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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. Surface Area of rectangular prism
2lw+2lh+2wh
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.
N x M
2(lw+wh+lh)

2. What is the factored version of 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.
½(base x height) [or (base x height)÷2]
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
(x-y)²

3. In a parabola - if the first term is positive - the parabola ________.
Opens up
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.
S^2
2(pi)r(r+h)

4. What do permutation problems often ask for?
A segment connecting the center of a circle to any point on the circle
x²-y²
Arrangements - orders - schedules - or lists.
(pi)r^2(h)

5. x^a * x^b = x^__
1/2bh
(a-b)(a+b)
b±[vb²-4ac]/2a
A+b

6. What is the area of a solid rectangle?
(x-y)²
2(pi)r
2(lw+wh+lh)
(a+b)(a-b)

7. How do you calculate the surface area of a rectangular box?
(x1+x2)/2 - (y1+y2)/2
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-b)(a²+ab+b²)
Bh

8. The length of one side of any triangle is ____ than the sum of the other two sides.
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.
Less
Bh
(n degrees/360) * 2(pi)r

9. What is the length of an arc?
Opens down
Pi*r^2
(n degrees/360) * 2(pi)r
(0 -0)

10. What do combination problems usually ask for?
Groups - teams - or committees.
Opens down
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.
Middle term

11. Define the range of a set of numbers.
(x-y)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.
(x+y)(x-y)
2Length + 2width [or (length + width) x 2]

12. In a coordinate system - identify the quadrants and describe their location.
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.
1/2bh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Lw

13. length of a sector
Arrangements - orders - schedules - or lists.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
x°/360 times (2 pi r) - where x is the degrees in the angle
x² + 2xy + y²

14. Circumference of a circle using radius
1/2bh
Pi*r^2
4s (where s = length of a side)
2pi*r

15. a²-b²
1/3pir^2*h
Equal
N x M
(a-b)(a+b)

16. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
2pi*r
1/x^a
(a+b)(a²-ab+b²)

17. When a line crosses two parallel lines - ________.
2pi*r
?r²
The four big angles are equal and the four small angles are equal
2l+2w

18. Chord
Arrangements - orders - schedules - or lists.
The distance from one point on the circle to another point on the circle.
S^2
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.

19. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
(a+b)²
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.
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.
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.

20. Circumference of a circle
Groups - teams - or committees.
2(pi)r(r+h)
(n/2) * (t1+tn)
?d OR 2?r

21. What is the volume of a solid rectangle?
y = kx
(0 -0)
Lwh
2(pi)r(r+h)

22. What is inversely proportional?
The distance from one point on the circle to another point on the circle.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
A²-b²
y = k/x

23. Circle
x°/360 times (2 pi r) - where x is the degrees in the angle
Lw
N x M
The set of points which are all the same distance (the radius) from a certain point (the center).

24. What is the 'Third side' rule for triangles?
y-y1=m(x-x1)
2(pi)r
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 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.

25. Perimeter of rectangle
S^2
Percentage Change = Difference/Original * 100
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2l+2w

26. Circumference of cirlce using diameter
Total distance/total time
(a+b)(a-b)
(n/2) * (t1+tn)
Pi*d

27. What is the side ratio for a 30:60:90 triangle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
S*v2
2(pi)r(r+h)
?r²

28. Area of Triangle
(n degrees/360) * 2(pi)r
2pir^2 + 2pir*h
1/2bh
?r²

29. a²+2ab+b²
Last term
(a+b)²
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. 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.

30. a³-b³
Less
(a-b)(a²+ab+b²)
T1 * r^(n-1)/(r-1)
N x M

31. Volume of Cone
1/3pir^2*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
1/2bh
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

32. Does order matter for a permutation? How about for a combination?
Pir^2h
Total distance/total time
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.
Order does matter for a permutation - but does not matter for a combination.

33. Explain the special properties of zero.
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) * (pi)r^2
(a+b)(a²-ab+b²)
x²-y²

34. What is the circumference of a circle?
Sum of the lengths of the sides
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Number of desired outcomes/number of total outcomes
2(pi)r

35. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
N x M
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
An ange whose vertex is the center of the circle

36. Define the 'Third side' rule for triangles

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37. What is the sum of the inside angles of an n-sided polygon?
2(pi)r
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
(n-2)180

38. a² - b² is equal to
Part of a circle connecting two points on the circle.
(a+b)(a-b)
S^2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

39. (a+b)(c+d)
1/1
Groups - teams - or committees.
Ac+ad+bc+bd
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

40. Lines reflected over the x or y axis have ____ slopes.
(a-b)(a+b)
4s
Negative
Total distance/total time

41. Perimeter of a square
Not necessarily. This is a trick question - because x could be either positive or negative.
4s (where s = length of a side)
Total distance/total time
A=?r2

42. Define a factorial of a number - and how it is written.
T1 + (n-1)d
C =?d
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.

43. How do you calculate a diagonal inside a 3-dimensional rectangular box?
C =?d
4/3pir^3
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Bh

44. How do you calculate the percentage of change?
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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(lw+wh+lh)

45. Area of a square
S² - where s = length of a side
1/3Bh
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
4s (where s = length of a side)

46. x^-a =
(a-b)(a²+ab+b²)
1/x^a
1.7
4s (where s = length of a side)

47. How do you find the sum of an arithmetic sequence?
An ange whose vertex is the center of the 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.
(n/2) * (t1+tn)
Arrangements - orders - schedules - or lists.

48. Rough est. of v1 =
The set of points which are all the same distance (the radius) from a certain point (the center).
1
1.4
1/3pir^2*h

49. Define 'proportionate' values
The four big angles are equal and the four small angles are equal
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(x+y)(x-y)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

50. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
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.
Lwh
(x-y)²