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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. Lines reflected over the x or y axis have ____ slopes.
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).
4s
Negative

2. Perimeter of polygon
(a+b)(a-ab+b)
Arrangements - orders - schedules - or lists.
The average - mean - median - or mode.
Sum of the lengths of the sides

3. a-b
Number of desired outcomes/number of total outcomes
(a-b)(a+b)
A=bh
Less

4. What is directly proportional?
y = kx
1/2 h (b1 + b2)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Add the exponents - retain the base. for example - x + x5 = x+5 = x7

5. Area of rectangle - square - parallelogram
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A=bh
y-y1=m(x-x1)
Negative

6. How do you find the midpoint?
?d OR 2?r
(x-y)
(x1+x2)/2 - (y1+y2)/2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

7. What do permutation problems often ask for?
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.
(a+b)(a-b)
N x M
Arrangements - orders - schedules - or lists.

8. Circle
The set of points which are all the same distance (the radius) from a certain point (the center).
T1 * r^(n-1)
(n degrees/360) * (pi)r^2
The four big angles are equal and the four small angles are equal

9. Central Angle
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.
Opens down
2pi*r
An ange whose vertex is the center of the circle

10. What is the factored version of (x+y)(x-y) ?
C =?d
(0 -0)
(a+b)
x-y

11. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
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.
T1 * r^(n-1)
1. Factored: x - y Unfactored: (x+y)(x-y) 2. Factored: (x+y) Unfactored: x + 2xy + y 3. Factored: (x-y) Unfactored: x - 2xy + y

12. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
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.
(x+y)
x/360 times (?r) - where x is the degrees in the angle
N x M

13. Define the mode of a set of numbers.
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.
Equal
The ratio of sides is x:x:xv2 - where xv2 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.

14. 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.
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
y-y1=m(x-x1)
T1 + (n-1)d

15. Slope
(pi)r^2
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.
T1 + (n-1)d
(y2-y1)/(x2-x1)

16. In intersecting lines - opposite angles are _____.
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.
T1 + (n-1)d
Equal
The set of points which are all the same distance (the radius) from a certain point (the center).

17. (a+b)(a-b)=
2pir^2 + 2pir*h
S*v2
A-b
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

18. What is the area of a solid rectangle?
A=?r2
Subtract the exponents - retain the base For example - x? x4 = x?-4 = x5
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2(lw+wh+lh)

19. What is inversely proportional?
1/2bh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
y = k/x
2lw+2lh+2wh

20. Perimeter of rectangle
1/3Bh
2pir^2 + 2pir*h
2l+2w
(n-2)180

21. Area of a triangle
x-y
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.
(base x height) [or (base x height)2]
(a+b)(a-ab+b)

22. Chord
The distance from one point on the circle to another point on the circle.
2l+2w
(x-y)
(x1+x2)/2 - (y1+y2)/2

23. Area of a trapezoid
The four big angles are equal and the four small angles are equal
(b1 +b2) x h [or (b1 +b2) x h2]
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.
1/x^a

24. What is the prime factorization of 200?
Probability A + Probability B
2x2x2x5x5
y = k/x
Less

25. What is the circumference of a circle?
2(pi)r
1/1
2 pi r
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.

26. How do you find the sum of a geometric sequence?
T1 * r^(n-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.
T1 * r^(n-1)/(r-1)
y = kx

27. What is the area of a circle?
(y2-y1)/(x2-x1)
(pi)r^2
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.
Equal

28. Area of a square
Pi*r^2
S - where s = length of a side
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The distance from one point on the circle to another point on the circle.

29. How do you find the slope?
Not necessarily. This is a trick question - because x could be either positive or negative.
y2-y1/x2-x1
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

30. a+b
Probability A + Probability B
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
(x+y)(x-y)
(a+b)(a-ab+b)

31. What is the unfactored version of (x-y) ?
1/2bh
1/2bh
x -2xy + y
2pi*r

32. What'S the most important thing to remember about charts you'll see on the GRE?
Between 0 and 1.
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.
(a+b)(a-b)
2pir^2 + 2pir*h

33. What is the 'Third side' rule for triangles?
4/3pir^3
2(pi)r(r+h)
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.

34. What is the area of a cylinder?
2(pi)r(r+h)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
Lw

35. How do you find the nth term of a geometric sequence?
(x1+x2)/2 - (y1+y2)/2
A+b
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.
T1 * r^(n-1)

36. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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.
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
T1 * r^(n-1)

37. Rough est. of v2 =
2Length + 2width [or (length + width) x 2]
1.4
S^2
2(pi)r(r+h)

38. How do you calculate the surface area of a rectangular box?
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.
(a-b)(a+ab+b)
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.

39. Area of a circle
Arrangements - orders - schedules - or lists.
?r
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.
x-y

40. Rough est. of v1 =
1
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.
(b1 +b2) x h [or (b1 +b2) x h2]
Sum of terms/number of terms

41. How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x + x5 = x+5 = x7
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Lwh
Arrangements - orders - schedules - or lists.

42. Define the 'Third side' rule for triangles
4s (where s = length of a side)
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.
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.
Probability A * Probability B

43. Surface Area of rectangular prism
(a-b)(a+ab+b)
2lw+2lh+2wh
b[vb-4ac]/2a
Part of a circle connecting two points on the circle.

44. What is the length of an arc?
(n degrees/360) * 2(pi)r
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x/360 times (2 pi r) - where x is the degrees in the angle
2(lw+wh+lh)

45. What is the average speed?
Sqr( x2 -x1) + (y2- y1)
Middle term
(a+b)
Total distance/total time

46. Area of Circles
2(pi)r
(x+y)
A=?r2
(n/2) * (t1+tn)

47. a-b
The set of points which are all the same distance (the radius) from a certain point (the center).
(a-b)(a+ab+b)
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.
4pir^2

48. How do you find the sum of an arithmetic sequence?
2(lw+wh+lh)
Subtract the exponents - retain the base For example - x? x4 = x?-4 = x5
(n/2) * (t1+tn)
Opens up

49. How do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
(x1+x2)/2 - (y1+y2)/2
y = kx
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.

50. What is the side ratio for a Right Isosceles triangle?
y2-y1/x2-x1
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.

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