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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. What is the area of a sector?
(n degrees/360) * (pi)r^2
Pi*r^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.
Last term

2. Area of a sector
?d OR 2?r
The average - mean - median - or mode.
x°/360 times (?r²) - where x is the degrees in the angle
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.

3. Area of Circles
Opens up
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
4s (where s = length of a side)
A=?r2

4. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Sqr( x2 -x1) + (y2- y1)
2pi*r
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.
y2-y1/x2-x1

5. How do you find the sum of an arithmetic sequence?
Opens down
Number of desired outcomes/number of total outcomes
(n/2) * (t1+tn)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

6. Area of Trapezoid
Ac+ad+bc+bd
Groups - teams - or committees.
Less
1/2 h (b1 + b2)

7. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or 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
The average - mean - median - or mode.
Probability A + Probability B
Lwh

8. Quadratic Formula
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
b±[vb²-4ac]/2a
Less

9. Volume of sphere
1/3Bh
4/3pir^3
Middle term
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

10. In a parabola - if the first term is positive - the parabola ________.
(n/2) * (t1+tn)
1/3pir^2*h
½(base x height) [or (base x height)÷2]
Opens up

11. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
(n degrees/360) * 2(pi)r
1.4
4/3pir^3

12. x^-a =
2Length + 2width [or (length + width) x 2]
1/x^a
Bh
The set of points which are all the same distance (the radius) from a certain point (the center).

13. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
(x+y)(x-y)
Opens down
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'.
N x M

14. When a line crosses two parallel lines - ________.
(n/2) * (t1+tn)
Ac+ad+bc+bd
1.7
The four big angles are equal and the four small angles are equal

15. How do you find the sum of a geometric sequence?
1/x^a
T1 * r^(n-1)/(r-1)
1/3Bh
Middle term

16. Rough est. of v3 =
1.7
Lw
A segment connecting the center of a circle to any point on the circle
(x+y)²

17. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
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.
2l+2w
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

18. What do combination problems usually ask for?
x°/360 times (2 pi r) - where x is the degrees in the angle
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/3Bh
Groups - teams - or committees.

19. Area of a triangle
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.
Lw
½(base x height) [or (base x height)÷2]
The set of points which are all the same distance (the radius) from a certain point (the center).

20. Define the 'Third side' rule for triangles

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21. Volume of Cone
1/x^a
?d OR 2?r
1/3pir^2*h
S² - where s = length of a side

22. Does order matter for a permutation? How about 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.
2(pi)r(r+h)
2Length + 2width [or (length + width) x 2]
Order does matter for a permutation - but does not matter for a combination.

23. What do permutation problems often ask for?
Sum of the lengths of the sides
Arrangements - orders - schedules - or lists.
(n degrees/360) * (pi)r^2
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

24. Sector
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)(a²+ab+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.
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.

25. (a+b)(a-b)=
Pi*r^2
Opens up
A²-b²
A=bh

26. Circumference of a circle using radius
?d OR 2?r
The total # of possible outcomes.
2pi*r
Lwh

27. What is the formula for the diagonal of any square?
x²-y²
S*v2
2(pi)r(r+h)
1/3Bh

28. What is the area of a triangle?
An ange whose vertex is the center of the circle
2 pi r
C =?d
1/2bh

29. Perimeter of a rectangle
(a-b)²
T1 + (n-1)d
2Length + 2width [or (length + width) x 2]
The total # of possible outcomes.

30. Perimeter of polygon
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
½(base x height) [or (base x height)÷2]
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Sum of the lengths of the sides

31. 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
(n degrees/360) * 2(pi)r
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°/360 times (?r²) - where x is the degrees in the angle

32. Volume of pyramid
2(pi)r(r+h)
1/3Bh
A²-b²
Arrangements - orders - schedules - or lists.

33. How do you solve a permutation?
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
Pi*d
Sum of terms/number of terms
Lwh

34. What is the average speed?
(n/2) * (t1+tn)
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.
Total distance/total time
Arrangements - orders - schedules - or lists.

35. What is the probability?
y2-y1/x2-x1
Number of desired outcomes/number of total outcomes
2Length + 2width [or (length + width) x 2]
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.

36. Explain the special properties of zero.
½(base x height) [or (base x height)÷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.
Pi*d
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.

37. Circumference of a circle
4s (where s = length of a side)
Middle term
(x+y)²
?d OR 2?r

38. How do you find the nth term of a geometric sequence?
Pir^2h
(n degrees/360) * 2(pi)r
?r²
T1 * r^(n-1)

39. What is the distance formula?
A segment connecting the center of a circle to any point on the circle
(x1+x2)/2 - (y1+y2)/2
N x M
Sqr( x2 -x1) + (y2- y1)

40. Rough est. of v1 =
1
y-y1=m(x-x1)
1/2 h (b1 + b2)
1.4

41. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
y = k/x
(pi)r^2
1/2 h (b1 + b2)

42. 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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43. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
(pi)r^2
Equal

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

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45. Arc
Part of a circle connecting two points on the circle.
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 = kx
The distance from one point on the circle to another point on the circle.

46. How do you calculate the surface area of a rectangular box?
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.
(a+b)(a²-ab+b²)
?d OR 2?r
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

47. a³-b³
2pi*r
Part of a circle connecting two points on the circle.
(a-b)(a²+ab+b²)
T1 * r^(n-1)/(r-1)

48. What is the factored version of (x+y)(x-y) ?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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
x²-y²

49. In a parabola - if the first term is negative - the parabola ________.
Opens down
x°/360 times (2 pi r) - where x is the degrees in the angle
2l+2w
(a-b)(a²+ab+b²)

50. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Opens down
4s
The set of points which are all the same distance (the radius) from a certain point (the center).