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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. What is the probability?
Middle term
(a+b)²
Number of desired outcomes/number of total outcomes
The total # of possible outcomes.

2. What do combination problems usually ask for?
2(pi)r
T1 * r^(n-1)/(r-1)
Groups - teams - or committees.
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.

3. Area of Triangle
Bh
1/2bh
T1 * r^(n-1)
Equal

4. Area of a trapezoid
1. Given event A: A + notA = 1.
(a-b)(a²+ab+b²)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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'.

5. What is a 'Right isosceles' triangle?
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.
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.
N x M
Bh

6. What is the area of a triangle?
1/2bh
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

7. What is the average?
Sum of terms/number of terms
x²-y²
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'.
(0 -0)

8. a²-2ab+b²
Bh
(a-b)²
Part of a circle connecting two points on the circle.
y = kx

9. What is the factored version of (x+y)(x-y) ?
?d OR 2?r
Order does matter for a permutation - but does not matter for a combination.
x²-y²
(n degrees/360) * (pi)r^2

10. Volume of Cylinder
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Pir^2h
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.
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.

11. Define the 'Third side' rule for triangles

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12. The length of one side of any triangle is ____ than the sum of the other two sides.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2Length + 2width [or (length + width) x 2]
(x+y)(x-y)
Less

13. Area of a triangle
½(base x height) [or (base x height)÷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.
1/2bh
(n degrees/360) * 2(pi)r

14. To divide powers with the same base...
Sqr( x2 -x1) + (y2- y1)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The total # of possible outcomes.
2 pi r

15. 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.
½(base x height) [or (base x height)÷2]
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.

16. What is the prime factorization of 200?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2x2x2x5x5
T1 + (n-1)d
Negative

17. Slope
(y2-y1)/(x2-x1)
(0 -0)
S*v2
2 pi r

18. Area of a circle
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1/3pir^2*h
?r²

19. a³-b³
4s (where s = length of a side)
(a-b)(a²+ab+b²)
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.
Sum of terms/number of terms

20. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
x°/360 times (?r²) - where x is the degrees in the angle
(n/2) * (t1+tn)
Arrangements - orders - schedules - or lists.

21. Area of rectangle - square - parallelogram
Negative
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
1/2bh
A=bh

22. How do you multiply powers with the same base?
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 part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x°/360 times (?r²) - where x is the degrees in the angle

23. What is the point-slope form?
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.
T1 * r^(n-1)/(r-1)
(y-y1)=m(x-x1)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

24. How do you find the midpoint?
2(pi)r(r+h)
T1 * r^(n-1)/(r-1)
(x1+x2)/2 - (y1+y2)/2
x² + 2xy + y²

25. Perimeter (circumference) of a circle
Last term
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.
2 pi r
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

26. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
(a+b)²
A=?r2
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.
(a+b)(a-b)

27. Quadratic Formula
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)²
Negative
b±[vb²-4ac]/2a

28. In a coordinate system - identify the quadrants and describe their location.
?r²
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'.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Number of desired outcomes/number of total outcomes

29. When you reverse FOIL - the term that needs to add out is the _____
Middle term
(pi)r^2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

30. What is the length of an arc?
1/2bh
(n degrees/360) * 2(pi)r
Negative
Not necessarily. This is a trick question - because x could be either positive or negative.

31. Surface Area of Sphere
4pir^2
(0 -0)
Opens up
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.

32. a²-b²
(a-b)(a+b)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Less
T1 + (n-1)d

33. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
The distance across the circle through the center of the circle.The diameter is twice the radius.
2l+2w
(x+y)²

34. What'S the most important thing to remember about charts you'll see on the GRE?
Last term
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'.
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.
4/3pir^3

35. Volume of sphere
(a-b)(a+b)
4/3pir^3
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.
y = kx

36. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

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37. What is the surface area of a cylinder?
The distance from one point on the circle to another point on the circle.
2(pi)r(r+h)
(pi)r^2
(a-b)(a+b)

38. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
N x M
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(a-b)(a²+ab+b²)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

39. What is the area of a cylinder?
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.
2(pi)r(r+h)
Sum of the lengths of the sides
Order does matter for a permutation - but does not matter for a combination.

40. Circumference of a circle
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'.
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.
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.
?d OR 2?r

41. What is the unfactored version of (x+y)² ?
2x2x2x5x5
x² + 2xy + y²
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.
?d OR 2?r

42. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
x°/360 times (?r²) - where x is the degrees in the angle
1/1
A+b

43. Circumference of a circle using radius
(a-b)(a+b)
½(base x height) [or (base x height)÷2]
2pi*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.

44. How do you find the sum of an arithmetic sequence?
2lw+2lh+2wh
(n/2) * (t1+tn)
y = kx
A=bh

45. Surface Area of rectangular prism
Opens up
2lw+2lh+2wh
(n degrees/360) * (pi)r^2
(a-b)²

46. (a+b)(c+d)
Sqr( x2 -x1) + (y2- y1)
Ac+ad+bc+bd
(x+y)(x-y)
T1 + (n-1)d

47. Perimeter of rectangle
2Length + 2width [or (length + width) x 2]
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
b±[vb²-4ac]/2a
2l+2w

48. Circle
Number of desired outcomes/number of total outcomes
The set of points which are all the same distance (the radius) from a certain point (the center).
S^2
Probability A * Probability B

49. Explain the special properties of zero.
Total distance/total time
The set of points which are all the same distance (the radius) from a certain point (the center).
A segment connecting the center of a circle to any point on the circle
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.

50. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Middle term
The total # of possible outcomes.

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GRE Math 2

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