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GRE Math 2

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 get rid of the fraction in this equation: 5x + 3/2 = 7x
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
N x M

2. Chord
The distance from one point on the circle to another point on the circle.
The set of points which are all the same distance (the radius) from a certain point (the center).
A=bh
Order does matter for a permutation - but does not matter for a combination.

3. How do you find the nth term of an arithmetic sequence?
Number of desired outcomes/number of total outcomes
Opens up
T1 + (n-1)d
C =?d

4. What is the 'distributive law'?
Groups - teams - or committees.
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.
Opens down
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

5. What is the circumference of a circle?
Order does matter for a permutation - but does not matter for a combination.
T1 * r^(n-1)
2(pi)r
A-b

6. Rough est. of v3 =
1.7
Sqr( x2 -x1) + (y2- y1)
y2-y1/x2-x1
2Length + 2width [or (length + width) x 2]

7. How do you multiply powers with the same base?
Sqr( x2 -x1) + (y2- y1)
(n degrees/360) * 2(pi)r
y-y1=m(x-x1)
Add the exponents - retain the base. for example - x + x5 = x+5 = x7

8. Volume of pyramid
(y-y1)=m(x-x1)
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.
Opens up
1/3Bh

9. Diameter
Probability A * Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The distance across the circle through the center of the circle.The diameter is twice the radius.
N x M

10. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
N x M
(b1 +b2) x h [or (b1 +b2) x h2]
2lw+2lh+2wh

11. What is the prime factorization of 200?
1/x^a
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.
Arrangements - orders - schedules - or lists.
2x2x2x5x5

12. Surface Area of Sphere
4pir^2
y2-y1/x2-x1
2l+2w
N x M

13. length of a sector
x/360 times (2 pi r) - where x is the degrees in the angle
The four big angles are equal and the four small angles are equal
(a-b)(a+ab+b)
(a-b)

14. (a+b)(c+d)
Lw
4/3pir^3
A=bh
Ac+ad+bc+bd

15. a+b
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.
2(pi)r(r+h)
(a+b)(a-ab+b)
N x M

16. Point-Slope form
A-b
y-y1=m(x-x1)
Pi*r^2
A=bh

17. What is the unfactored version of (x+y) ?
x + 2xy + y
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.
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.
Order does matter for a permutation - but does not matter for a combination.

18. Explain the difference between a digit and a number.
Opens down
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Pi*d
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.

19. Area of Parallelogram
The set of points which are all the same distance (the radius) from a certain point (the center).
That they often have not just one answer - but two. For example - solving x -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
Bh
(x+y)

20. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
Less
That they often have not just one answer - but two. For example - solving x -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
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.

21. Radius (Radii)
y2-y1/x2-x1
A segment connecting the center of a circle to any point on the circle
x-y
?r

22. Area of Square
S^2
(x+y)
(x-y)
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.

23. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
(x+y)(x-y)
(n-2)180
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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

24. Surface Area of Cylinder
2pir^2 + 2pir*h
1/3Bh
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-b)(a+b)

25. a - b is equal to
(pi)r^2
Lwh
Arrangements - orders - schedules - or lists.
(a+b)(a-b)

26. If something is possible but not certain - what is the numeric range of probability of it happening?
That they often have not just one answer - but two. For example - solving x -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
An ange whose vertex is the center of the circle
A segment connecting the center of a circle to any point on the circle
Between 0 and 1.

27. 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.
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.
1.4
x -2xy + y

28. Volume of Cylinder
Total distance/total time
Pir^2h
y = k/x
y = mx + b -- where: x -y are the coordinates of any point on the line (allows you to locate) m is the slope of the line b is the intercept (where the line crosses the y-axis) - Sometimes on the GRE - 'a' is substituted for 'm' - as in 'y = ax + b'.

29. Area of Trapezoid
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.
1/2 h (b1 + b2)
(0 -0)
1.4

30. What is the point-slope form?
(y-y1)=m(x-x1)
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.
(a-b)(a+ab+b)
y = kx

31. Circumference of a circle
(base x height) [or (base x height)2]
?d OR 2?r
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.
Part of a circle connecting two points on the circle.

32. Rough est. of v1 =
1
S*v2
N x M
Part of a circle connecting two points on the circle.

33. Lines reflected over the x or y axis have ____ slopes.
1/3Bh
The distance across the circle through the center of the circle.The diameter is twice the radius.
Negative
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2) = 1/4.2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287 = 1.

34. What is the average?
Sum of terms/number of terms
Number of desired outcomes/number of total outcomes
T1 * r^(n-1)
Pi*d

35. What is the area of a sector?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x 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.
y2-y1/x2-x1
(n degrees/360) * (pi)r^2

36. Area of a circle
The distance across the circle through the center of the circle.The diameter is twice the radius.
2pir^2 + 2pir*h
1/1
?r

37. Volume of sphere
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Between 0 and 1.
4/3pir^3
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.

38. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/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.
2pir^2 + 2pir*h
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.

39. How do you calculate the percentage of change?
x/360 times (?r) - where x is the degrees in the angle
Percentage Change = Difference/Original * 100
4s
4/3pir^3

40. What are the side ratios for a 30:60:90 triangle?
Probability A * Probability B
4s
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

41. What do combination problems usually ask for?
x -2xy + y
Percentage Change = Difference/Original * 100
Groups - teams - or committees.
(x-y)

42. What is a '30:60:90' triangle?
x/360 times (?r) - where x is the degrees in the angle
Sum of terms/number of terms
y = kx
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

43. What is the side ratio for a Right Isosceles triangle?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
Groups - teams - or committees.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

44. What is the factored version of x + 2xy + y ?
(x+y)
?d OR 2?r
The total # of possible outcomes.
x + 2xy + y

45. What must be true before a quadratic equation can be solved?
Not necessarily. This is a trick question - because x could be either positive or negative.
C =?d
Between 0 and 1.
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.

46. Define the range of a set of numbers.
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.
(n-2)180
Sqr( x2 -x1) + (y2- y1)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

47. a-2ab+b
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.
2pi*r
(a-b)
?r

48. Circumference of cirlce using diameter
Pi*d
Subtract the exponents - retain the base For example - x? x4 = x?-4 = x5
1/x^a
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.

49. Area of Triangle
?d OR 2?r
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.
2pi*r
1/2bh

50. What is the volume of a cylinder?
(pi)r^2(h)
The total # of possible outcomes.
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.
1/2bh

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