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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 unfactored version of (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.
Percentage Change = Difference/Original * 100
y = kx
x² + 2xy + y²

2. Volume of sphere
1/1
y = k/x
4/3pir^3
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

3. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
S*v2
2Length + 2width [or (length + width) x 2]
1. Given event A: A + notA = 1.

4. 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.
Sum of terms/number of terms
?d OR 2?r
4s

5. What is the distance formula?
S^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
?d OR 2?r
Sqr( x2 -x1) + (y2- y1)

6. Sector
S^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.
N x M
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

7. Area of Circles
A=?r2
(a+b)(a²-ab+b²)
T1 * r^(n-1)
1/2bh

8. Arc
1/2bh
Part of a circle connecting two points on the circle.
Arrangements - orders - schedules - or lists.
Percentage Change = Difference/Original * 100

9. How do you find the nth term 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'.
T1 + (n-1)d
Negative
(x-y)²

10. x^-a =
1/x^a
Between 0 and 1.
(x-y)²
Number of desired outcomes/number of total outcomes

11. x^a * x^b = x^__
A+b
A segment connecting the center of a circle to any point on the circle
2x2x2x5x5
1/x^a

12. What is the point-slope form?
2(pi)r
4pir^2
x² + 2xy + y²
(y-y1)=m(x-x1)

13. List two odd behaviors of exponents
Total distance/total time
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Between 0 and 1.
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.

14. 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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15. Define the formula for calculating slope.
Probability A + Probability B
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
x°/360 times (?r²) - where x is the degrees in the angle
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

16. What is the area of a solid rectangle?
(a-b)(a+b)
Bh
(y2-y1)/(x2-x1)
2(lw+wh+lh)

17. What is the area of a triangle?
y-y1=m(x-x1)
A²-b²
1/2bh
2 pi r

18. Area of Rectangle
(x1+x2)/2 - (y1+y2)/2
A=bh
y = k/x
Lw

19. Surface Area of Sphere
2pir^2 + 2pir*h
4pir^2
T1 * r^(n-1)
½(base x height) [or (base x height)÷2]

20. What is the area of a circle?
2(pi)r(r+h)
S*v2
(pi)r^2
?r²

21. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
1/2bh
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.
y = k/x
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.

22. Rough est. of v3 =
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.
(x+y)²
1.7
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

23. What is the circumference of a circle?
2(pi)r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
T1 + (n-1)d
Pi*r^2

24. Volume of pyramid
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.
2pir^2 + 2pir*h
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/3Bh

25. (a+b)(a-b)=
A=?r2
1/2 h (b1 + b2)
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.
A²-b²

26. Perimeter of polygon
x°/360 times (2 pi r) - where x is the degrees in the angle
(y2-y1)/(x2-x1)
Lw
Sum of the lengths of the sides

27. How do you multiply and divide square roots?
(x+y)(x-y)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

28. Define the mode of a set of numbers.
A=?r2
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.
The length of any one side of a triangle must be less than the sum of the other two sides. It must also be greater than the difference between the other two sides. So - 'A' will always be < B+C - and > B-C or C-B.
Probability A * Probability B

29. Central Angle
An ange whose vertex is the center of the circle
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.
?d OR 2?r
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

30. What is the side ratio for a Right Isosceles triangle?
2l+2w
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The average - mean - median - or mode.

31. Rough est. of v1 =
1
2Length + 2width [or (length + width) x 2]
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

32. Area of Trapezoid
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.
1/2 h (b1 + b2)
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.
The distance from one point on the circle to another point on the circle.

33. How do you find the slope?
(n-2)180
4/3pir^3
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
y2-y1/x2-x1

34. What is the factored version of x² -2xy + y² ?
Probability A + Probability B
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Groups - teams - or committees.
(x-y)²

35. Perimeter (circumference) of a circle
Total distance/total time
Groups - teams - or committees.
2 pi r
2pi*r

36. What is the factored version of x² + 2xy + y² ?
1.7
(x+y)²
Bh
Order does matter for a permutation - but does not matter for a combination.

37. What do combination problems usually ask for?
Bh
Groups - teams - or committees.
2 pi r
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.

38. (a+b)(c+d)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
S^2
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Ac+ad+bc+bd

39. When you reverse FOIL - the term that needs to add out is the _____
Not necessarily. This is a trick question - because x could be either positive or negative.
Middle term
(y2-y1)/(x2-x1)
Percentage Change = Difference/Original * 100

40. Area of Square
S^2
Lwh
(a+b)(a²-ab+b²)
4pir^2

41. Volume of Cylinder
The length of any one side of a triangle must be less than the sum of the other two sides. It must also be greater than the difference between the other two sides. So - 'A' will always be < B+C - and > B-C or C-B.
Order does matter for a permutation - but does not matter for a combination.
Pir^2h
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.

42. For a bell curve - what three terms might be used to describe the number in the middle?
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
The average - mean - median - or mode.
S*v2
y = k/x

43. a²+2ab+b²
An ange whose vertex is the center of the circle
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a+b)²

44. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(a+b)(a²-ab+b²)
Pi*d
Probability A * Probability B

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

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46. In a coordinate system - identify the quadrants and describe their location.
y = k/x
S*v2
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Between 0 and 1.

47. Circumference of cirlce using diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
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*d
1.4

48. If something is certain to happen - how is the probability of this event expressed mathematically?
A=?r2
2 pi r
1/1
Part of a circle connecting two points on the circle.

49. What is the factored version of (x+y)(x-y) ?
Pi*d
x²-y²
(x+y)²
(a-b)²

50. Area of Parallelogram
Bh
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.
Total distance/total time
The distance from one point on the circle to another point on the circle.

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GRE Math 2

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