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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. Sector
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.
(x+y)²
Sqr( x2 -x1) + (y2- y1)
2(pi)r(r+h)

2. If x² = 144 - does v144 = x?
y = kx
(a+b)²
Not necessarily. This is a trick question - because x could be either positive or negative.
The four big angles are equal and the four small angles are equal

3. Define the formula for calculating slope.
(y-y1)=m(x-x1)
(a+b)(a²-ab+b²)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(x1+x2)/2 - (y1+y2)/2

4. The length of one side of any triangle is ____ than the sum of the other two sides.
2(pi)r
Less
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
An ange whose vertex is the center of the circle

5. How do you find the sum of a geometric sequence?
Order does matter for a permutation - but does not matter for a combination.
T1 * r^(n-1)/(r-1)
Arrangements - orders - schedules - or lists.
1

6. When you reverse FOIL - the term that needs to add out is the _____
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.
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.
Middle term
1/2 h (b1 + b2)

7. What is the unfactored version of (x+y)² ?
x² + 2xy + y²
4s
Total distance/total time
4/3pir^3

8. What is the area of a triangle?
1/2bh
Opens down
1
(a-b)²

9. How do you find the nth term of a geometric sequence?
Total distance/total time
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
2(pi)r(r+h)
T1 * r^(n-1)

10. What is directly proportional?
2x2x2x5x5
y-y1=m(x-x1)
y = kx
Lw

11. Define a factorial of a number - and how it is written.
y = k/x
y2-y1/x2-x1
4s (where s = length of a side)
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.

12. When you reverse FOIL - the term that needs to multiply out is the _____
Less
Last term
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.
Part of a circle connecting two points on the circle.

13. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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
1/1
S² - where s = length of a side

14. How do you multiply powers with the same base?
Number of desired outcomes/number of total outcomes
A segment connecting the center of a circle to any point on the circle
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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

15. a² - b² is equal to
(0 -0)
(a+b)(a-b)
(a+b)(a²-ab+b²)
Part of a circle connecting two points on the circle.

16. What is the volume of a solid rectangle?
Sum of the lengths of the sides
Lwh
The distance across the circle through the center of the circle.The diameter is twice the radius.
S*v2

17. Rough est. of v2 =
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.
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.
1.4
The total # of possible outcomes.

18. What do permutation problems often ask for?
T1 * r^(n-1)
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.
4s
Arrangements - orders - schedules - or lists.

19. What is an 'equilateral' triangle?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Total distance/total time
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Groups - teams - or committees.

20. If something is certain to happen - how is the probability of this event expressed mathematically?
Part of a circle connecting two points on the circle.
Sqr( x2 -x1) + (y2- y1)
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.
1/1

21. What is a 'Right isosceles' triangle?
2x2x2x5x5
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.
(x1+x2)/2 - (y1+y2)/2
½(base x height) [or (base x height)÷2]

22. What is the distance formula?
(x-y)²
The distance from one point on the circle to another point on the circle.
x² + 2xy + y²
Sqr( x2 -x1) + (y2- y1)

23. To divide powers with the same base...
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
Pi*r^2

24. Volume of sphere
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
The four big angles are equal and the four small angles are equal
4/3pir^3
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.

25. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Sum of the lengths of the sides
1/2bh

26. Area of Trapezoid
A²-b²
Probability A + Probability B
1/2 h (b1 + b2)
(n degrees/360) * (pi)r^2

27. Volume of Cylinder
C =?d
y = k/x
Pir^2h
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

28. Define the range of a set of numbers.
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 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.
1/2bh
4/3pir^3

29. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

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30. How do you calculate the surface area of a rectangular box?
2x2x2x5x5
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.
A=?r2
y2-y1/x2-x1

31. What is the area of a solid rectangle?
2(lw+wh+lh)
b±[vb²-4ac]/2a
Less
C =?d

32. What is a '30:60:90' triangle?
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
(x+y)²
4/3pir^3
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.

33. Define the mode of a set of numbers.
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-y1)=m(x-x1)
?r²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

34. What is the factored version of (x+y)(x-y) ?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x²-y²
4pir^2
4s

35. What is the point-slope form?
2 pi r
Equal
(y-y1)=m(x-x1)
T1 + (n-1)d

36. How do you calculate the probability of two events in a row? (Probability of A and B)
Ac+ad+bc+bd
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
C =?d
Probability A * Probability B

37. Rough est. of v3 =
2 pi r
1.7
(y2-y1)/(x2-x1)
1/1

38. Perimeter (circumference) of a circle
2 pi r
y2-y1/x2-x1
Bh
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

39. What is the side ratio for a 30:60:90 triangle?
Probability A + Probability B
?r²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
T1 * r^(n-1)

40. 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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41. Define 'proportionate' values
(n-2)180
1/x^a
(y-y1)=m(x-x1)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

42. Arc
Part of a circle connecting two points on the circle.
Between 0 and 1.
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.
1/3Bh

43. Volume of prism
2(lw+wh+lh)
Bh
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(h)

44. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
Sqr( x2 -x1) + (y2- y1)
Not necessarily. This is a trick question - because x could be either positive or negative.
y = kx

45. (a+b)(c+d)
y = k/x
Ac+ad+bc+bd
4s (where s = length of a side)
The four big angles are equal and the four small angles are equal

46. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
(pi)r^2(h)
1.4
½(b1 +b2) x h [or (b1 +b2) x h÷2]
N x M

47. Point-Slope form
1/2bh
Probability A * Probability B
Lw
y-y1=m(x-x1)

48. Area of Circles
A=?r2
1.7
Ac+ad+bc+bd
(pi)r^2(h)

49. Area of Parallelogram
(pi)r^2(h)
(0 -0)
A segment connecting the center of a circle to any point on the circle
Bh

50. x^-a =
1/x^a
(x-y)²
2Length + 2width [or (length + width) x 2]
S^2