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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. To divide powers with the same base...
N x M
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Total distance/total time
Sum of the lengths of the sides

2. How do you solve a permutation?
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.
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.
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
1/3pir^2*h

3. a²+2ab+b²
Order does matter for a permutation - but does not matter for a combination.
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.
(a+b)²
y-y1=m(x-x1)

4. Rough est. of v3 =
(x-y)²
1/3Bh
1.7
N x M

5. Define the mode of a set of numbers.
?d OR 2?r
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.
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
T1 * r^(n-1)

6. How do you find the sum of a geometric sequence?
(a+b)(a-b)
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.
?d OR 2?r
T1 * r^(n-1)/(r-1)

7. Diameter
1/1
(x+y)(x-y)
1.4
The distance across the circle through the center of the circle.The diameter is twice the radius.

8. What is the probability?
2(pi)r(r+h)
The distance from one point on the circle to another point on the circle.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Number of desired outcomes/number of total outcomes

9. Explain the special properties of zero.
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.
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'.
(y2-y1)/(x2-x1)
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.

10. (a+b)(a-b)=
Pi*r^2
A²-b²
4s (where s = length of a side)
T1 * r^(n-1)

11. What is the area of a triangle?
(pi)r^2(h)
Opens up
1/2bh
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.

12. Slope
y = k/x
(y2-y1)/(x2-x1)
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.

13. Area of a sector
Bh
(x+y)(x-y)
x°/360 times (?r²) - where x is the degrees in the angle
2pi*r

14. What is the prime factorization of 200?
2pir^2 + 2pir*h
The four big angles are equal and the four small angles are equal
1. Given event A: A + notA = 1.
2x2x2x5x5

15. When you reverse FOIL - the term that needs to add out is the _____
2(lw+wh+lh)
Pi*d
Middle term
1. Given event A: A + notA = 1.

16. What is the factored version of x² -2xy + y² ?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(0 -0)
(x-y)²
Opens down

17. What is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2(pi)r(r+h)
Between 0 and 1.
The distance from one point on the circle to another point on the circle.

18. Area of Triangle
Opens up
4pir^2
1/2bh
Less

19. Circle
The set of points which are all the same distance (the radius) from a certain point (the center).
C =?d
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
Last term

20. What do permutation problems often ask for?
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.
1/3pir^2*h
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.

21. What is the area of a solid rectangle?
y = k/x
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.
2(lw+wh+lh)
Percentage Change = Difference/Original * 100

22. Rough est. of v1 =
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*r^2
Last term
1

23. What is the area of a sector?
T1 * r^(n-1)
Pir^2h
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.
(n degrees/360) * (pi)r^2

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

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25. Volume of Cone
Opens down
1/1
1/3pir^2*h
1. Given event A: A + notA = 1.

26. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
4s (where s = length of a side)
1
Probability A * Probability B
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

27. How do you multiply and divide square roots?
T1 + (n-1)d
(a+b)²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Pi*r^2

28. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Arrangements - orders - schedules - or lists.
The total # of possible outcomes.
2x2x2x5x5

29. Point-Slope form
A²-b²
(n degrees/360) * (pi)r^2
y-y1=m(x-x1)
y = kx

30. Arc
4pir^2
Part of a circle connecting two points on 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.
Probability A + Probability B

31. Central Angle
x°/360 times (?r²) - where x is the degrees in the angle
(a-b)(a²+ab+b²)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
An ange whose vertex is the center of the circle

32. What is the 'Third side' rule for triangles?
Middle term
The total # of possible outcomes.
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.
x² + 2xy + y²

33. Circumference of a circle
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.
?d OR 2?r
Sum of the lengths of the sides
Last term

34. What is the average speed?
Total distance/total time
2(pi)r(r+h)
1/2bh
2pi*r

35. 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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36. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
Sum of the lengths of the sides
1.4
2(pi)r(r+h)

37. 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
Arrangements - orders - schedules - or lists.
4pir^2
(pi)r^2

38. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

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39. Perimeter (circumference) of a circle
2 pi r
Bh
x°/360 times (2 pi r) - where x is the degrees in the angle
Sum of the lengths of the sides

40. What is the volume of a solid rectangle?
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.
Lwh
2(pi)r

41. Perimeter of rectangle
2l+2w
An ange whose vertex is the center of the circle
y-y1=m(x-x1)
Sqr( x2 -x1) + (y2- y1)

42. What is the side ratio for a 30:60:90 triangle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
S² - where s = length of a side
Sqr( x2 -x1) + (y2- y1)
Ac+ad+bc+bd

43. Lines reflected over the x or y axis have ____ slopes.
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
Negative
y2-y1/x2-x1
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

44. a²-b²
?d OR 2?r
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
4s
(a-b)(a+b)

45. What is the length of an arc?
(n degrees/360) * 2(pi)r
S² - where s = length of a side
4/3pir^3
(n-2)180

46. Area of a triangle
½(base x height) [or (base x height)÷2]
(a-b)(a+b)
Probability A * Probability B
Sqr( x2 -x1) + (y2- y1)

47. Volume of Cylinder
Pir^2h
(y2-y1)/(x2-x1)
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.
Not necessarily. This is a trick question - because x could be either positive or negative.

48. What is the equation of a line?

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49. Does order matter for a permutation? How about for a combination?
(x-y)²
(y-y1)=m(x-x1)
x°/360 times (2 pi r) - where x is the degrees in the angle
Order does matter for a permutation - but does not matter for a combination.

50. Surface Area of Sphere
Opens up
4pir^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.
2l+2w

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GRE Math 2

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