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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 calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
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 = kx
?r²
Probability A + Probability B

2. Area of Square
S^2
A+b
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.
2Length + 2width [or (length + width) x 2]

3. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Order does matter for a permutation - but does not matter for a combination.

4. Quadratic Formula
b±[vb²-4ac]/2a
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'.
Pi*r^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

5. What do permutation problems often ask for?
Lwh
2lw+2lh+2wh
(x-y)²
Arrangements - orders - schedules - or lists.

6. How do you find the sum of an arithmetic sequence?
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.
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
(n/2) * (t1+tn)
S*v2

7. Define the 'Third side' rule for triangles

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8. What is inversely proportional?
2x2x2x5x5
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
y = k/x
(n degrees/360) * 2(pi)r

9. What is the distance formula?
1/x^a
Arrangements - orders - schedules - or lists.
Sqr( x2 -x1) + (y2- y1)
A²-b²

10. a³+b³
(a+b)(a²-ab+b²)
x²-y²
Probability A + Probability B
Lwh

11. What is the surface area of a cylinder?
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.
2(pi)r(r+h)
A=?r2
(x+y)(x-y)

12. What is the factored version of x² -2xy + y² ?
(x-y)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
1.4
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.

13. Diameter
Arrangements - orders - schedules - or lists.
The distance across the circle through the center of the circle.The diameter is twice the radius.
(a-b)(a+b)
Sqr( x2 -x1) + (y2- y1)

14. When you reverse FOIL - the term that needs to multiply out is the _____
x°/360 times (?r²) - where x is the degrees in the angle
1/3pir^2*h
Last term
(0 -0)

15. In a parabola - if the first term is negative - the parabola ________.
A segment connecting the center of a circle to any point on the circle
Opens down
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Order does matter for a permutation - but does not matter for a combination.

16. Rough est. of v3 =
1.7
Order does matter for a permutation - but does not matter for a combination.
The distance from one point on the circle to another point on the circle.
(n degrees/360) * (pi)r^2

17. Volume of Cylinder
A+b
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Pir^2h

18. What is the factored version of (x+y)(x-y) ?
2l+2w
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.
Pi*r^2
x²-y²

19. What is the average speed?
Bh
(a-b)(a²+ab+b²)
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.
Total distance/total time

20. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
Percentage Change = Difference/Original * 100
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Lw

21. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Number of desired outcomes/number of total outcomes
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.
N x M

22. What is the side ratio for a Right Isosceles triangle?
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

23. Explain the special properties of zero.
2l+2w
1/x^a
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.
x²-y²

24. Radius (Radii)
1/2bh
A segment connecting the center of a circle to any point 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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

25. In a parabola - if the first term is positive - the parabola ________.
Part of a circle connecting two points on the circle.
Opens up
The total # of possible outcomes.
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.

26. Area of Circles
A=?r2
S² - where s = length of a side
Total distance/total time
1.4

27. (a+b)(c+d)
T1 + (n-1)d
C =?d
Ac+ad+bc+bd
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.

28. List two odd behaviors of exponents
Opens up
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Percentage Change = Difference/Original * 100

29. (a+b)(a-b)=
A segment connecting the center of a circle to any point on the circle
Opens up
A²-b²
A+b

30. What is the side ratio for a 30:60:90 triangle?
2Length + 2width [or (length + width) x 2]
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/2bh
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.

31. Central Angle
Opens down
An ange whose vertex is the center of the circle
The distance from one point on the circle to another point on the circle.
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'.

32. What is the volume of a solid rectangle?
Lwh
Pi*d
y-y1=m(x-x1)
Arrangements - orders - schedules - or lists.

33. In intersecting lines - opposite angles are _____.
Percentage Change = Difference/Original * 100
Equal
1.4
y2-y1/x2-x1

34. To divide powers with the same base...
Percentage Change = Difference/Original * 100
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Part of a circle connecting two points on the circle.
Total distance/total time

35. What is the factored version of x² + 2xy + y² ?
(n/2) * (t1+tn)
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.
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
(x+y)²

36. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
1/2 h (b1 + b2)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
(x+y)(x-y)

37. Point-Slope form
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The average - mean - median - or mode.
b±[vb²-4ac]/2a
y-y1=m(x-x1)

38. What do combination problems usually ask for?
Groups - teams - or committees.
A=bh
(a+b)(a²-ab+b²)
A+b

39. x^-a =
1/x^a
Less
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.
4/3pir^3

40. a²-b²
(a-b)(a²+ab+b²)
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
(a-b)(a+b)

41. Volume of sphere
A=bh
2l+2w
4/3pir^3
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

42. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Total distance/total time
x² + 2xy + y²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1. Given event A: A + notA = 1.

43. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
Negative
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.
Lwh

44. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
T1 + (n-1)d

45. Volume of prism
Bh
S^2
1.7
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

46. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
b±[vb²-4ac]/2a
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.

47. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
4pir^2
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.
Number of desired outcomes/number of total outcomes

48. a²-2ab+b²
S*v2
(x-y)²
(a-b)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.

49. When a line crosses two parallel lines - ________.
The four big angles are equal and the four small angles are equal
Percentage Change = Difference/Original * 100
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.
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.

50. What is directly proportional?
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.
4/3pir^3
y = kx

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GRE Math 2

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