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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. Explain the difference between a digit and a number.

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2. How do you find the slope?
y2-y1/x2-x1
(pi)r^2(h)
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'.
(a+b)(a-b)

3. Perimeter of polygon
The four big angles are equal and the four small angles are equal
1/3pir^2*h
S^2
Sum of the lengths of the sides

4. What do permutation problems often ask for?
(n degrees/360) * (pi)r^2
Pir^2h
A=?r2
Arrangements - orders - schedules - or lists.

5. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
(a+b)(a-b)
2lw+2lh+2wh
Bh

6. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
Lw
(y-y1)=m(x-x1)
y = kx

7. (a+b)(a-b)=
A²-b²
x°/360 times (2 pi r) - where x is the degrees in the angle
T1 + (n-1)d
(a-b)(a²+ab+b²)

8. How do you calculate the surface area of a rectangular box?
y = kx
(x+y)²
(x-y)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.

9. For a bell curve - what three terms might be used to describe the number in the middle?
2pi*r
Pi*d
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.
The average - mean - median - or mode.

10. Circumference of a circle using radius
4pir^2
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.
2pi*r
(n-2)180

11. Volume of Cone
2pir^2 + 2pir*h
1/3pir^2*h
Probability A + Probability B
(pi)r^2

12. Area of a sector
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 - and greater than the difference between the other two sides.
T1 + (n-1)d
Lw

13. What is the volume of a solid rectangle?
Probability A * Probability B
Percentage Change = Difference/Original * 100
1/2bh
Lwh

14. In intersecting lines - opposite angles are _____.
½(base x height) [or (base x height)÷2]
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.
Equal
(pi)r^2

15. a³-b³
(a-b)(a²+ab+b²)
(x+y)²
Order does matter for a permutation - but does not matter for a combination.
(n-2)180

16. How do you calculate the percentage of change?
1/1
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
Pir^2h
Percentage Change = Difference/Original * 100

17. Arc
(n degrees/360) * (pi)r^2
(n/2) * (t1+tn)
The set of points which are all the same distance (the radius) from a certain point (the center).
Part of a circle connecting two points on the circle.

18. When a line crosses two parallel lines - ________.
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.
2Length + 2width [or (length + width) x 2]
The four big angles are equal and the four small angles are equal
A=bh

19. The length of one side of any triangle is ____ than the sum of the other two sides.
Pi*r^2
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Less
1.7

20. If something is possible but not certain - what is the numeric range of probability of it happening?
Last term
Between 0 and 1.
?r²
1.7

21. What is the circumference of a circle?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Less
2(pi)r
(n/2) * (t1+tn)

22. In a coordinate system - what is the origin?
Opens up
(x+y)²
(0 -0)
Bh

23. What is the factored version of x² + 2xy + y² ?
2Length + 2width [or (length + width) x 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
Part of a circle connecting two points on the circle.
(x+y)²

24. Area of rectangle - square - parallelogram
A+b
A=bh
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Pi*d

25. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
Probability A * Probability B
A=bh
2(lw+wh+lh)

26. What is the 'Third side' rule for triangles?
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.
2(lw+wh+lh)
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.
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.

27. Quadratic Formula
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.
(a+b)(a-b)
b±[vb²-4ac]/2a
T1 * r^(n-1)

28. Volume of sphere
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'.
b±[vb²-4ac]/2a
1. Given event A: A + notA = 1.
4/3pir^3

29. Volume of prism
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Bh
(a-b)(a+b)
S*v2

30. Sector
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.
(n/2) * (t1+tn)
C =?d
2 pi r

31. How do you find the sum of an arithmetic sequence?
(a-b)(a+b)
2Length + 2width [or (length + width) x 2]
(n/2) * (t1+tn)
Negative

32. Point-Slope form
4s (where s = length of a side)
2(lw+wh+lh)
y-y1=m(x-x1)
T1 + (n-1)d

33. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
S*v2
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

34. Rough est. of v2 =
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.
(a+b)(a-b)
1.4
1/3pir^2*h

35. What is the unfactored version of (x-y)² ?
1/1
x² -2xy + y²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

36. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
Bh
N x M
½(base x height) [or (base x height)÷2]
4s (where s = length of a side)

37. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(y-y1)=m(x-x1)
(x+y)²

38. What is directly proportional?
y = kx
A segment connecting the center of a circle to any point on the circle
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Probability A * Probability B

39. 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.
2(pi)r(r+h)
1/2bh
(a-b)(a+b)

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

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41. What is the area of a triangle?
(x+y)(x-y)
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
2pir^2 + 2pir*h
1/2bh

42. What number goes on the bottom of a probability fraction?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x²-y²
T1 * r^(n-1)/(r-1)
The total # of possible outcomes.

43. Area of Rectangle
A=?r2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
Lw

44. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
Between 0 and 1.
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'.

45. What is the unfactored version of x²-y² ?
(pi)r^2(h)
(x+y)(x-y)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Not necessarily. This is a trick question - because x could be either positive or negative.

46. perimeter of square
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4s
b±[vb²-4ac]/2a
Pi*r^2

47. Slope
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(y2-y1)/(x2-x1)

48. What is the factored version of x² -2xy + y² ?
(x-y)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.
The four big angles are equal and the four small angles are equal
(pi)r^2(h)

49. Area of a circle
The set of points which are all the same distance (the radius) from a certain point (the center).
The distance from one point on the circle to another point on the circle.
?r²
A+b

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

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GRE Math 2

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