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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Area of Triangle
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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1/2bh
?r²

2. Volume of Cone
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.
T1 * r^(n-1)/(r-1)
1/3pir^2*h

3. a³-b³
x°/360 times (2 pi r) - where x is the degrees in the angle
?r²
(a-b)(a²+ab+b²)
2(pi)r(r+h)

4. In a parabola - if the first term is negative - the parabola ________.
1
Opens up
S^2
Opens down

5. What is the circumference of a circle?
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.
(y-y1)=m(x-x1)
(x-y)²
2(pi)r

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

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7. (a+b)(a-b)=
(a+b)(a-b)
(0 -0)
A²-b²
A=bh

8. When a line crosses two parallel lines - ________.
x² -2xy + y²
The four big angles are equal and the four small angles are equal
Less
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

9. Define the mode of a set of numbers.
Lw
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.
Opens up
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.

10. What must be true before a quadratic equation can be solved?

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11. Area of a square
4s
(a-b)(a+b)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
S² - where s = length of a side

12. What is 'absolute value' - and how is it represented?

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13. How do you multiply and divide square roots?
y = kx
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Bh

14. What is an 'equilateral' triangle?
(n degrees/360) * 2(pi)r
Negative
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

15. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
N x M
Pi*r^2
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.
T1 * r^(n-1)

16. How do you find the slope?
x² + 2xy + y²
1
y2-y1/x2-x1
A=?r2

17. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.
2pi*r
2x2x2x5x5

18. Circumference of cirlce using diameter
(a+b)(a²-ab+b²)
2Length + 2width [or (length + width) x 2]
Pi*d
Total distance/total time

19. Volume of sphere
4/3pir^3
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.
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.

20. Volume of Cylinder
Bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Pir^2h
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.

21. 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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22. How do you solve a permutation?
(n degrees/360) * 2(pi)r
y = k/x
Probability A + Probability 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

23. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
Lw
?d OR 2?r
(a-b)(a+b)

24. Circumference of a circle using radius
Total distance/total time
Less
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.
2pi*r

25. Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
C =?d

26. What are the side ratios for a 30:60:90 triangle?
y = k/x
Ac+ad+bc+bd
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a+b)²

27. What is the formula for the diagonal of any square?
2l+2w
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)
S*v2

28. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Bh
b±[vb²-4ac]/2a
(x+y)(x-y)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

29. What is the area of a cylinder?
2(pi)r(r+h)
Sum of terms/number of terms
The four big angles are equal and the four small angles are equal
1

30. Area of a trapezoid
2(lw+wh+lh)
2x2x2x5x5
Negative
½(b1 +b2) x h [or (b1 +b2) x h÷2]

31. Area of Circles
1. Given event A: A + notA = 1.
A=?r2
1/3pir^2*h
(a+b)(a-b)

32. What is the area of a circle?
4s (where s = length of a side)
(pi)r^2
1.7
?r²

33. How do you calculate the percentage of change?
Sum of the lengths of the sides
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
Lwh
Percentage Change = Difference/Original * 100

34. How do you find the nth term of a geometric sequence?
(a-b)²
T1 * r^(n-1)
y = k/x
(n-2)180

35. What do permutation problems often ask for?
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 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.
Ac+ad+bc+bd
Arrangements - orders - schedules - or lists.

36. Area of a triangle
(a+b)(a-b)
Not necessarily. This is a trick question - because x could be either positive or negative.
S*v2
½(base x height) [or (base x height)÷2]

37. a²-2ab+b²
1. Given event A: A + notA = 1.
A²-b²
(a-b)²
Part of a circle connecting two points on the circle.

38. Quadratic Formula
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
b±[vb²-4ac]/2a

39. In a coordinate system - what is the origin?
A=bh
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
2Length + 2width [or (length + width) x 2]
(0 -0)

40. What is the area of a triangle?
(a-b)(a+b)
(y2-y1)/(x2-x1)
1/2bh
Pir^2h

41. How do you calculate the probability of two events in a row? (Probability of A and B)
Groups - teams - or committees.
T1 * r^(n-1)
Probability A * Probability B
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.

42. Area of Trapezoid
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
1/2 h (b1 + b2)
1/3pir^2*h
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.

43. Rough est. of v3 =
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.
1.7
x°/360 times (2 pi r) - where x is the degrees in the angle

44. To divide powers with the same base...
(n/2) * (t1+tn)
4/3pir^3
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

45. Area of a circle
Groups - teams - or committees.
x°/360 times (2 pi r) - where x is the degrees in the angle
?r²
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

46. What is the factored version of (x+y)(x-y) ?
Negative
Pi*d
x²-y²
A+b

47. a³+b³
(a+b)(a²-ab+b²)
2(pi)r(r+h)
(pi)r^2(h)
2(lw+wh+lh)

48. How do you find the midpoint?
Opens down
(x1+x2)/2 - (y1+y2)/2
x°/360 times (2 pi r) - where x is the degrees in the angle
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.

49. Surface Area of Sphere
The set of points which are all the same distance (the radius) from a certain point (the center).
Between 0 and 1.
4pir^2
T1 * r^(n-1)

50. When you reverse FOIL - the term that needs to multiply out is the _____
(a+b)(a²-ab+b²)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Last term
Pi*d

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GRE Math 2

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