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GRE Math 2

Subjects : gre, math

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. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
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.
2l+2w
T1 * r^(n-1)

2. Does order matter for a permutation? How about for a combination?
2l+2w
Order does matter for a permutation - but does not matter for a combination.
x°/360 times (?r²) - where x is the degrees in the angle
2 pi r

3. If x² = 144 - does v144 = x?
A=bh
(0 -0)
Not necessarily. This is a trick question - because x could be either positive or negative.
x²-y²

4. Quadratic Formula
Not necessarily. This is a trick question - because x could be either positive or negative.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Part of a circle connecting two points on the circle.
b±[vb²-4ac]/2a

5. What is a 'Right isosceles' triangle?
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.
2(pi)r(r+h)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

6. What is the area of a cylinder?
2(pi)r(r+h)
(a-b)(a²+ab+b²)
1/3pir^2*h
(x1+x2)/2 - (y1+y2)/2

7. a²+2ab+b²
1/2bh
(n degrees/360) * 2(pi)r
2(lw+wh+lh)
(a+b)²

8. Rough est. of v3 =
x²-y²
1.7
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(a+b)(a-b)

9. Explain the special properties of zero.
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.
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 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.
2l+2w

10. Diameter
4s
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The set of points which are all the same distance (the radius) from a certain point (the center).
The distance across the circle through the center of the circle.The diameter is twice the radius.

11. How do you find the sum of a geometric sequence?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
T1 * r^(n-1)/(r-1)
C =?d

12. Define a factorial of a number - and how it is written.
Lw
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.
Less
1/3Bh

13. What is the volume of a cylinder?
1
y = kx
A segment connecting the center of a circle to any point on the circle
(pi)r^2(h)

14. Rough est. of v2 =
1.4
4pir^2
(a-b)(a+b)
The set of points which are all the same distance (the radius) from a certain point (the center).

15. How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2 pi r
1/2bh
(n-2)180

16. What is the equation of a line?

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17. Central Angle
A=bh
1
An ange whose vertex is the center of the circle
S*v2

18. a²-2ab+b²
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-b)²
1.7
½(base x height) [or (base x height)÷2]

19. a³-b³
Ac+ad+bc+bd
y = k/x
(a-b)(a²+ab+b²)
4/3pir^3

20. 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.
A=bh
A segment connecting the center of a circle to any point on the circle
Negative

21. How do you calculate the percentage of change?
The set of points which are all the same distance (the radius) from a certain point (the center).
S² - where s = length of a side
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.
Percentage Change = Difference/Original * 100

22. What is the probability?
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Number of desired outcomes/number of total outcomes
x°/360 times (?r²) - where x is the degrees in the angle

23. Perimeter (circumference) of a circle
Total distance/total time
2 pi 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.
Pir^2h

24. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
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.
1/2bh
C =?d

25. What number goes on the bottom of a probability fraction?
Not necessarily. This is a trick question - because x could be either positive or negative.
(pi)r^2
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.
The total # of possible outcomes.

26. Define the range of a set of numbers.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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. 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.
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.

27. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
½(base x height) [or (base x height)÷2]
(a+b)(a-b)
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.

28. When you reverse FOIL - the term that needs to multiply out is the _____
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
Last term
x°/360 times (2 pi r) - where x is the degrees in the angle
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.

29. What is the formula for the diagonal of any square?
S*v2
Lw
Opens up
(a+b)(a²-ab+b²)

30. Volume of pyramid
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.
1/3Bh
y = kx
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.

31. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Pi*d
Opens down
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

32. What is the factored version of x² + 2xy + y² ?
Pi*d
(n-2)180
Pi*r^2
(x+y)²

33. Area of a circle
x°/360 times (2 pi r) - where x is the degrees in the angle
?r²
The total # of possible outcomes.
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.

34. Circle
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Equal
The set of points which are all the same distance (the radius) from a certain point (the center).
Lw

35. What'S the most important thing to remember about charts you'll see on the GRE?
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.
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.
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.

36. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
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-b)(a+b)
T1 * r^(n-1)

37. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
2pir^2 + 2pir*h
N x M
A=bh
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.

38. Volume of Cone
A²-b²
x°/360 times (2 pi r) - where x is the degrees in the angle
1/3pir^2*h
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.

39. Area of a sector
1/2bh
Sum of terms/number of terms
(y2-y1)/(x2-x1)
x°/360 times (?r²) - where x is the degrees in the angle

40. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
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.
(x1+x2)/2 - (y1+y2)/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.

41. To divide powers with the same base...
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.
Sum of the lengths of the sides
Not necessarily. This is a trick question - because x could be either positive or negative.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

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

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43. Slope
(y2-y1)/(x2-x1)
Total distance/total time
Arrangements - orders - schedules - or lists.
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.

44. How do you find the nth term of a geometric sequence?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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'.
Opens down
T1 * r^(n-1)

45. What is the volume of a solid rectangle?
(a+b)²
(n/2) * (t1+tn)
A+b
Lwh

46. What is the area of a circle?
(pi)r^2
1/3pir^2*h
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.
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.

47. When you reverse FOIL - the term that needs to add out is the _____
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Middle term
Lw
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

48. How do you calculate a diagonal inside a 3-dimensional rectangular box?
x°/360 times (?r²) - where x is the degrees in the angle
4s (where s = length of a side)
2pir^2 + 2pir*h
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

49. What is the 'distributive law'?
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.
T1 * r^(n-1)
1/3pir^2*h
x²-y²

50. What is the point-slope form?
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Less
(y-y1)=m(x-x1)

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GRE Math 2

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