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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. If x² = 144 - does v144 = x?
S² - where s = length of a side
(x+y)(x-y)
Not necessarily. This is a trick question - because x could be either positive or negative.
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.

2. What is the probability?
1/1
Number of desired outcomes/number of total outcomes
Order does matter for a permutation - but does not matter for a combination.
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.

3. a²-b²
(a-b)(a+b)
Last term
1/x^a
Percentage Change = Difference/Original * 100

4. What is the side ratio for a Right Isosceles triangle?
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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

5. What is the point-slope form?
An ange whose vertex is the center of the circle
Sum of terms/number of terms
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.
(y-y1)=m(x-x1)

6. How do you find the nth term of a geometric sequence?
Middle term
?d OR 2?r
Probability A * Probability B
T1 * r^(n-1)

7. What is the volume of a solid rectangle?
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+b
The distance from one point on the circle to another point on the circle.
Lwh

8. When a line crosses two parallel lines - ________.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
4s (where s = length of a side)
The four big angles are equal and the four small angles are equal
1.7

9. Area of Parallelogram
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.
4/3pir^3
Bh
b±[vb²-4ac]/2a

10. Area of Triangle
1/2bh
(a-b)(a+b)
The four big angles are equal and the four small angles are equal
Lw

11. Define a factorial of a number - and how it is written.
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.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Negative

12. What is the area of a sector?
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.
(n degrees/360) * (pi)r^2
(0 -0)
2(lw+wh+lh)

13. How do you find the slope?
(x+y)(x-y)
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
y2-y1/x2-x1

14. What is the 'distributive law'?
x² + 2xy + y²
Opens down
2pi*r
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.

15. How do you find the sum of a geometric sequence?
Groups - teams - or committees.
T1 * r^(n-1)/(r-1)
1.7
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.

16. Area of Circle
Pi*d
(pi)r^2
2Length + 2width [or (length + width) x 2]
Pi*r^2

17. How do you calculate the probability of two events in a row? (Probability of A and B)
(y2-y1)/(x2-x1)
Probability A * Probability B
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
1/3pir^2*h

18. What is the factored version of x² -2xy + y² ?
The four big angles are equal and the four small angles are equal
Order does matter for a permutation - but does not matter for a combination.
2(pi)r
(x-y)²

19. Rough est. of v1 =
4s
(a-b)(a²+ab+b²)
1
Sum of the lengths of the sides

20. Volume of prism
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The four big angles are equal and the four small angles are equal
The distance across the circle through the center of the circle.The diameter is twice the radius.
Bh

21. Area of Circles
A=?r2
(x1+x2)/2 - (y1+y2)/2
1.4
2l+2w

22. What do permutation problems often ask for?
2l+2w
Arrangements - orders - schedules - or lists.
(a+b)(a-b)
1/1

23. Circumference Formula
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.
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.
C =?d
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. Chord
1/1
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.
A+b
The distance from one point on the circle to another point on the circle.

25. Define 'proportionate' values
1/1
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2 pi r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

26. How do you find the midpoint?
(pi)r^2
Sum of the lengths of the sides
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.
(x1+x2)/2 - (y1+y2)/2

27. Surface Area of Cylinder
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
2pir^2 + 2pir*h

28. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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. Given event A: A + notA = 1.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(pi)r^2

29. What is directly proportional?
(n degrees/360) * (pi)r^2
y = kx
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(n/2) * (t1+tn)

30. What is the side ratio for a 30:60:90 triangle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Less
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2Length + 2width [or (length + width) x 2]

31. What is the formula for the diagonal of any square?
Bh
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
S*v2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

32. What is the equation of a line?

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33. Define the formula for calculating slope.
2(pi)r(r+h)
Opens up
Bh
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

34. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
(a+b)(a-b)
(n/2) * (t1+tn)
(a+b)(a²-ab+b²)

35. Central Angle
Sum of the lengths of the sides
An ange whose vertex is the center of the circle
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]

36. 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.
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.
The set of points which are all the same distance (the radius) from a certain point (the center).
1

37. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
Sqr( x2 -x1) + (y2- y1)
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.
Lwh

38. What is the 'Third side' rule for triangles?
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.
(n degrees/360) * 2(pi)r
Pir^2h
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.

39. Perimeter of polygon
(x+y)²
Sum of the lengths of the sides
x²-y²
(x-y)²

40. How do you find the nth term of an arithmetic sequence?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
?d OR 2?r
T1 + (n-1)d

41. Explain the special properties of zero.
(n degrees/360) * 2(pi)r
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.
A+b
Pi*d

42. Area of Square
y2-y1/x2-x1
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.
Opens up
S^2

43. What is the area of a cylinder?
An ange whose vertex is the center of the circle
Negative
(0 -0)
2(pi)r(r+h)

44. What is the average?
2(pi)r(r+h)
(a+b)(a-b)
Between 0 and 1.
Sum of terms/number of terms

45. Define the range of a set of numbers.
2(pi)r
Pir^2h
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

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

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47. How do you calculate the percentage of change?
x°/360 times (?r²) - where x is the degrees in the angle
x² + 2xy + y²
Pir^2h
Percentage Change = Difference/Original * 100

48. Volume of Cone
Less
1/3pir^2*h
b±[vb²-4ac]/2a
Not necessarily. This is a trick question - because x could be either positive or negative.

49. What is inversely proportional?
A=?r2
The set of points which are all the same distance (the radius) from a certain point (the center).
(x1+x2)/2 - (y1+y2)/2
y = k/x

50. Volume of sphere
4/3pir^3
4pir^2
Pi*d
y = kx