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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. length of a sector
Last term
A=?r2
(a+b)(a²-ab+b²)
x°/360 times (2 pi r) - where x is the degrees in the angle

2. When a line crosses two parallel lines - ________.
The four big angles are equal and the four small angles are equal
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
x°/360 times (2 pi r) - where x is the degrees in the angle
Between 0 and 1.

3. How do you calculate a diagonal inside a 3-dimensional rectangular box?
(a-b)(a²+ab+b²)
?r²
x²-y²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

4. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Number of desired outcomes/number of total outcomes
(x+y)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.

5. What are the side ratios 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.
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.
4s
Probability A * Probability B

6. Quadratic Formula
1
1/2bh
2(pi)r(r+h)
b±[vb²-4ac]/2a

7. For a bell curve - what three terms might be used to describe the number in the middle?
2(pi)r(r+h)
4/3pir^3
The average - mean - median - or mode.
(x1+x2)/2 - (y1+y2)/2

8. When you reverse FOIL - the term that needs to multiply out is the _____
2x2x2x5x5
2(pi)r
Last term
x°/360 times (?r²) - where x is the degrees in the angle

9. If something is possible but not certain - what is the numeric range of probability of it happening?
Sum of terms/number of terms
(a+b)(a-b)
1/x^a
Between 0 and 1.

10. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
N x M
Sqr( x2 -x1) + (y2- y1)
(n degrees/360) * (pi)r^2

11. How do you multiply powers with the same base?
Opens up
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
b±[vb²-4ac]/2a
(0 -0)

12. Slope
(y2-y1)/(x2-x1)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Pir^2h
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.

13. What is the distance formula?
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
Sum of terms/number of terms
Sqr( x2 -x1) + (y2- y1)

14. Sector
(a-b)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.
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.
The distance from one point on the circle to another point on the circle.

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

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16. How do you find the nth term of a geometric sequence?
Pi*d
T1 * r^(n-1)
The four big angles are equal and the four small angles are equal
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

17. What is a '30:60:90' triangle?
Ac+ad+bc+bd
(y2-y1)/(x2-x1)
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. Given event A: A + notA = 1.

18. In intersecting lines - opposite angles are _____.
(x+y)²
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.
Equal
The average - mean - median - or mode.

19. What is an 'equilateral' triangle?
The distance across the circle through the center of the circle.The diameter is twice the radius.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The distance from one point on the circle to another point on the circle.
Sum of the lengths of the sides

20. In a coordinate system - identify the quadrants and describe their location.
Pir^2h
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2pi*r
2(pi)r(r+h)

21. What is 'absolute value' - and how is it represented?

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22. Explain the difference between a digit and a number.

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23. What is the sum of the inside angles of an n-sided polygon?
The set of points which are all the same distance (the radius) from a certain point (the center).
(n-2)180
Opens down
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.

24. In a coordinate system - what is the origin?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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
(0 -0)
Negative

25. What number goes on the bottom of a probability fraction?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The total # of possible outcomes.
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
2 pi r

26. Area of a triangle
The set of points which are all the same distance (the radius) from a certain point (the center).
A=bh
A segment connecting the center of a circle to any point on the circle
½(base x height) [or (base x height)÷2]

27. 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.
(x+y)(x-y)
y = k/x
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

28. Circumference of a circle using radius
2pi*r
Opens up
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.
Middle term

29. What is the area of a cylinder?
4s
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.
2(pi)r(r+h)
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.

30. a³-b³
S*v2
(a-b)(a²+ab+b²)
4s (where s = length of a side)
T1 * r^(n-1)

31. What is the equation of a line?

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32. Surface Area of Cylinder
Probability A * Probability B
1.4
(y-y1)=m(x-x1)
2pir^2 + 2pir*h

33. How do you find the sum of a geometric sequence?
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.
T1 * r^(n-1)/(r-1)
(a+b)(a-b)
2Length + 2width [or (length + width) x 2]

34. Define a factorial of a number - and how it is written.
Probability A + Probability B
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.
(x1+x2)/2 - (y1+y2)/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.

35. Area of Circle
T1 * r^(n-1)
The average - mean - median - or mode.
Pi*r^2
1.7

36. Area of Triangle
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.
1/2bh
1/3Bh

37. The length of one side of any triangle is ____ than the sum of the other two sides.
(pi)r^2(h)
Pir^2h
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Less

38. Surface Area of rectangular prism
(n/2) * (t1+tn)
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2lw+2lh+2wh

39. Area of rectangle - square - parallelogram
(a-b)(a+b)
1.7
A=bh
y2-y1/x2-x1

40. What is the probability?
x² -2xy + y²
2 pi r
1.7
Number of desired outcomes/number of total outcomes

41. Circumference Formula
y2-y1/x2-x1
(n-2)180
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.
C =?d

42. Volume of pyramid
1/3Bh
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/x^a
(0 -0)

43. Surface Area of Sphere
(n/2) * (t1+tn)
N x M
4pir^2
1/2bh

44. (a+b)(c+d)
Probability A * Probability B
2lw+2lh+2wh
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.
Ac+ad+bc+bd

45. What is the factored version of x² + 2xy + y² ?
(x+y)²
Bh
Probability A + Probability B
Percentage Change = Difference/Original * 100

46. 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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Sum of terms/number of terms
(y2-y1)/(x2-x1)

47. Volume of sphere
4/3pir^3
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.
(n/2) * (t1+tn)
Less

48. Perimeter of rectangle
Probability A * Probability B
2(pi)r(r+h)
2(pi)r(r+h)
2l+2w

49. (a+b)(a-b)=
y2-y1/x2-x1
A²-b²
(a-b)²
Sum of the lengths of the sides

50. Explain the special properties of zero.
Lwh
Number of desired outcomes/number of total outcomes
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.
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.