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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 sum of a geometric sequence?
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
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.
T1 * r^(n-1)/(r-1)
(n degrees/360) * (pi)r^2

2. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
N x M
1/3pir^2*h
Pi*r^2
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.

3. Surface Area of Sphere
(x1+x2)/2 - (y1+y2)/2
4pir^2
(y2-y1)/(x2-x1)
Total distance/total time

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

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5. a³+b³
?d OR 2?r
(x+y)²
(a+b)(a²-ab+b²)
Order does matter for a permutation - but does not matter for a combination.

6. What is the prime factorization of 200?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
S² - where s = length of a side
2x2x2x5x5

7. List two odd behaviors of exponents
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(a+b)(a²-ab+b²)
(a+b)(a-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.

8. (a+b)(c+d)
x² + 2xy + y²
Ac+ad+bc+bd
2 pi r
Equal

9. How do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
y2-y1/x2-x1
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

10. Surface Area of rectangular prism
2lw+2lh+2wh
Middle term
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

11. a²-b²
(a-b)(a+b)
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.
(a-b)(a²+ab+b²)
Lwh

12. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
x²-y²
(x-y)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
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.

13. What is the area of a solid rectangle?
Percentage Change = Difference/Original * 100
2(lw+wh+lh)
Between 0 and 1.
Last term

14. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
T1 * r^(n-1)/(r-1)
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 segment connecting the center of a circle to any point on the circle

15. What is the surface area of a cylinder?
2(pi)r(r+h)
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
y = k/x
(0 -0)

16. What is the factored version of x² + 2xy + y² ?
1.4
(x+y)²
Probability A + Probability B
The average - mean - median - or mode.

17. What is the area of a sector?
(n degrees/360) * (pi)r^2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
An ange whose vertex is the center of the circle

18. The length of one side of any triangle is ____ than the sum of the other two sides.
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.
2l+2w
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Less

19. Rough est. of v1 =
1
S^2
2pir^2 + 2pir*h
Sum of terms/number of terms

20. Define the formula for calculating slope.
2(pi)r
2pi*r
Sum of terms/number of terms
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

21. Area of Trapezoid
y = kx
1/2 h (b1 + b2)
2pi*r
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.

22. Area of Square
S^2
x² + 2xy + y²
An ange whose vertex is the center of the circle
1

23. What is the circumference of a circle?
2(pi)r
y2-y1/x2-x1
(n degrees/360) * 2(pi)r
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

24. Area of rectangle - square - parallelogram
Bh
(n/2) * (t1+tn)
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
A=bh

25. What is the side ratio for a 30:60:90 triangle?
(x+y)²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
x² -2xy + y²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

26. Define the mode of a set of numbers.
A+b
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.
A²-b²
(a-b)(a+b)

27. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Percentage Change = Difference/Original * 100
x°/360 times (?r²) - where x is the degrees in the angle
The distance across the circle through the center of the circle.The diameter is twice the radius.

28. Define a factorial of a number - and how it is written.
4pir^2
(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.
Last term

29. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the 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.
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.
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

30. In a coordinate system - identify the quadrants and describe their location.
x² -2xy + y²
Between 0 and 1.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.

31. What is the average speed?
b±[vb²-4ac]/2a
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.
Total distance/total time
Pi*r^2

32. Area of Circles
2lw+2lh+2wh
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(a-b)²
A=?r2

33. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
1
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2pir^2 + 2pir*h

34. What is the 'distributive law'?
Opens up
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.
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 pi r

35. In intersecting lines - opposite angles are _____.
(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.
Last term
Equal

36. What is the equation of a line?

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37. How do you calculate the percentage of change?
2lw+2lh+2wh
Percentage Change = Difference/Original * 100
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
S*v2

38. How do you calculate the probability of two events in a row? (Probability of A and B)
2(pi)r(r+h)
(a+b)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.
Probability A * Probability B

39. In a parabola - if the first term is negative - the parabola ________.
?r²
Between 0 and 1.
Opens down
S² - where s = length of a side

40. What is the probability?
1/1
Pi*r^2
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.
Number of desired outcomes/number of total outcomes

41. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

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42. What is the side ratio for a Right Isosceles triangle?
?r²
Number of desired outcomes/number of total outcomes
A=bh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

43. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
(a+b)(a²-ab+b²)
Pir^2h
Sum of the lengths of the sides

44. x^a * x^b = x^__
A+b
2Length + 2width [or (length + width) x 2]
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(n degrees/360) * 2(pi)r

45. What is the 'Third side' rule for triangles?
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
(n-2)180
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.
Number of desired outcomes/number of total outcomes

46. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Middle term

47. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
(pi)r^2(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.
Less
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.

48. What is the unfactored version of (x-y)² ?
x² -2xy + y²
(x1+x2)/2 - (y1+y2)/2
The distance across the circle through the center of the circle.The diameter is twice the radius.
?d OR 2?r

49. When you reverse FOIL - the term that needs to add out is the _____
S*v2
Middle term
T1 + (n-1)d
Pi*d

50. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
Arrangements - orders - schedules - or lists.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.