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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. a² - b² is equal to
x² -2xy + y²
(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
Between 0 and 1.

2. Central Angle
Lwh
Opens down
An ange whose vertex is the center of the circle
Bh

3. Volume of Cone
Pi*r^2
(pi)r^2(h)
y = k/x
1/3pir^2*h

4. Volume of prism
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.
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.
Bh
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.

5. How do you find the nth term of an arithmetic sequence?
Sum of terms/number of terms
Groups - teams - or committees.
T1 + (n-1)d
2pi*r

6. Circumference of cirlce using diameter
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
Pi*d
y = kx
2(lw+wh+lh)

7. What is the 'distributive law'?
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Bh
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.

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

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9. What is the circumference of a circle?
(a-b)(a²+ab+b²)
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.
2(pi)r
½(b1 +b2) x h [or (b1 +b2) x h÷2]

10. Perimeter of a square
2(pi)r(r+h)
T1 * r^(n-1)/(r-1)
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.
4s (where s = length of a side)

11. How do you solve a permutation?
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 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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
S^2

12. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Pi*r^2
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
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).

13. 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.
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.
x² + 2xy + y²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

14. (a+b)(c+d)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Ac+ad+bc+bd
(pi)r^2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

15. a²+2ab+b²
Opens up
(a+b)²
The average - mean - median - or mode.
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.

16. How do you find the nth term of a geometric sequence?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Equal
T1 * r^(n-1)
(a+b)(a-b)

17. What is inversely proportional?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
y = k/x
1.4
(a+b)(a-b)

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

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19. Area of a triangle
S² - where s = length of a side
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
(n degrees/360) * 2(pi)r
½(base x height) [or (base x height)÷2]

20. Define a factorial of a number - and how it is written.
?r²
1. Given event A: A + notA = 1.
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.
2Length + 2width [or (length + width) x 2]

21. The probability of an event happening and the probability of an event NOT happening must add up to what number?
2pir^2 + 2pir*h
2Length + 2width [or (length + width) x 2]
1. Given event A: A + notA = 1.
1

22. x^a * x^b = x^__
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.
A+b
1/2 h (b1 + b2)
Middle term

23. Lines reflected over the x or y axis have ____ slopes.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(a-b)²
Negative
½(b1 +b2) x h [or (b1 +b2) x h÷2]

24. Perimeter of rectangle
A segment connecting the center of a circle to any point on the circle
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
A=?r2

25. Volume of Cylinder
(n/2) * (t1+tn)
Pir^2h
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
(x1+x2)/2 - (y1+y2)/2

26. Area of Triangle
1/2bh
(n-2)180
4pir^2
The distance from one point on the circle to another point on the circle.

27. What is the surface area of a cylinder?
2(pi)r(r+h)
Middle term
S² - where s = length of a side
T1 + (n-1)d

28. What is the average speed?
A segment connecting the center of a circle to any point on the circle
Total distance/total time
(x1+x2)/2 - (y1+y2)/2
1

29. What is the length of an arc?
(n degrees/360) * 2(pi)r
An ange whose vertex is the center of the 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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

30. Point-Slope form
y-y1=m(x-x1)
N x M
Bh
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.

31. What is the prime factorization of 200?
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.
2x2x2x5x5
An ange whose vertex is the center of the circle
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

32. Area of Square
Negative
Total distance/total time
(x+y)²
S^2

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

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34. What is the side ratio for a 30:60:90 triangle?
4/3pir^3
Arrangements - orders - schedules - or lists.
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.

35. What is the side ratio for a Right Isosceles triangle?
A+b
2(pi)r(r+h)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1/2 h (b1 + b2)

36. What'S the most important thing to remember about charts you'll see on the GRE?
The distance from one point on the circle to another point on the circle.
N x M
Sum of the lengths of the sides
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.

37. What do combination problems usually ask for?
Middle term
Groups - teams - or committees.
1
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.

38. Circumference of a circle
(y2-y1)/(x2-x1)
?d OR 2?r
y = k/x
Middle term

39. What is the formula for the diagonal of any square?
S*v2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
A²-b²
(a-b)²

40. When a line crosses two parallel lines - ________.
The four big angles are equal and the four small angles are equal
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)(a²-ab+b²)
2Length + 2width [or (length + width) x 2]

41. Define 'proportionate' values
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.
(n-2)180
b±[vb²-4ac]/2a
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

42. Area of a square
y = k/x
S² - where s = length of a side
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
½(base x height) [or (base x height)÷2]

43. How do you find the midpoint?
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.
(x1+x2)/2 - (y1+y2)/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.
4/3pir^3

44. What are the side ratios for a 30:60:90 triangle?
½(b1 +b2) x h [or (b1 +b2) x h÷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.
1/2bh

45. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
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.
Middle term
N x M
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

46. How do you find the sum of a geometric sequence?
The total # of possible outcomes.
T1 * r^(n-1)/(r-1)
2(pi)r(r+h)
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.

47. a²-b²
(a-b)(a+b)
(n degrees/360) * (pi)r^2
(a-b)(a²+ab+b²)
Sqr( x2 -x1) + (y2- y1)

48. Rough est. of v2 =
1.4
x°/360 times (2 pi r) - where x is the degrees in the angle
(pi)r^2
2pir^2 + 2pir*h

49. Area of Trapezoid
Number of desired outcomes/number of total outcomes
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.
A+b
1/2 h (b1 + b2)

50. Area of Parallelogram
Bh
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.
Pi*r^2
N x M