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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 is an 'equilateral' triangle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Arrangements - orders - schedules - or lists.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

2. 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.
The four big angles are equal and the four small angles are equal
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.
A+b

3. Area of a triangle
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
½(base x height) [or (base x height)÷2]
2(pi)r(r+h)
Pir^2h

4. Area of a square
(n degrees/360) * 2(pi)r
S² - where s = length of a side
1/1
?r²

5. What is the unfactored version of (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
x² -2xy + y²
4s (where s = length of a side)
S*v2

6. 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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7. What is inversely proportional?
N x M
y = k/x
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

8. Perimeter of a square
Arrangements - orders - schedules - or lists.
?d OR 2?r
Negative
4s (where s = length of a side)

9. What is the circumference of a circle?
A segment connecting the center of a circle to any point on the circle
2(pi)r
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Sum of terms/number of terms

10. For a bell curve - what three terms might be used to describe the number in the middle?
Pi*r^2
The average - mean - median - or mode.
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.
(x-y)²

11. Radius (Radii)
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 segment connecting the center of a circle to any point on 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.
(n degrees/360) * 2(pi)r

12. a²-b²
(a-b)(a+b)
Between 0 and 1.
?d OR 2?r
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.

13. What number goes on the bottom of a probability fraction?
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.
A+b
The total # of possible outcomes.
Equal

14. How do you find the slope?
The distance across the circle through the center of the circle.The diameter is twice the radius.
y2-y1/x2-x1
4s (where s = length of a side)
1/2bh

15. Central Angle
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.
An ange whose vertex is the center of the circle
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.

16. What is the distance formula?
(n degrees/360) * (pi)r^2
Sqr( x2 -x1) + (y2- y1)
y-y1=m(x-x1)
An ange whose vertex is the center of the circle

17. How do you calculate the percentage of change?
T1 + (n-1)d
1
Percentage Change = Difference/Original * 100
A segment connecting the center of a circle to any point on the circle

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

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19. What is the area of a cylinder?
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
Bh
½(base x height) [or (base x height)÷2]
2(pi)r(r+h)

20. What is the factored version of x² + 2xy + y² ?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A²-b²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(x+y)²

21. x^a * x^b = x^__
A+b
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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
T1 * r^(n-1)

22. x^-a =
Pi*d
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/x^a
Lwh

23. Surface Area of Cylinder
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The distance from one point on the circle to another point on the circle.
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
2pir^2 + 2pir*h

24. Volume of Cylinder
An ange whose vertex is the center of the circle
The set of points which are all the same distance (the radius) from a certain point (the center).
The total # of possible outcomes.
Pir^2h

25. What is the probability?
A²-b²
2x2x2x5x5
Number of desired outcomes/number of total outcomes
4pir^2

26. Does order matter for a permutation? How about for a combination?
x² -2xy + y²
(n degrees/360) * (pi)r^2
x² + 2xy + y²
Order does matter for a permutation - but does not matter for a combination.

27. Volume of prism
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'.
Bh
(a-b)²
1/x^a

28. How do you solve a permutation?
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.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.

29. What is directly proportional?
T1 + (n-1)d
(n degrees/360) * 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.
y = kx

30. What is the equation of a line?

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31. How do you calculate the surface area of a rectangular box?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
The distance from one point on the circle to another point on the circle.

32. Quadratic Formula
b±[vb²-4ac]/2a
(a+b)(a-b)
Sqr( x2 -x1) + (y2- y1)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

33. What is the area of a sector?
The average - mean - median - or mode.
(n degrees/360) * (pi)r^2
(y2-y1)/(x2-x1)
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.

34. Circumference of cirlce using diameter
Negative
Pi*d
1/2bh
1/3pir^2*h

35. How do you find the sum of an arithmetic sequence?
Part of a circle connecting two points on the circle.
½(base x height) [or (base x height)÷2]
(n/2) * (t1+tn)
Percentage Change = Difference/Original * 100

36. What is the volume of a solid rectangle?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2lw+2lh+2wh
Pir^2h
Lwh

37. What is the formula for the diagonal of any square?
S*v2
Ac+ad+bc+bd
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.
The set of points which are all the same distance (the radius) from a certain point (the center).

38. a² - b² is equal to
1.7
(a+b)(a-b)
x² -2xy + y²
(n degrees/360) * (pi)r^2

39. Volume of sphere
The distance from one point on the circle to another point on the circle.
The total # of possible outcomes.
T1 * r^(n-1)/(r-1)
4/3pir^3

40. Define the 'Third side' rule for triangles

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41. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
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.
Number of desired outcomes/number of total outcomes
Not necessarily. This is a trick question - because x could be either positive or negative.
N x M

42. What is the volume of a cylinder?
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
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
A segment connecting the center of a circle to any point on the circle
(pi)r^2(h)

43. Volume of pyramid
Probability A * Probability B
Ac+ad+bc+bd
1.7
1/3Bh

44. How do you find the nth term of a geometric sequence?
½(base x height) [or (base x height)÷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.
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.
T1 * r^(n-1)

45. The probability of an event happening and the probability of an event NOT happening must add up to what number?
A segment connecting the center of a circle to any point on the circle
(y-y1)=m(x-x1)
1. Given event A: A + notA = 1.
2x2x2x5x5

46. When a line crosses two parallel lines - ________.
(y-y1)=m(x-x1)
Ac+ad+bc+bd
2l+2w
The four big angles are equal and the four small angles are equal

47. What is the area of a circle?
Less
Sum of the lengths of the sides
(pi)r^2
A segment connecting the center of a circle to any point on the circle

48. Perimeter of rectangle
2l+2w
(x-y)²
(a-b)(a+b)
Sum of the lengths of the sides

49. What is the unfactored version of x²-y² ?
(x+y)(x-y)
C =?d
The distance from one point on the circle to another point on the circle.
S^2

50. How do you multiply powers with the same base?
Groups - teams - or committees.
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.
Number of desired outcomes/number of total outcomes
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7