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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. a³-b³
1/x^a
4s (where s = length of a side)
(n-2)180
(a-b)(a²+ab+b²)

2. When you reverse FOIL - the term that needs to add out is the _____
1
2(lw+wh+lh)
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

3. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(a+b)(a-b)
1/1
Probability A + Probability B

4. What is the equation of a line?

5. What is the area of a triangle?
x² -2xy + y²
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
Lw

6. (a+b)(a-b)=
(n degrees/360) * (pi)r^2
(0 -0)
(x+y)(x-y)
A²-b²

7. In a coordinate system - what is the origin?
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'.
(0 -0)
(x+y)(x-y)
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.

8. What is the volume of a cylinder?
A segment connecting the center of a circle to any point on the circle
Less
1
(pi)r^2(h)

9. What is the probability?
(a+b)(a-b)
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.
Number of desired outcomes/number of total outcomes
Bh

10. What is inversely proportional?
x°/360 times (2 pi r) - where x is the degrees in the angle
x°/360 times (?r²) - where x is the degrees in the angle
y2-y1/x2-x1
y = k/x

11. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
1. Given event A: A + notA = 1.
Lwh
(pi)r^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

12. How do you multiply and divide square roots?
Sqr( x2 -x1) + (y2- y1)
4pir^2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2x2x2x5x5

13. Circle
b±[vb²-4ac]/2a
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The set of points which are all the same distance (the radius) from a certain point (the center).
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.

14. How do you calculate the surface area of a rectangular box?
Pi*r^2
(pi)r^2(h)
A median is the middle value of a set of numbers. For an odd number of values - it'S simply the middle number. For an even number of values - take the average of the center two values.
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.

15. 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)
4/3pir^3
T1 * r^(n-1)

16. What are the side ratios for a 30:60:90 triangle?
x²-y²
?r²
T1 * r^(n-1)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

17. Area of Circles
2 pi r
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
A=?r2
Probability A + Probability B

18. a²-2ab+b²
2(pi)r(r+h)
(x+y)(x-y)
(a-b)²
(a+b)²

19. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
Arrangements - orders - schedules - or lists.
1/1
½(base x height) [or (base x height)÷2]

20. Area of Circle
Between 0 and 1.
(a-b)(a+b)
2Length + 2width [or (length + width) x 2]
Pi*r^2

21. Area of Rectangle
1/3pir^2*h
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
N x M
Lw

22. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
Lw
N x M
Less
(x+y)²

23. How do you find the nth term of an arithmetic sequence?
(y-y1)=m(x-x1)
The set of points which are all the same distance (the radius) from a certain point (the center).
T1 + (n-1)d
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.

24. a² - b² is equal to
A=?r2
(a+b)(a-b)
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.
(a+b)²

25. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
(x+y)(x-y)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

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

27. What is the area of a solid rectangle?
1/3Bh
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
2(lw+wh+lh)

28. Perimeter (circumference) of a circle
Order does matter for a permutation - but does not matter for a combination.
2 pi r
The four big angles are equal and the four small angles are equal
The set of points which are all the same distance (the radius) from a certain point (the center).

29. Circumference of a circle
1/3pir^2*h
?d OR 2?r
(a+b)(a²-ab+b²)
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.

30. Rough est. of v2 =
1.4
(n-2)180
Ac+ad+bc+bd
Part of a circle connecting two points on the circle.

31. In intersecting lines - opposite angles are _____.
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.
Equal
1
(y2-y1)/(x2-x1)

32. Rough est. of v3 =
(y-y1)=m(x-x1)
4s
Bh
1.7

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

34. Surface Area of rectangular prism
(0 -0)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2x2x2x5x5
2lw+2lh+2wh

35. What is a 'Right isosceles' triangle?
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.
b±[vb²-4ac]/2a
4s
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

36. What is the average?
Sum of terms/number of terms
Groups - teams - or committees.
C =?d
(a-b)²

37. Chord
x² + 2xy + y²
2l+2w
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.
The distance from one point on the circle to another point on the circle.

38. What is the area of a sector?
Order does matter for a permutation - but does not matter for a combination.
2(pi)r(r+h)
A=bh
(n degrees/360) * (pi)r^2

39. Define the mode of a set of numbers.
x°/360 times (?r²) - where x is the degrees in the angle
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.
S*v2
1. Given event A: A + notA = 1.

40. (a+b)(c+d)
Ac+ad+bc+bd
Lwh
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.
y2-y1/x2-x1

41. What is the prime factorization of 200?
(y-y1)=m(x-x1)
2x2x2x5x5
2l+2w
N x M

42. Area of Square
N x M
S^2
A segment connecting the center of a circle to any point on the circle
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'.

43. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
1/2bh
1.4
A²-b²
Probability A + Probability B

44. Define a factorial of a number - and how it is written.
Groups - teams - or committees.
Sum of terms/number of terms
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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

45. Rough est. of v1 =
1
2(pi)r(r+h)
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.
2pi*r

46. Area of Parallelogram
1
1/2bh
Pi*r^2
Bh

47. What is the factored version of x² -2xy + y² ?
(y2-y1)/(x2-x1)
Number of desired outcomes/number of total outcomes
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
(x-y)²

48. How do you find the sum of a geometric sequence?
Last term
T1 * r^(n-1)/(r-1)
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°/360 times (?r²) - where x is the degrees in the angle

49. 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.
Groups - teams - or committees.
x°/360 times (2 pi r) - where x is the degrees in the angle
(a+b)(a²-ab+b²)

50. In a coordinate system - identify the quadrants and describe their location.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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
S² - where s = length of a side