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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. Area of Rectangle
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(n degrees/360) * 2(pi)r
Lw
S² - where s = length of a side

2. How do you find the nth term of a geometric sequence?
1/2bh
2pi*r
T1 * r^(n-1)
1. Given event A: A + notA = 1.

3. How do you calculate the probability of two events in a row? (Probability of A and B)
T1 + (n-1)d
b±[vb²-4ac]/2a
1/x^a
Probability A * Probability B

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

5. In intersecting lines - opposite angles are _____.
(a-b)²
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.
Equal
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.

6. a² - b² is equal to
(a+b)(a-b)
y = kx
(x+y)(x-y)
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.

7. When a line crosses two parallel lines - ________.
Groups - teams - or committees.
The four big angles are equal and the four small angles are equal
Pi*d
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.

8. Surface Area of Sphere
4pir^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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

9. Define the 'Third side' rule for triangles

10. What is the length of an arc?
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 degrees/360) * 2(pi)r
(a-b)²
Arrangements - orders - schedules - or lists.

11. How do you find the sum of an arithmetic sequence?
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.
The four big angles are equal and the four small angles are equal
y = k/x
(n/2) * (t1+tn)

12. How do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
S² - where s = length of a side
(a+b)(a-b)
2pir^2 + 2pir*h

13. Circumference Formula
(x-y)²
C =?d
Last term
Equal

14. What is the side ratio for a 30:60:90 triangle?
T1 * r^(n-1)/(r-1)
Groups - teams - or committees.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/x^a

15. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

16. perimeter of square
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
S² - where s = length of a side
Number of desired outcomes/number of total outcomes
4s

17. What is the 'Third side' rule for triangles?
A=bh
(a+b)(a-b)
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.
An ange whose vertex is the center of the circle

18. What is the area of a solid rectangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2(lw+wh+lh)
1/3pir^2*h

19. Perimeter of rectangle
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Part of a circle connecting two points on the circle.
1/2bh
2l+2w

20. What is the distance formula?
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.
Sqr( x2 -x1) + (y2- y1)
(a-b)(a²+ab+b²)
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.

21. What is the volume of a solid rectangle?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Lwh
A+b

22. What is the unfactored version of x²-y² ?
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Pi*d
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)

23. What is the unfactored version of (x+y)² ?
2l+2w
(a-b)(a²+ab+b²)
N x M
x² + 2xy + y²

24. How do you multiply powers with the same base?
Sum of the lengths of the sides
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
4s (where s = length of a side)

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

26. What is the volume of a cylinder?
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
?d OR 2?r
(pi)r^2(h)
A²-b²

27. What is the area of a sector?
1.7
(n degrees/360) * (pi)r^2
Sqr( x2 -x1) + (y2- y1)
(x-y)²

28. Perimeter of polygon
Sum of the lengths of the sides
Number of desired outcomes/number of total outcomes
1/x^a
Negative

29. What is the formula for the diagonal of any square?
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.
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.
S*v2

30. What is the area of a triangle?
(x+y)²
1/2bh
Groups - teams - or committees.
Opens up

31. Circumference of cirlce using diameter
C =?d
Pi*d
2pi*r
The set of points which are all the same distance (the radius) from a certain point (the center).

32. If x² = 144 - does v144 = x?
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
A=?r2
(x1+x2)/2 - (y1+y2)/2

33. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
1/3pir^2*h
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
2Length + 2width [or (length + width) x 2]

34. a²-2ab+b²
(x1+x2)/2 - (y1+y2)/2
Less
(a-b)²
Lw

35. Sector
Pir^2h
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
(pi)r^2

36. Volume of sphere
4/3pir^3
2pi*r
Not necessarily. This is a trick question - because x could be either positive or negative.
2(pi)r

37. What do combination problems usually ask for?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Groups - teams - or committees.
Total distance/total time
4pir^2

38. Perimeter of a square
4s (where s = length of a side)
1
x²-y²
Probability A + Probability B

39. Rough est. of v2 =
y-y1=m(x-x1)
1.4
The average - mean - median - or mode.
½(base x height) [or (base x height)÷2]

40. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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(h)
The total # of possible outcomes.

41. What is the unfactored version of (x-y)² ?
A=?r2
x² -2xy + y²
1
2(pi)r(r+h)

42. Quadratic Formula
Opens down
b±[vb²-4ac]/2a
Bh
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

43. (a+b)(a-b)=
Middle term
A²-b²
x²-y²
Last term

44. Area of Parallelogram
x² -2xy + y²
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
b±[vb²-4ac]/2a
Bh

45. Perimeter (circumference) of a circle
2 pi r
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.
S² - where s = length of a side
(x+y)(x-y)

46. Slope
(y2-y1)/(x2-x1)
y2-y1/x2-x1
Between 0 and 1.
(n-2)180

47. Define 'proportionate' values
(y2-y1)/(x2-x1)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(0 -0)

48. How do you find the slope?
y2-y1/x2-x1
1/2 h (b1 + b2)
The four big angles are equal and the four small angles are equal
(x1+x2)/2 - (y1+y2)/2

49. What is the prime factorization of 200?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2x2x2x5x5
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.

50. Point-Slope form
y-y1=m(x-x1)
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]
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.