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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. Circle
1.7
The set of points which are all the same distance (the radius) from a certain point (the center).
Bh
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.

2. How do you multiply and divide square roots?
The distance across the circle through the center of the circle.The diameter is twice the radius.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/2 h (b1 + b2)
(a-b)²

3. length of a sector
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
x°/360 times (2 pi r) - where x is the degrees in the angle
b±[vb²-4ac]/2a

4. a³+b³
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.
1/1
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a+b)(a²-ab+b²)

5. What is the unfactored version of (x-y)² ?
x² -2xy + y²
S^2
½(base x height) [or (base x height)÷2]
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

6. Perimeter of a square
4s (where s = length of a side)
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
The four big angles are equal and the four small angles are equal

7. How do you calculate a diagonal inside a 3-dimensional rectangular box?
(pi)r^2
Ac+ad+bc+bd
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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

8. Define the range of a set of numbers.
Sqr( x2 -x1) + (y2- y1)
(n degrees/360) * (pi)r^2
2 pi r
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.

9. Sector
Less
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.

10. What is the 'Third side' rule for triangles?
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. 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.
S² - where s = length of a side
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.

11. What is an 'equilateral' triangle?
1/1
Lw
2Length + 2width [or (length + width) x 2]
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

12. In a parabola - if the first term is positive - the parabola ________.
1/3pir^2*h
Equal
Opens up
2pir^2 + 2pir*h

13. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
(pi)r^2
2 pi r
C =?d

14. Surface Area of Sphere
2(pi)r
S^2
4pir^2
Pi*d

15. Area of a square
S² - where s = length of a side
Probability A + Probability B
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2(pi)r

16. Area of rectangle - square - parallelogram
(x1+x2)/2 - (y1+y2)/2
A=?r2
A=bh
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

17. Area of a triangle
T1 + (n-1)d
The four big angles are equal and the four small angles are equal
S*v2
½(base x height) [or (base x height)÷2]

18. In a coordinate system - what is the origin?
y = k/x
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
1.4
(0 -0)

19. In intersecting lines - opposite angles are _____.
2(pi)r(r+h)
Equal
A=bh
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.

20. How do you solve a permutation?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A+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
Middle term

21. What is the probability?
(y-y1)=m(x-x1)
Number of desired outcomes/number of total outcomes
Equal
Probability A + Probability B

22. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Number of desired outcomes/number of total outcomes
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.
?r²
Opens down

23. Slope
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)(a²+ab+b²)
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
(y2-y1)/(x2-x1)

24. What is the unfactored version of x²-y² ?
x² -2xy + y²
N x M
(x+y)(x-y)
(x+y)²

25. What is the prime factorization of 200?
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'.
Opens up
2x2x2x5x5
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

26. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
(a-b)(a+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.
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.
N x M

27. Define 'proportionate' values
Part of a circle connecting two points on the circle.
Pir^2h
?d OR 2?r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

28. Surface Area of rectangular prism
Number of desired outcomes/number of total outcomes
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.
2lw+2lh+2wh
Equal

29. What is the side ratio for a 30:60:90 triangle?
Probability A + Probability B
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(n degrees/360) * (pi)r^2
Pi*d

30. x^a * x^b = x^__
Lw
An ange whose vertex is the center of the circle
A+b
1/x^a

31. a² - b² is equal to
(n degrees/360) * (pi)r^2
(a+b)(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.
Sum of the lengths of the sides

32. Perimeter (circumference) of a circle
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
Middle term
2 pi r
1/2 h (b1 + b2)

33. Volume of sphere
Opens down
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.
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
4/3pir^3

34. What is directly proportional?
x°/360 times (?r²) - where x is the degrees in the angle
y = kx
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.
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

35. perimeter of square
A²-b²
The average - mean - median - or mode.
Opens down
4s

36. What is the average?
Sum of terms/number of terms
b±[vb²-4ac]/2a
x² + 2xy + y²
Lwh

37. 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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38. Area of a trapezoid
Pi*d
½(b1 +b2) x h [or (b1 +b2) x h÷2]
y = kx
y = k/x

39. What is the circumference of a circle?
2(pi)r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2(pi)r(r+h)
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.

40. Volume of prism
S*v2
Bh
The average - mean - median - or mode.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

41. Point-Slope form
(y-y1)=m(x-x1)
Negative
y-y1=m(x-x1)
x°/360 times (2 pi r) - where x is the degrees in the angle

42. What is the distance formula?
S² - where s = length of a side
Sqr( x2 -x1) + (y2- y1)
Between 0 and 1.
y2-y1/x2-x1

43. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
(n degrees/360) * 2(pi)r
Part of a circle connecting two points 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
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

44. In a parabola - if the first term is negative - the parabola ________.
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.
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.
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.
Opens down

45. Area of Rectangle
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/x^a
Lw
(a-b)(a²+ab+b²)

46. What is the area of a triangle?
Percentage Change = Difference/Original * 100
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.
1/2bh
4s

47. The length of one side of any triangle is ____ than the sum of the other two sides.
(0 -0)
A segment connecting the center of a circle to any point on the circle
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Less

48. Area of Circle
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.
b±[vb²-4ac]/2a
Sum of the lengths of the sides
Pi*r^2

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

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50. Volume of Cone
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.
Less
1/3pir^2*h
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.