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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. How do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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
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.

2. a²-2ab+b²
Lwh
N x M
(a-b)²
2pi*r

3. Rough est. of v2 =
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
1.4
2(pi)r(r+h)

4. What is a '30:60:90' triangle?
1. Given event A: A + notA = 1.
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
T1 + (n-1)d
Sqr( x2 -x1) + (y2- y1)

5. What is the surface area of a cylinder?
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.
Less
2(pi)r(r+h)
1/2 h (b1 + b2)

6. a³+b³
(a+b)(a²-ab+b²)
½(b1 +b2) x h [or (b1 +b2) x h÷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.
S*v2

7. What is a 'Right isosceles' triangle?
(y2-y1)/(x2-x1)
Pi*r^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.
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.

8. What is the probability?
Number of desired outcomes/number of total outcomes
Pi*d
T1 * r^(n-1)
1/3pir^2*h

9. Define 'proportionate' values
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.
y = kx
(a-b)(a+b)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

10. Area of rectangle - square - parallelogram
Between 0 and 1.
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.
A=bh
Lw

11. Lines reflected over the x or y axis have ____ slopes.
Negative
2(lw+wh+lh)
4/3pir^3
N x M

12. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Bh
(y-y1)=m(x-x1)
2l+2w

13. Central Angle
Part of a circle connecting two points on the circle.
x² + 2xy + y²
An ange whose vertex is the center of the circle
b±[vb²-4ac]/2a

14. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Number of desired outcomes/number of total outcomes
1. Given event A: A + notA = 1.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.

15. Area of Parallelogram
Bh
Probability A + Probability B
1. Given event A: A + notA = 1.
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.

16. List two odd behaviors of exponents
2(pi)r(r+h)
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. 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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

17. What is the area of a circle?
(pi)r^2
Groups - teams - or committees.
Ac+ad+bc+bd
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

18. Does order matter for a permutation? How about for a combination?
(a-b)(a+b)
Order does matter for a permutation - but does not matter for a combination.
The set of points which are all the same distance (the radius) from a certain point (the center).
The total # of possible outcomes.

19. What is the volume of a cylinder?
(pi)r^2(h)
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. 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.
Arrangements - orders - schedules - or lists.

20. Circumference of cirlce using diameter
b±[vb²-4ac]/2a
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Pi*d
Pi*r^2

21. Circumference of a circle using radius
N x M
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.
y = k/x
2pi*r

22. What is the formula for the diagonal of any square?
y2-y1/x2-x1
An ange whose vertex is the center of the circle
b±[vb²-4ac]/2a
S*v2

23. Area of Square
C =?d
2(pi)r(r+h)
S^2
Between 0 and 1.

24. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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/2) * (t1+tn)
T1 + (n-1)d
T1 * r^(n-1)

25. Slope
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
(x+y)(x-y)
(y2-y1)/(x2-x1)

26. 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
2lw+2lh+2wh
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

27. What is the factored version of x² -2xy + y² ?
A=?r2
2x2x2x5x5
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(x-y)²

28. 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.
y-y1=m(x-x1)
T1 * r^(n-1)
The total # of possible outcomes.

29. What do permutation problems often ask for?
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
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.
Arrangements - orders - schedules - or lists.

30. length of a sector
The distance from one point on the circle to another point on the 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'.
x°/360 times (2 pi r) - where x is the degrees in the angle
Sum of terms/number of terms

31. x^a * x^b = x^__
Groups - teams - or committees.
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.
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

32. How do you find the slope?
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 distance across the circle through the center of the circle.The diameter is twice the radius.
Percentage Change = Difference/Original * 100
y2-y1/x2-x1

33. What'S the most important thing to remember about charts you'll see on the GRE?
Sum of terms/number of terms
Lw
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.
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.

34. a²-b²
(a-b)(a+b)
(a-b)²
(n-2)180
1. Given event A: A + notA = 1.

35. Perimeter of polygon
(n degrees/360) * (pi)r^2
Sum of the lengths of the sides
The set of points which are all the same distance (the radius) from a certain point (the center).
½(base x height) [or (base x height)÷2]

36. Area of Circles
(pi)r^2(h)
A=?r2
(a+b)²
?d OR 2?r

37. Area of Circle
Pi*r^2
(x+y)(x-y)
Total distance/total time
The set of points which are all the same distance (the radius) from a certain point (the center).

38. Define the range of a set of numbers.
Sum of terms/number of terms
x² -2xy + y²
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.
Pi*r^2

39. Perimeter of a rectangle
2 pi r
2Length + 2width [or (length + width) x 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.
1/3pir^2*h

40. What is the volume of a solid rectangle?
2lw+2lh+2wh
Lwh
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.

41. What is directly proportional?
y = kx
Pi*d
?d OR 2?r
Number of desired outcomes/number of total outcomes

42. What is the area of a sector?
(x-y)²
(n degrees/360) * (pi)r^2
Less
Ac+ad+bc+bd

43. Volume of Cylinder
Probability A * Probability 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.
Middle term
Pir^2h

44. Area of a triangle
½(base x height) [or (base x height)÷2]
S² - where s = length of a side
A²-b²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

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

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46. Circumference Formula
C =?d
Sum of terms/number of terms
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

47. a³-b³
?r²
(a-b)(a²+ab+b²)
2 pi r
T1 * r^(n-1)

48. In a coordinate system - identify the quadrants and describe their location.
T1 + (n-1)d
N x M
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/2bh

49. What is the equation of a line?

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50. How do you calculate the surface area of a rectangular box?
Ac+ad+bc+bd
2pir^2 + 2pir*h
Lwh
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.