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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. What is the volume of a solid rectangle?
(x1+x2)/2 - (y1+y2)/2
An ange whose vertex is the center of the circle
Lwh
1.4

2. List two odd behaviors of exponents
4pir^2
(pi)r^2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.

3. Circumference of a circle using radius
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(n degrees/360) * (pi)r^2
N x M
2pi*r

4. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
4s (where s = length of a side)
1/2bh

5. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
(a+b)²
2lw+2lh+2wh
Probability A * Probability B

6. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
?d OR 2?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
(n/2) * (t1+tn)
Sqr( x2 -x1) + (y2- y1)

7. What is the unfactored version of (x-y)² ?
x² -2xy + y²
y = kx
1/1
x°/360 times (?r²) - where x is the degrees in the angle

8. How do you calculate a diagonal inside a 3-dimensional rectangular box?
(n/2) * (t1+tn)
N x M
(pi)r^2(h)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

9. a³+b³
(a+b)(a²-ab+b²)
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.
(a-b)(a²+ab+b²)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

10. In intersecting lines - opposite angles are _____.
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
Number of desired outcomes/number of total outcomes
S² - where s = length of a side
Equal

11. What is the area of a cylinder?
1/x^a
(a-b)(a+b)
2(pi)r(r+h)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

12. What is the point-slope form?
(y-y1)=m(x-x1)
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.
?r²
C =?d

13. When a line crosses two parallel lines - ________.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x² -2xy + y²
Number of desired outcomes/number of total outcomes
The four big angles are equal and the four small angles are equal

14. Area of a sector
1/2bh
A+b
x°/360 times (?r²) - where x is the degrees in the angle
Bh

15. Area of Circle
4s
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.
Part of a circle connecting two points on the circle.
Pi*r^2

16. Perimeter of a square
4s (where s = length of a side)
Last term
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.

17. What is a 'Right isosceles' triangle?
x°/360 times (?r²) - where x is the degrees in the angle
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.
2(lw+wh+lh)
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.

18. How do you multiply powers with the same base?
S² - where s = length of a side
Sqr( x2 -x1) + (y2- y1)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

19. 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
2(pi)r(r+h)
(a-b)²
Opens down

20. What is the length of an arc?
2 pi r
(n degrees/360) * 2(pi)r
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 - and greater than the difference between the other two sides.

21. Arc
?d OR 2?r
Total distance/total time
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.
Part of a circle connecting two points on the circle.

22. Volume of pyramid
Total distance/total time
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.
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.
1/3Bh

23. What do combination problems usually ask for?
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.
1. Given event A: A + notA = 1.
N x M
Groups - teams - or committees.

24. What'S the most important thing to remember about charts you'll see on the GRE?
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.
T1 + (n-1)d
1/3pir^2*h
T1 * r^(n-1)/(r-1)

25. Volume of sphere
1/1
?r²
A=bh
4/3pir^3

26. What is the volume of a cylinder?
Number of desired outcomes/number of total outcomes
(pi)r^2(h)
Pi*d
1/2bh

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

28. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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. 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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.

29. When you reverse FOIL - the term that needs to add out is the _____
(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.
Middle term
Last term

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

31. Does order matter for a permutation? How about for a combination?
Sum of the lengths of the sides
4/3pir^3
x°/360 times (2 pi r) - where x is the degrees in the angle
Order does matter for a permutation - but does not matter for a combination.

32. Area of a triangle
(a+b)(a²-ab+b²)
½(base x height) [or (base x height)÷2]
x² -2xy + y²
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.

33. Area of Trapezoid
1/2 h (b1 + b2)
T1 * r^(n-1)/(r-1)
A=bh
T1 + (n-1)d

34. What is the area of a triangle?
2x2x2x5x5
2lw+2lh+2wh
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.
1/2bh

35. What is the unfactored version of (x+y)² ?
(x-y)²
A=bh
x² + 2xy + y²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

36. What is the factored version of x² -2xy + y² ?
(x-y)²
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.
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.
Pi*d

37. Surface Area of rectangular prism
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.
2lw+2lh+2wh
y = kx
Sum of the lengths of the sides

38. Chord
The distance from one point on the circle to another point on the circle.
N x M
(0 -0)
(pi)r^2(h)

39. What is the average?
S² - where s = length of a side
2lw+2lh+2wh
(x+y)²
Sum of terms/number of terms

40. What is the circumference of a circle?
Equal
Pir^2h
2(pi)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.

41. What number goes on the bottom of a probability fraction?
x°/360 times (2 pi r) - where x is the degrees in the angle
The total # of possible outcomes.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2(pi)r

42. Define the range of a set of numbers.
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.
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.
2pir^2 + 2pir*h
(0 -0)

43. What is the equation of a line?

44. What is the area of a solid rectangle?
2(lw+wh+lh)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(a-b)²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

45. How do you calculate the percentage of change?
Between 0 and 1.
Percentage Change = Difference/Original * 100
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

46. What is the probability?
2l+2w
Number of desired outcomes/number of total outcomes
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.
A²-b²

47. What is the 'Third side' rule for triangles?
(x1+x2)/2 - (y1+y2)/2
T1 * r^(n-1)
Percentage Change = Difference/Original * 100
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.

48. Circle
(0 -0)
Order does matter for a permutation - but does not matter for a combination.
The total # of possible outcomes.
The set of points which are all the same distance (the radius) from a certain point (the center).

49. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
Sqr( x2 -x1) + (y2- y1)
2(pi)r(r+h)
Ac+ad+bc+bd

50. What is the side ratio for a 30:60:90 triangle?
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
2pi*r
Not necessarily. This is a trick question - because x could be either positive or negative.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.