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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. How do you calculate the surface area of a rectangular box?
(a-b)(a+b)
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.
(n/2) * (t1+tn)
b±[vb²-4ac]/2a

2. What is the volume of a cylinder?
Ac+ad+bc+bd
(pi)r^2(h)
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.
A²-b²

3. What is the equation of a line?

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4. 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.
Lwh
y2-y1/x2-x1
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.

5. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
Groups - teams - or committees.
A+b
x² -2xy + y²

6. Quadratic Formula
(a-b)²
b±[vb²-4ac]/2a
The average - mean - median - or mode.
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.

7. x^a * x^b = x^__
A+b
(0 -0)
y = k/x
A²-b²

8. How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
4s (where s = length of a side)
The four big angles are equal and the four small angles are equal
2(lw+wh+lh)

9. What is a 'Right isosceles' triangle?
Lw
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.
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.
The set of points which are all the same distance (the radius) from a certain point (the center).

10. Perimeter of rectangle
Lwh
Arrangements - orders - schedules - or lists.
2l+2w
2(pi)r(r+h)

11. Volume of Cone
Sum of the lengths of the sides
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/3pir^2*h
(n degrees/360) * 2(pi)r

12. Point-Slope form
Percentage Change = Difference/Original * 100
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2(pi)r(r+h)
y-y1=m(x-x1)

13. perimeter of square
4s
(a-b)(a+b)
Order does matter for a permutation - but does not matter for a combination.
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.

14. a²+2ab+b²
Bh
Sum of the lengths of the sides
(a+b)²
1/2bh

15. When a line crosses two parallel lines - ________.
C =?d
The set of points which are all the same distance (the radius) from a certain point (the center).
The four big angles are equal and the four small angles are equal
(a+b)²

16. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
Opens down
Bh
(a-b)(a+b)

17. Area of a sector
1/3Bh
C =?d
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.
x°/360 times (?r²) - where x is the degrees in the angle

18. Define the 'Third side' rule for triangles

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19. a² - b² is equal to
(a+b)(a-b)
Pir^2h
The set of points which are all the same distance (the radius) from a certain point (the center).
4pir^2

20. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
The average - mean - median - or mode.
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]

21. What is the point-slope form?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(y-y1)=m(x-x1)
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'.
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.

22. In a coordinate system - what is the origin?
(0 -0)
(x+y)(x-y)
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.
x² + 2xy + y²

23. Area of Trapezoid
Last term
1/2 h (b1 + 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
4pir^2

24. a³+b³
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a+b)(a²-ab+b²)
(n/2) * (t1+tn)
Number of desired outcomes/number of total outcomes

25. a²-b²
(pi)r^2
(a-b)(a²+ab+b²)
4/3pir^3
(a-b)(a+b)

26. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
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
T1 + (n-1)d
x² + 2xy + y²

27. Volume of sphere
4/3pir^3
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Pir^2h
2x2x2x5x5

28. Circumference of cirlce using diameter
2(pi)r(r+h)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Pi*d
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

29. What is the factored version of x² -2xy + y² ?
An ange whose vertex is the center of the circle
(x-y)²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a+b)(a²-ab+b²)

30. Rough est. of v1 =
2 pi r
1/1
Lwh
1

31. Area of a trapezoid
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
x² + 2xy + y²
4s
½(b1 +b2) x h [or (b1 +b2) x h÷2]

32. What is the distance formula?
Pir^2h
Bh
(n degrees/360) * (pi)r^2
Sqr( x2 -x1) + (y2- y1)

33. Does order matter for a permutation? How about for a combination?
Bh
2 pi r
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.
Order does matter for a permutation - but does not matter for a combination.

34. Circle
2 pi r
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 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.
The set of points which are all the same distance (the radius) from a certain point (the center).

35. Area of a triangle
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.
½(base x height) [or (base x height)÷2]
Order does matter for a permutation - but does not matter for a combination.
1/3pir^2*h

36. Define the mode of a set of numbers.
T1 * r^(n-1)
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.
(x1+x2)/2 - (y1+y2)/2
2 pi r

37. What is the average speed?
4s
Total distance/total time
2(lw+wh+lh)
(x+y)²

38. Surface Area of Sphere
The distance across the circle through the center of the circle.The diameter is twice the radius.
(a+b)(a-b)
4pir^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.

39. (a+b)(a-b)=
y = k/x
A²-b²
Pi*d
(n/2) * (t1+tn)

40. Chord
(n/2) * (t1+tn)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The distance from one point on the circle to another point on the circle.
C =?d

41. How do you find the sum of a geometric sequence?
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)/(r-1)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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

42. What is the surface area of a cylinder?
(a-b)(a+b)
2(pi)r(r+h)
A segment connecting the center of a circle to any point on the circle
Arrangements - orders - schedules - or lists.

43. Perimeter of a rectangle
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2Length + 2width [or (length + width) x 2]
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.

44. Central Angle
2(pi)r
An ange whose vertex is the center of the circle
N x M
The distance from one point on the circle to another point on the circle.

45. What is the unfactored version of (x-y)² ?
x² -2xy + y²
A+b
y2-y1/x2-x1
Sum of terms/number of terms

46. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
Lw
C =?d
Pi*d

47. What is the factored version of x² + 2xy + y² ?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(n-2)180
(x+y)²
The average - mean - median - or mode.

48. Area of rectangle - square - parallelogram
A=bh
(a+b)²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x² + 2xy + y²

49. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
Not necessarily. This is a trick question - because x could be either positive or negative.
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
Pi*r^2

50. a²-2ab+b²
(a-b)²
S^2
(x+y)²
?d OR 2?r