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GRE Math 2

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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 circle?
2(pi)r
(pi)r^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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

2. When you reverse FOIL - the term that needs to add out is the _____
2(lw+wh+lh)
(a+b)(a²-ab+b²)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Middle term

3. What is the area of a sector?
Between 0 and 1.
(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
(a-b)(a²+ab+b²)

4. Area of Rectangle
Lw
1/3pir^2*h
1. Given event A: A + notA = 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.

5. What is the area of a 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
1/2bh
C =?d
?r²

6. To divide powers with the same base...
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.
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.
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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

7. Chord
2Length + 2width [or (length + width) x 2]
The distance from one point on the circle to another point on the circle.
Less
T1 * r^(n-1)/(r-1)

8. a²-2ab+b²
Order does matter for a permutation - but does not matter for a combination.
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.
1/1
(a-b)²

9. Area of Circles
1
A=?r2
1/3Bh
T1 * r^(n-1)/(r-1)

10. What is the formula for the diagonal of any square?
4/3pir^3
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.
S*v2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

11. a³-b³
(a-b)(a²+ab+b²)
Not necessarily. This is a trick question - because x could be either positive or negative.
y-y1=m(x-x1)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

12. Surface Area of Cylinder
Sum of the lengths of the sides
2pir^2 + 2pir*h
x²-y²
2pi*r

13. What is the prime factorization of 200?
(x-y)²
(n-2)180
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2x2x2x5x5

14. Area of Square
The set of points which are all the same distance (the radius) from a certain point (the center).
(a-b)(a²+ab+b²)
S^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.

15. In a coordinate system - what is the origin?
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
Probability A + Probability B
y2-y1/x2-x1
(0 -0)

16. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Bh
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2x2x2x5x5
?d OR 2?r

17. How do you find the slope?
y2-y1/x2-x1
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.
The distance from one point on the circle to another point on the circle.
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.

18. Circumference of a circle using radius
2pir^2 + 2pir*h
Pi*d
2pi*r
1/3Bh

19. x^-a =
The distance from one point on the circle to another point on the circle.
1/x^a
Groups - teams - or committees.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

20. What do combination problems usually ask for?
Last term
1/2bh
1/1
Groups - teams - or committees.

21. What do permutation problems often ask for?
2l+2w
Ac+ad+bc+bd
Order does matter for a permutation - but does not matter for a combination.
Arrangements - orders - schedules - or lists.

22. What is the area of a solid rectangle?
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.
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 distance from one point on the circle to another point on the circle.
2(lw+wh+lh)

23. Volume of prism
(a+b)(a²-ab+b²)
Bh
(x-y)²
2x2x2x5x5

24. What is the equation of a line?

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25. Area of Triangle
A segment connecting the center of a circle to any point on the circle
1/2bh
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
(n/2) * (t1+tn)

26. Volume of Cylinder
A=bh
x² + 2xy + y²
Pir^2h
Opens down

27. What is the unfactored version of x²-y² ?
(a-b)(a²+ab+b²)
The distance across the circle through the center of the circle.The diameter is twice the radius.
(x+y)(x-y)
1.4

28. a²-b²
(a-b)(a+b)
1. Given event A: A + notA = 1.
Lwh
1/x^a

29. How do you multiply powers with the same base?
Equal
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2 pi r
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

30. What is the unfactored version of (x-y)² ?
T1 * r^(n-1)/(r-1)
x² -2xy + y²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(x+y)²

31. How do you find the midpoint?
y = k/x
(y-y1)=m(x-x1)
b±[vb²-4ac]/2a
(x1+x2)/2 - (y1+y2)/2

32. What is the circumference of a circle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2(pi)r
Total distance/total time
The four big angles are equal and the four small angles are equal

33. If something is possible but not certain - what is the numeric range of probability of it happening?
2(pi)r
Between 0 and 1.
Last term
(pi)r^2(h)

34. How do you calculate the probability of two events in a row? (Probability of A and B)
Lw
(n degrees/360) * (pi)r^2
Last term
Probability A * Probability B

35. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
x² -2xy + y²
2(pi)r(r+h)

36. 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.
4s
2(pi)r(r+h)

37. Area of a sector
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
T1 + (n-1)d
The average - mean - median - or mode.

38. Area of a square
x²-y²
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.
S² - where s = length of a side
(n degrees/360) * 2(pi)r

39. Perimeter of a rectangle
Lw
Probability A * Probability B
2Length + 2width [or (length + width) x 2]
T1 + (n-1)d

40. Perimeter of rectangle
½(base x height) [or (base x height)÷2]
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(pi)r^2(h)
2l+2w

41. What is the area of a cylinder?
Pi*r^2
(pi)r^2(h)
2(pi)r(r+h)
Probability A + Probability B

42. Quadratic Formula
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(n degrees/360) * 2(pi)r
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
b±[vb²-4ac]/2a

43. Point-Slope form
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(n degrees/360) * (pi)r^2
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'.
y-y1=m(x-x1)

44. Circle
Ac+ad+bc+bd
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The set of points which are all the same distance (the radius) from a certain point (the center).
x°/360 times (2 pi r) - where x is the degrees in the angle

45. List two odd behaviors of exponents
The set of points which are all the same distance (the radius) from a certain point (the center).
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.
Pir^2h
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.

46. Rough est. of v1 =
1
2(lw+wh+lh)
1/1
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

47. perimeter of square
A²-b²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
4s
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

48. Rough est. of v3 =
Probability A + Probability B
1.7
S² - where s = length of a side
Sqr( x2 -x1) + (y2- y1)

49. Radius (Radii)
Total distance/total time
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.
A segment connecting the center of a circle to any point on the circle
2(lw+wh+lh)

50. (a+b)(c+d)
1/3pir^2*h
Ac+ad+bc+bd
y = k/x
4pir^2

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GRE Math 2

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