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GRE Math 2

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. What do combination problems usually ask for?
Groups - teams - or committees.
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.
Lw
Opens down

2. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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 - and greater than the difference between the other two sides.
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
Order does matter for a permutation - but does not matter for a combination.

3. Define the range of a set of numbers.
The set of points which are all the same distance (the radius) from a certain point (the center).
Pi*r^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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

4. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
N x M
x°/360 times (?r²) - where x is the degrees in the angle
(y2-y1)/(x2-x1)

5. (a+b)(a-b)=
Arrangements - orders - schedules - or lists.
(a-b)(a+b)
A²-b²
A segment connecting the center of a circle to any point on the circle

6. What is directly proportional?
y = kx
The average - mean - median - or mode.
2(lw+wh+lh)
(0 -0)

7. How do you solve a permutation?
A²-b²
The four big angles are equal and the four small angles are equal
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
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.

8. What is the 'distributive law'?
y = k/x
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.

9. x^-a =
1/x^a
The distance from one point on the circle to another point on the circle.
(x+y)²
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. Rough est. of v1 =
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.
1
(x+y)²
A segment connecting the center of a circle to any point on the circle

11. length of a sector
Probability A * Probability B
(a-b)²
(a-b)(a²+ab+b²)
x°/360 times (2 pi r) - where x is the degrees in the angle

12. a² - b² is equal to
Ac+ad+bc+bd
Opens up
2(lw+wh+lh)
(a+b)(a-b)

13. When you reverse FOIL - the term that needs to multiply out is the _____
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.
Last term
x²-y²

14. What is the factored version of (x+y)(x-y) ?
x²-y²
Arrangements - orders - schedules - or lists.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

15. How do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
x² -2xy + y²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2(pi)r(r+h)

16. Rough est. of v2 =
4s (where s = length of a side)
2Length + 2width [or (length + width) x 2]
1.4
Opens up

17. Volume of Cone
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.
x² + 2xy + y²
1/3pir^2*h
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.

18. perimeter of square
A segment connecting the center of a circle to any point on the circle
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4s
Pir^2h

19. Volume of prism
The four big angles are equal and the four small angles are equal
x² -2xy + y²
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.
Bh

20. What is the surface area of a cylinder?
(x+y)²
(pi)r^2(h)
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
2(pi)r(r+h)

21. What is the length of an arc?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(n degrees/360) * 2(pi)r
(a-b)²
(pi)r^2(h)

22. In intersecting lines - opposite angles are _____.
1/2 h (b1 + b2)
Middle term
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Equal

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

24. Area of Parallelogram
Opens down
Not necessarily. This is a trick question - because x could be either positive or negative.
Bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

25. Area of Circles
2pir^2 + 2pir*h
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
Percentage Change = Difference/Original * 100
A=?r2

26. a³+b³
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(a+b)(a²-ab+b²)
x°/360 times (?r²) - where x is the degrees in the angle
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

27. Perimeter of polygon
1/2bh
The total # of possible outcomes.
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.
Sum of the lengths of the sides

28. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Sqr( x2 -x1) + (y2- y1)
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.
4s (where s = length of a side)
1/2 h (b1 + b2)

29. Circumference Formula
x°/360 times (?r²) - where x is the degrees in the angle
4pir^2
A=?r2
C =?d

30. What is an 'equilateral' triangle?
1/2bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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
(a+b)(a²-ab+b²)

31. How do you calculate the surface area of a rectangular box?
Sqr( x2 -x1) + (y2- y1)
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.
2 pi r
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.

32. What is the average?
Equal
(y-y1)=m(x-x1)
(pi)r^2
Sum of terms/number of terms

33. Perimeter (circumference) of a circle
2 pi r
(a+b)(a-b)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
4/3pir^3

34. In a coordinate system - identify the quadrants and describe their location.
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.
Arrangements - orders - schedules - or lists.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

35. When you reverse FOIL - the term that needs to add out is the _____
Middle term
Order does matter for a permutation - but does not matter for a combination.
Pir^2h
A²-b²

36. Rough est. of v3 =
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.
y = kx
Probability A + Probability B
1.7

37. What is the distance formula?
1/x^a
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Sqr( x2 -x1) + (y2- y1)

38. How do you calculate the percentage of change?
½(base x height) [or (base x height)÷2]
The average - mean - median - or mode.
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.
Percentage Change = Difference/Original * 100

39. Sector
Probability A * Probability B
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.
Pi*r^2
4s

40. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
4s (where s = length of a side)
A²-b²

41. What is inversely proportional?
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
y = k/x
(y2-y1)/(x2-x1)

42. Define the formula for calculating slope.
(y-y1)=m(x-x1)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
1/2bh
Total distance/total time

43. Arc
Part of a circle connecting two points on the circle.
Bh
N x M
Lwh

44. The length of one side of any triangle is ____ than the sum of the other two sides.
(pi)r^2
(0 -0)
(x-y)²
Less

45. Radius (Radii)
Equal
A segment connecting the center of a circle to any point on the circle
Probability A * Probability 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.

46. What is the unfactored version of x²-y² ?
(x+y)(x-y)
1.4
y-y1=m(x-x1)
Sum of terms/number of terms

47. What are the side ratios for a 30:60:90 triangle?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
?d OR 2?r
y-y1=m(x-x1)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

48. Surface Area of Sphere
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.
4pir^2
Sum of terms/number of terms
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

49. Perimeter of rectangle
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
S*v2
2l+2w
?r²

50. What is the formula for the diagonal of any square?
(a-b)(a+b)
y2-y1/x2-x1
Negative
S*v2