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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 find the midpoint?
2Length + 2width [or (length + width) x 2]
(x1+x2)/2 - (y1+y2)/2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Sum of the lengths of the sides

2. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
(pi)r^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.
2(pi)r(r+h)

3. Sector
x² -2xy + y²
2pir^2 + 2pir*h
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.
Between 0 and 1.

4. What is the sum of the inside angles of an n-sided polygon?
A²-b²
(n-2)180
N x M
(a-b)(a²+ab+b²)

5. Area of Triangle
1/2bh
(a+b)²
1/2 h (b1 + b2)
(0 -0)

6. How do you solve a permutation?
A segment connecting the center of a circle to any point on the circle
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
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

7. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

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8. Area of a square
The distance across the circle through the center of the circle.The diameter is twice the radius.
(y-y1)=m(x-x1)
4s
S² - where s = length of a side

9. Circumference of a circle
2pir^2 + 2pir*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.
?d OR 2?r
Opens down

10. How do you multiply and divide square roots?
Arrangements - orders - schedules - or lists.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

11. Lines reflected over the x or y axis have ____ slopes.
Negative
Pi*d
Part of a circle connecting two points on the circle.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

12. Area of Circle
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.
Part of a circle connecting two points on the circle.
Opens down
Pi*r^2

13. (a+b)(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
A²-b²
Between 0 and 1.
b±[vb²-4ac]/2a

14. What is the area of a cylinder?
A segment connecting the center of a circle to any point on the circle
x² -2xy + y²
2(pi)r(r+h)
The total # of possible outcomes.

15. What is the equation of a line?

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16. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
?r²
Groups - teams - or committees.
A+b

17. Circumference of cirlce using diameter
Pi*d
1
½(base x height) [or (base x height)÷2]
1/1

18. Arc
Bh
1/3Bh
Less
Part of a circle connecting two points on the circle.

19. What'S the most important thing to remember about charts you'll see on the GRE?
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.
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.
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.
The set of points which are all the same distance (the radius) from a certain point (the center).

20. Area of Circles
y = k/x
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/2bh
A=?r2

21. What is the factored version of x² + 2xy + y² ?
(x+y)²
(x+y)(x-y)
(y-y1)=m(x-x1)
Probability A + Probability B

22. Area of a circle
?r²
(n degrees/360) * (pi)r^2
2x2x2x5x5
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

23. Area of Trapezoid
2(pi)r
(x+y)²
1/2 h (b1 + b2)
b±[vb²-4ac]/2a

24. 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.
2l+2w
A²-b²
Lwh

25. Define the mode of a set of numbers.
(a-b)(a+b)
T1 * r^(n-1)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.

26. a³+b³
(a+b)(a²-ab+b²)
2lw+2lh+2wh
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.
Probability A * Probability B

27. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
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.
S*v2
(x-y)²

28. What is the probability?
(x+y)(x-y)
4pir^2
(n/2) * (t1+tn)
Number of desired outcomes/number of total outcomes

29. a² - b² is equal to
1/1
(a+b)(a-b)
A=bh
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

30. What is the side ratio for a 30:60:90 triangle?
Bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/3Bh
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.

31. x^-a =
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Between 0 and 1.
1/x^a
(a-b)(a²+ab+b²)

32. What is the unfactored version of (x-y)² ?
x² -2xy + y²
Equal
Pi*d
Between 0 and 1.

33. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
4s (where s = length of a side)
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.
1/2bh
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.

34. Surface Area of rectangular prism
2pi*r
y = kx
2Length + 2width [or (length + width) x 2]
2lw+2lh+2wh

35. Radius (Radii)
1/3pir^2*h
1/x^a
A segment connecting the center of a circle to any point on the circle
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.

36. What is the unfactored version of x²-y² ?
(x+y)(x-y)
1/2 h (b1 + b2)
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'.
S² - where s = length of a side

37. a²-2ab+b²
(a+b)(a-b)
Middle term
(a-b)²
x²-y²

38. What is the area of a 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.
Less
2(lw+wh+lh)
(pi)r^2

39. How do you calculate the probability of two events in a row? (Probability of A and B)
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.
A segment connecting the center of a circle to any point on the circle
Lwh
Probability A * Probability B

40. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
1/x^a
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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

41. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
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.
2l+2w

42. Perimeter of rectangle
A segment connecting the center of a circle to any point on the circle
Ac+ad+bc+bd
2l+2w
4pir^2

43. When you reverse FOIL - the term that needs to add out is the _____
Number of desired outcomes/number of total outcomes
Middle term
2pi*r
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

44. What is the point-slope form?
y = k/x
(y-y1)=m(x-x1)
4pir^2
Negative

45. Define the 'Third side' rule for triangles

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46. How do you calculate the percentage of change?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(x1+x2)/2 - (y1+y2)/2
y = k/x
Percentage Change = Difference/Original * 100

47. In intersecting lines - opposite angles are _____.
2 pi r
Equal
Opens down
(pi)r^2(h)

48. Perimeter of polygon
1/2bh
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Sum of the lengths of the sides
Lw

49. What is the area of a sector?
(n degrees/360) * (pi)r^2
The total # of possible outcomes.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2 pi r

50. Area of rectangle - square - parallelogram
1/1
(a+b)(a-b)
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.
A=bh