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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. How do you find the sum of an arithmetic sequence?
Ac+ad+bc+bd
(n/2) * (t1+tn)
A segment connecting the center of a circle to any point on the circle
Pir^2h

2. To divide powers with the same base...
(x+y)(x-y)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A²-b²
4s (where s = length of a side)

3. What is the area of a triangle?
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2l+2w
1/2bh

4. a²+2ab+b²
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)²
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.
S² - where s = length of a side

5. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Last term
Total distance/total time
Probability A + Probability B

6. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Pi*r^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
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
1

7. What is the unfactored version of (x-y)² ?
x² -2xy + y²
(n degrees/360) * 2(pi)r
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.
2(pi)r

8. Circumference of cirlce using diameter
A²-b²
1/2 h (b1 + b2)
Pi*d
(x1+x2)/2 - (y1+y2)/2

9. What is the circumference of a circle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Percentage Change = Difference/Original * 100
Ac+ad+bc+bd
2(pi)r

10. Central Angle
2(pi)r(r+h)
?r²
An ange whose vertex is the center of the circle
Pir^2h

11. In intersecting lines - opposite angles are _____.
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'.
Equal
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.
Sqr( x2 -x1) + (y2- y1)

12. Perimeter of polygon
1.7
(n degrees/360) * 2(pi)r
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Sum of the lengths of the sides

13. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
A=bh
S^2
1.7

14. What is the side ratio for a 30:60:90 triangle?
1/2bh
N x M
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
y-y1=m(x-x1)

15. Perimeter (circumference) of a circle
A+b
2 pi r
Ac+ad+bc+bd
?d OR 2?r

16. What is the factored version of x² + 2xy + y² ?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(x+y)²
2pi*r
Bh

17. Volume of pyramid
1/3Bh
Sum of terms/number of terms
1.4
Middle term

18. What is the volume of a cylinder?
The set of points which are all the same distance (the radius) from a certain point (the center).
(pi)r^2(h)
The average - mean - median - or mode.
1/3pir^2*h

19. List two odd behaviors of exponents
(a-b)(a²+ab+b²)
x°/360 times (2 pi r) - where x is the degrees in the angle
A²-b²
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.

20. Define 'proportionate' values
(0 -0)
2pi*r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Opens up

21. What is inversely proportional?
2x2x2x5x5
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.
y = k/x
x°/360 times (2 pi r) - where x is the degrees in the angle

22. What are the side ratios for a 30:60:90 triangle?
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4/3pir^3
(n-2)180

23. Explain the difference between a digit and a number.

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24. What is the area of a cylinder?
2(pi)r(r+h)
(y2-y1)/(x2-x1)
x² -2xy + y²
(a+b)(a-b)

25. When you reverse FOIL - the term that needs to add out is the _____
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.
x² -2xy + y²
Middle term
Number of desired outcomes/number of total outcomes

26. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Bh
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
Ac+ad+bc+bd

27. What is the area of a solid rectangle?
Number of desired outcomes/number of total outcomes
2(lw+wh+lh)
The distance from one point on the circle to another point on the circle.
Pir^2h

28. Chord
T1 * r^(n-1)
S² - where s = length of a side
The distance from one point on the circle to another point on the circle.
C =?d

29. (a+b)(a-b)=
x² + 2xy + y²
(a-b)²
Middle term
A²-b²

30. Area of a triangle
The four big angles are equal and the four small angles are equal
½(base x height) [or (base x height)÷2]
?r²
x² -2xy + y²

31. Diameter
T1 * r^(n-1)
The distance across the circle through the center of the circle.The diameter is twice the radius.
S^2
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

32. Sector
The set of points which are all the same distance (the radius) from a certain point (the center).
A=?r2
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.

33. Area of Circle
Pi*r^2
An ange whose vertex is the center of the circle
Total distance/total time
1/2bh

34. x^a * x^b = x^__
A+b
(n-2)180
?r²
x²-y²

35. What is the volume of a solid rectangle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(pi)r^2(h)
Number of desired outcomes/number of total outcomes
Lwh

36. 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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37. What is the probability?
A²-b²
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.
Number of desired outcomes/number of total outcomes
1.4

38. perimeter of square
y = k/x
4s
T1 + (n-1)d
(a-b)(a+b)

39. Rough est. of v2 =
4/3pir^3
4pir^2
1.4
(a+b)(a²-ab+b²)

40. Does order matter for a permutation? How about for a combination?
2(pi)r(r+h)
Order does matter for a permutation - but does not matter for a combination.
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.
y = k/x

41. Define the range of a set of numbers.
The four big angles are equal and the four small angles are equal
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The distance from one point on the circle to another point on the circle.

42. When a line crosses two parallel lines - ________.
Order does matter for a permutation - but does not matter for a combination.
y = kx
1.7
The four big angles are equal and the four small angles are equal

43. Area of Parallelogram
Opens down
2Length + 2width [or (length + width) x 2]
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Bh

44. Define the 'Third side' rule for triangles

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45. a² - b² is equal to
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(a+b)(a-b)
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
x² + 2xy + y²

46. Area of Triangle
4s (where s = length of a side)
1/2bh
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.

47. The length of one side of any triangle is ____ than the sum of the other two sides.
(pi)r^2
Less
2(pi)r
A=bh

48. a³-b³
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a-b)(a²+ab+b²)
The distance from one point on the circle to another point on the circle.
1/2bh

49. What is an 'equilateral' triangle?
x°/360 times (2 pi r) - where x is the degrees in the angle
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1
Sum of the lengths of the sides

50. x^-a =
Sqr( x2 -x1) + (y2- y1)
Probability A * Probability B
1/x^a
A²-b²

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GRE Math 2

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