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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. Volume of sphere
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
A+b
Sum of the lengths of the sides

2. How do you find the sum of an arithmetic sequence?
4s
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(n/2) * (t1+tn)
Less

3. How do you find the nth term of an arithmetic sequence?
The total # of possible outcomes.
S² - where s = length of a side
T1 + (n-1)d
?r²

4. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
x² -2xy + y²
An ange whose vertex is the center of the circle
1/2bh

5. Perimeter (circumference) of a circle
(n-2)180
Pi*r^2
2 pi r
(0 -0)

6. What is the area of a triangle?
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.
1/2bh
A=?r2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

7. Define the formula for calculating slope.
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
2x2x2x5x5
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.

8. How do you find the sum of a geometric sequence?
(pi)r^2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A segment connecting the center of a circle to any point on the circle
T1 * r^(n-1)/(r-1)

9. Area of Triangle
Sum of the lengths of the sides
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.
1/2bh

10. When you reverse FOIL - the term that needs to add out is the _____
Lw
1/2 h (b1 + b2)
Middle term
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.

11. What is the circumference of a circle?
Lw
2(pi)r
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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 unfactored version of (x-y)² ?
Sum of terms/number of terms
x² -2xy + y²
Not necessarily. This is a trick question - because x could be either positive or negative.
2(pi)r(r+h)

13. What is directly proportional?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
4s
y = kx

14. What is the equation of a line?

15. What is the side ratio for a 30:60:90 triangle?
1. Given event A: A + notA = 1.
y = kx
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

16. Volume of Cone
1.4
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.
1/3pir^2*h
x² -2xy + y²

17. What are the side ratios for a 30:60:90 triangle?
C =?d
x°/360 times (2 pi r) - where x is the degrees in the angle
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a+b)(a-b)

18. What'S the most important thing to remember about charts you'll see on the GRE?
1.4
Groups - teams - or committees.
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.
2(pi)r(r+h)

19. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
The distance from one point on the circle to another point on the circle.
The distance across the circle through the center of the circle.The diameter is twice the radius.
(y2-y1)/(x2-x1)

20. Volume of Cylinder
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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
(y2-y1)/(x2-x1)
Pir^2h

21. Circumference of cirlce using diameter
N x M
Part of a circle connecting two points on the circle.
Pi*d
Lw

22. Lines reflected over the x or y axis have ____ slopes.
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.
Negative
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
?d OR 2?r

23. What is the factored version of (x+y)(x-y) ?
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.
(n degrees/360) * (pi)r^2
x°/360 times (2 pi r) - where x is the degrees in the angle
x²-y²

24. Area of a circle
1/1
1/3pir^2*h
Total distance/total time
?r²

25. a²+2ab+b²
(a+b)²
The set of points which are all the same distance (the radius) from a certain point (the center).
2lw+2lh+2wh
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

26. In a coordinate system - identify the quadrants and describe their location.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
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.

27. What is the prime factorization of 200?
(pi)r^2(h)
2x2x2x5x5
Pir^2h
A+b

28. What is the surface area of a cylinder?
2(pi)r(r+h)
x² + 2xy + y²
The distance from one point on the circle to another point on the circle.
1/3pir^2*h

29. What is the unfactored version of x²-y² ?
x² -2xy + y²
(x+y)(x-y)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Bh

30. a²-b²
T1 + (n-1)d
2pi*r
(a-b)(a+b)
b±[vb²-4ac]/2a

31. 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.
1.4
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(n degrees/360) * (pi)r^2

32. Area of a triangle
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
½(base x height) [or (base x height)÷2]
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.

33. Define 'proportionate' values
2(pi)r(r+h)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Arrangements - orders - schedules - or lists.
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.

34. In a coordinate system - what is the origin?
(pi)r^2(h)
(n/2) * (t1+tn)
(0 -0)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

35. Area of a trapezoid
Probability A * Probability B
½(b1 +b2) x h [or (b1 +b2) x h÷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.
A=bh

36. What is the volume of a cylinder?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2x2x2x5x5
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'.
(pi)r^2(h)

37. What is an 'equilateral' triangle?
1/2bh
x²-y²
2x2x2x5x5
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

38. Area of Rectangle
4s (where s = length of a side)
(y-y1)=m(x-x1)
1/1
Lw

39. How do you calculate the probability of two events in a row? (Probability of A and B)
Sum of the lengths of the sides
Probability A * Probability B
2lw+2lh+2wh
(n degrees/360) * 2(pi)r

40. Point-Slope form
x² + 2xy + y²
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
y-y1=m(x-x1)
Sum of terms/number of terms

41. Define a factorial of a number - and how it is written.
(a-b)²
½(base x height) [or (base x height)÷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.
x°/360 times (2 pi r) - where x is the degrees in the angle

42. To divide powers with the same base...
Sqr( x2 -x1) + (y2- y1)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(x+y)²

43. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
2x2x2x5x5
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
N x M
x² -2xy + y²

44. Does order matter for a permutation? How about for a combination?
Pir^2h
b±[vb²-4ac]/2a
Order does matter for a permutation - but does not matter for a combination.
1/1

45. Diameter
T1 + (n-1)d
x²-y²
Sum of the lengths of the sides
The distance across the circle through the center of the circle.The diameter is twice the radius.

46. a² - b² is equal to
y-y1=m(x-x1)
Middle term
1/3pir^2*h
(a+b)(a-b)

47. What is the average?
Sum of terms/number of terms
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.
Probability A + Probability B
Sqr( x2 -x1) + (y2- y1)

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

49. What is the length of an arc?
Order does matter for a permutation - but does not matter for a combination.
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
Arrangements - orders - schedules - or lists.
(n degrees/360) * 2(pi)r

50. a²-2ab+b²
Between 0 and 1.
(a-b)²
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
(a-b)(a+b)