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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. Area of Trapezoid
4/3pir^3
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.
1/2 h (b1 + b2)
Not necessarily. This is a trick question - because x could be either positive or negative.

2. What is the side ratio for a Right Isosceles triangle?
2lw+2lh+2wh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
S - where s = length of a side
A+b

3. Perimeter of a square
2 pi r
1/2 h (b1 + 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.
4s (where s = length of a side)

4. Area of a triangle
Probability A * Probability B
(base x height) [or (base x height)2]
1/2 h (b1 + b2)
?d OR 2?r

5. What is the circumference of a circle?
The distance across the circle through the center of the circle.The diameter is twice the radius.
1/3Bh
2(pi)r
Arrangements - orders - schedules - or lists.

6. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
1/x^a
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
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.

7. a-b
(a-b)(a+b)
(a+b)(a-b)
x/360 times (?r) - where x is the degrees in the angle
Bh

8. What is the sum of the inside angles of an n-sided polygon?
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'.
Order does matter for a permutation - but does not matter for a combination.
(n-2)180
2lw+2lh+2wh

9. What must be true before a quadratic equation can be solved?
1/3pir^2*h
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.
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.
x + 2xy + y

10. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
Probability A + Probability B
4s
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

11. What is the 'distributive law'?
2l+2w
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.
(a+b)(a-b)
Number of desired outcomes/number of total outcomes

12. What is 'absolute value' - and how is it represented?
(pi)r^2(h)
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.
x -2xy + y
The average - mean - median - or mode.

13. What is the side ratio for a 30:60:90 triangle?
Lwh
(x+y)
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 - and greater than the difference between the other two sides.

14. a - b is equal to
C =?d
y2-y1/x2-x1
x -2xy + y
(a+b)(a-b)

15. Explain the special properties of zero.
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]
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.
Groups - teams - or committees.

16. Area of a circle
(y2-y1)/(x2-x1)
(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.
?r

17. What is the unfactored version of (x+y) ?
(n/2) * (t1+tn)
(a+b)(a-ab+b)
2(pi)r(r+h)
x + 2xy + y

18. How do you find the nth term of an arithmetic sequence?
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
T1 + (n-1)d
1/2 h (b1 + b2)

19. List two odd behaviors of exponents
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.
The average - mean - median - or mode.
S*v2
A segment connecting the center of a circle to any point on the circle

20. What do combination problems usually ask for?
Groups - teams - or committees.
2lw+2lh+2wh
Subtract the exponents - retain the base For example - x? x4 = x?-4 = x5
x/360 times (2 pi r) - where x is the degrees in the angle

21. What do permutation problems often ask for?
x/360 times (2 pi r) - where x is the degrees in the angle
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.
Sqr( x2 -x1) + (y2- y1)
Arrangements - orders - schedules - or lists.

22. What'S the most important thing to remember about charts you'll see on the GRE?
S^2
(n degrees/360) * 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.
2pir^2 + 2pir*h

23. How do you find the nth term of a geometric sequence?
The distance from one point on the circle to another point on the circle.
T1 * r^(n-1)
Lw
Middle term

24. How do you find the slope?
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.
y2-y1/x2-x1
The distance across the circle through the center of the circle.The diameter is twice the radius.
Opens down

25. Does order matter for a permutation? How about for a combination?
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.
Between 0 and 1.
Order does matter for a permutation - but does not matter for a combination.
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'.

26. Perimeter (circumference) of a circle
2 pi r
(n-2)180
(a-b)(a+b)
y = kx

27. The probability of an event happening and the probability of an event NOT happening must add up to what number?
x -2xy + y
N x M
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.
1. Given event A: A + notA = 1.

28. What is the area of a sector?
(n degrees/360) * (pi)r^2
y2-y1/x2-x1
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.
y-y1=m(x-x1)

29. What is a 'Right isosceles' triangle?
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.
b[vb-4ac]/2a
x/360 times (2 pi r) - where x is the degrees in the angle
1.7

30. What is the point-slope form?
(y-y1)=m(x-x1)
The distance from one point on the circle to another point on the circle.
Last term
(a-b)(a+ab+b)

31. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
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.
N x M
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.
?d OR 2?r

32. How do you solve a permutation?
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.
4pir^2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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

33. What is an 'equilateral' triangle?
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.
?d OR 2?r
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
T1 + (n-1)d

34. How do you find the midpoint?
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
1/2bh
(x1+x2)/2 - (y1+y2)/2
y = k/x

35. (a+b)(c+d)
T1 + (n-1)d
Ac+ad+bc+bd
Less
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.

36. What is the unfactored version of (x-y) ?
(a+b)(a-ab+b)
2pir^2 + 2pir*h
x -2xy + y
Not necessarily. This is a trick question - because x could be either positive or negative.

37. a+2ab+b
A segment connecting the center of a circle to any point on the circle
(a+b)
A=?r2
The distance from one point on the circle to another point on the circle.

38. Surface Area of Cylinder
4s
2pir^2 + 2pir*h
(a+b)(a-ab+b)
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'.

39. Rough est. of v3 =
Not necessarily. This is a trick question - because x could be either positive or negative.
1.7
A=bh
1/2bh

40. Volume of prism
Bh
(a+b)
Less
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

41. What is the 'Third side' rule for triangles?
The set of points which are all the same distance (the radius) from a certain point (the center).
2(pi)r(r+h)
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.

42. Lines reflected over the x or y axis have ____ slopes.
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.
The total # of possible outcomes.
Negative
y-y1=m(x-x1)

43. Area of Square
A segment connecting the center of a circle to any point on the circle
(n degrees/360) * 2(pi)r
S^2
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.

44. What are the side ratios for a 30:60:90 triangle?
T1 + (n-1)d
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Lw
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

45. In a coordinate system - identify the quadrants and describe their location.
T1 * r^(n-1)
1
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(a+b)(a-b)

46. What is the distance formula?
?d OR 2?r
S*v2
Sqr( x2 -x1) + (y2- y1)
Not necessarily. This is a trick question - because x could be either positive or negative.

47. What is the length of an arc?
An ange whose vertex is the center of the circle
1.4
(n degrees/360) * 2(pi)r
(x+y)(x-y)

48. a-2ab+b
Not necessarily. This is a trick question - because x could be either positive or negative.
2 pi r
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.
(a-b)

49. Area of Rectangle
(a-b)(a+ab+b)
Lw
Last term
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.

50. Slope
Bh
T1 * r^(n-1)/(r-1)
(y2-y1)/(x2-x1)
?r

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