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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. Volume of Cone
2l+2w
A=bh
1/3pir^2*h
2lw+2lh+2wh

2. What number goes on the bottom of a probability fraction?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The total # of possible outcomes.
4pir^2
Negative

3. What is the factored version of x² -2xy + y² ?
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.
(x-y)²

4. What is the formula for the diagonal of any square?
(x+y)²
S*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.
(n-2)180

5. How do you multiply and divide square roots?
Between 0 and 1.
Groups - teams - or committees.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2(pi)r(r+h)

6. When you reverse FOIL - the term that needs to multiply out is the _____
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.
Last term
(pi)r^2
The distance across the circle through the center of the circle.The diameter is twice the radius.

7. What is the area of a cylinder?
2(pi)r(r+h)
(a+b)(a-b)
1/3Bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

8. What is the prime factorization of 200?
2x2x2x5x5
(n degrees/360) * 2(pi)r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2pi*r

9. What is the side ratio for a 30:60:90 triangle?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
x² + 2xy + y²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Sum of the lengths of the sides

10. What is the factored version of x² + 2xy + y² ?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1/2bh
A=?r2
(x+y)²

11. x^-a =
1/x^a
?r²
1
(a-b)(a²+ab+b²)

12. Area of Square
S^2
(n degrees/360) * (pi)r^2
S*v2
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

13. In a parabola - if the first term is positive - the parabola ________.
Opens up
(a+b)²
A+b
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.

14. a²-2ab+b²
(n/2) * (t1+tn)
(a-b)²
Number of desired outcomes/number of total outcomes
?d OR 2?r

15. List two odd behaviors of exponents
1/2bh
An ange whose vertex is the center of the circle
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.

16. What is the unfactored version of x²-y² ?
1. Given event A: A + notA = 1.
1.7
(x+y)(x-y)
Pi*d

17. What is the 'Third side' rule for triangles?
Less
Pi*r^2
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 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.

18. Circle
A=bh
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
Order does matter for a permutation - but does not matter for a combination.
The set of points which are all the same distance (the radius) from a certain point (the center).

19. What is the area of a triangle?
(a-b)(a+b)
4/3pir^3
1/2bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

20. Area of a trapezoid
The four big angles are equal and the four small angles are equal
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
x°/360 times (2 pi r) - where x is the degrees in the angle

21. What is a 'Right isosceles' 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.
Total distance/total time
?d OR 2?r
Arrangements - orders - schedules - or lists.

22. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
S*v2
An ange whose vertex is the center of the circle
2(pi)r(r+h)
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.

23. In a parabola - if the first term is negative - the parabola ________.
Opens down
(x-y)²
T1 * r^(n-1)/(r-1)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

24. a³+b³
(a-b)²
(a+b)(a²-ab+b²)
Last term
C =?d

25. How do you find the sum of an arithmetic sequence?
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'.
(x1+x2)/2 - (y1+y2)/2
(n/2) * (t1+tn)
The distance from one point on the circle to another point on the circle.

26. How do you calculate the probability of two events in a row? (Probability of A and B)
(x-y)²
(n-2)180
Probability A + Probability B
Probability A * Probability B

27. Rough est. of v1 =
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.
y = k/x
2(pi)r(r+h)
1

28. Circumference of a circle using radius
2pi*r
A=?r2
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.
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.

29. What'S the most important thing to remember about charts you'll see on the GRE?
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.
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
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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

30. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
2(pi)r
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.
2Length + 2width [or (length + width) x 2]

31. In intersecting lines - opposite angles are _____.
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.
Pi*r^2
The four big angles are equal and the four small angles are equal
Equal

32. Explain the special properties of zero.
Probability A + Probability B
A=?r2
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.
1. Given event A: A + notA = 1.

33. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
S^2
Between 0 and 1.
1/2bh

34. What is the volume of a solid rectangle?
2(pi)r
Lwh
T1 + (n-1)d
x°/360 times (2 pi r) - where x is the degrees in the angle

35. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
Groups - teams - or committees.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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

36. Central Angle
An ange whose vertex is the center of the circle
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
A²-b²
(x-y)²

37. Area of a triangle
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.
4/3pir^3
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.
½(base x height) [or (base x height)÷2]

38. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
2(pi)r(r+h)

39. Rough est. of v2 =
1.4
x°/360 times (2 pi r) - where x is the degrees in the angle
(a+b)(a-b)
Middle term

40. 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.
(x-y)²
?d OR 2?r
2 pi r

41. What is the volume of a cylinder?
Negative
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
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
(pi)r^2(h)

42. What is the area of a sector?
T1 * r^(n-1)
y = k/x
(n degrees/360) * (pi)r^2
A²-b²

43. For a bell curve - what three terms might be used to describe the number in the middle?
2 pi r
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.
The average - mean - median - or mode.
x² + 2xy + y²

44. What is the unfactored version of (x+y)² ?
(a+b)(a²-ab+b²)
(y2-y1)/(x2-x1)
x² + 2xy + y²
(n degrees/360) * 2(pi)r

45. (a+b)(a-b)=
1/1
(n degrees/360) * 2(pi)r
2 pi r
A²-b²

46. How do you find the sum of a geometric sequence?
x°/360 times (?r²) - where x is the degrees in the angle
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
T1 * r^(n-1)/(r-1)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

47. What is the average?
Pi*d
Sum of terms/number of terms
x°/360 times (2 pi r) - where x is the degrees in the angle
2lw+2lh+2wh

48. What is the side ratio for a Right Isosceles triangle?
C =?d
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
Probability A + Probability B

49. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
b±[vb²-4ac]/2a
y2-y1/x2-x1
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

50. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2x2x2x5x5
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.
Part of a circle connecting two points on the circle.

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GRE Math 2

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