1


14. Point-Slope form
x°/360 times (2 pi r) - where x is the degrees in the angle
1. Given event A: A + notA = 1.
y-y1=m(x-x1)
x² + 2xy + y²


15. a²-2ab+b²
(a-b)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
Lw
y = k/x


16. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷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.
Ac+ad+bc+bd
T1 * r^(n-1)


17. When you reverse FOIL - the term that needs to multiply out is the _____
(a-b)(a²+ab+b²)
(n-2)180
The set of points which are all the same distance (the radius) from a certain point (the center).
Last term


18. When you reverse FOIL - the term that needs to add out is the _____
Middle term
Number of desired outcomes/number of total outcomes
1. Given event A: A + notA = 1.
Opens down


19. In a parabola - if the first term is negative - the parabola ________.
2(pi)r(r+h)
Opens down
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.
N x M


20. What is the area of a cylinder?
2(pi)r(r+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.
1
y2-y1/x2-x1


21. x^-a =
(x+y)(x-y)
A=bh
1/2bh
1/x^a


22. Volume of Cone
1/3pir^2*h
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
T1 * r^(n-1)/(r-1)


23. Area of a square
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.
(pi)r^2
4s
S² - where s = length of a side


24. To divide powers with the same base...
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The average - mean - median - or mode.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(pi)r^2


25. Surface Area of rectangular prism
2lw+2lh+2wh
4pir^2
(x1+x2)/2 - (y1+y2)/2
Not necessarily. This is a trick question - because x could be either positive or negative.


26. What is the area of a triangle?
Sum of the lengths of the sides
1/3pir^2*h
1/2bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


27. Central Angle
An ange whose vertex is the center of the circle
1/1
Opens up
Bh


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

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

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30. Area of Parallelogram
2(lw+wh+lh)
Groups - teams - or committees.
Sum of terms/number of terms
Bh


31. Surface Area of Cylinder
2lw+2lh+2wh
2pir^2 + 2pir*h
4pir^2
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.


32. What'S the most important thing to remember about charts you'll see on the GRE?
S² - where s = length of a side
Pi*d
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.
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'.


33. How do you find the nth term of a geometric sequence?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Equal
T1 * r^(n-1)
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


34. How do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
S^2
y = k/x
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


35. What is the side ratio for a Right Isosceles triangle?
1/3Bh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
(n degrees/360) * (pi)r^2


36. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
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-y1)=m(x-x1)
(n degrees/360) * 2(pi)r


37. Perimeter of rectangle
Lw
2l+2w
2lw+2lh+2wh
Pir^2h


38. Define the range of a set of numbers.
2(pi)r(r+h)
x² -2xy + y²
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.
x°/360 times (2 pi r) - where x is the degrees in the angle


39. In a parabola - if the first term is positive - the parabola ________.
Opens up
Negative
(pi)r^2(h)
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


40. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
Number of desired outcomes/number of total outcomes
1.7
y-y1=m(x-x1)


41. Circumference of a circle
?d OR 2?r
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Between 0 and 1.


42. Explain the special properties of zero.
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.
T1 * r^(n-1)/(r-1)
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.


43. Quadratic Formula
A²-b²
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.
b±[vb²-4ac]/2a
(a+b)(a²-ab+b²)


44. Perimeter of polygon
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.
(a-b)(a+b)
Sum of the lengths of the sides
S² - where s = length of a side


45. Area of Triangle
2(pi)r
S² - where s = length of a side
1/2bh
C =?d


46. Chord
S² - where s = length of a side
The distance from one point on the circle to another point on the circle.
Lw
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


47. Arc
T1 + (n-1)d
Part of a circle connecting two points on the circle.
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.
A=bh


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

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49. How do you calculate the probability of two events in a row? (Probability of A and B)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/3pir^2*h
Probability A * Probability B
2(lw+wh+lh)


50. 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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