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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. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
b±[vb²-4ac]/2a
y2-y1/x2-x1
4pir^2

2. Circumference Formula
C =?d
Pir^2h
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
(n-2)180

3. What is the 'Third side' rule for triangles?
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(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.
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.

4. What is the surface area of a cylinder?
The four big angles are equal and the four small angles are equal
2(pi)r(r+h)
A+b
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

5. How do you calculate the probability of two events in a row? (Probability of A and B)
(y2-y1)/(x2-x1)
(a+b)(a-b)
Probability A * Probability B
(n-2)180

6. In a coordinate system - identify the quadrants and describe their location.
(a-b)²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The average - mean - median - or mode.
(pi)r^2

7. 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.
Opens down
(a-b)²
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.

8. a²-b²
S*v2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(a-b)(a+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

9. How do you calculate the percentage of change?
Not necessarily. This is a trick question - because x could be either positive or negative.
Lwh
Arrangements - orders - schedules - or lists.
Percentage Change = Difference/Original * 100

10. To divide powers with the same base...
1.4
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4s (where s = length of a side)

11. The length of one side of any triangle is ____ than the sum of the other two sides.
Sqr( x2 -x1) + (y2- y1)
Less
(x+y)²
2l+2w

12. Area of Rectangle
Lw
1.4
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
1/3Bh

13. Area of Circle
Pi*r^2
(n/2) * (t1+tn)
Lw
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.

14. Surface Area of rectangular prism
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(pi)r^2
Bh
2lw+2lh+2wh

15. When you reverse FOIL - the term that needs to multiply out is the _____
(a-b)(a+b)
(x1+x2)/2 - (y1+y2)/2
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'.

16. a³+b³
(x1+x2)/2 - (y1+y2)/2
(a-b)(a²+ab+b²)
A=bh
(a+b)(a²-ab+b²)

17. Circumference of a circle using radius
4s (where s = length of a side)
(y2-y1)/(x2-x1)
2pi*r
(n degrees/360) * (pi)r^2

18. Perimeter of rectangle
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2l+2w
y-y1=m(x-x1)
Bh

19. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
2pir^2 + 2pir*h
T1 * r^(n-1)/(r-1)
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.

20. What do combination problems usually ask for?
1/1
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.
1. Given event A: A + notA = 1.

21. When you reverse FOIL - the term that needs to add out is the _____
2(pi)r(r+h)
1/x^a
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'.
Middle term

22. Area of Parallelogram
(x-y)²
Bh
S^2
Lwh

23. Volume of Cone
1/3pir^2*h
1.4
2pir^2 + 2pir*h
y-y1=m(x-x1)

24. Define the range of a set of numbers.
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.
T1 + (n-1)d
Total distance/total time
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.

25. What is the point-slope form?
2 pi r
x² -2xy + y²
(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.

26. Circumference of cirlce using diameter
1.7
Pi*d
2(lw+wh+lh)
An ange whose vertex is the center of the circle

27. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
(x+y)(x-y)
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.
x°/360 times (?r²) - where x is the degrees in the angle

28. What is the unfactored version of x²-y² ?
x² -2xy + y²
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2l+2w
(x+y)(x-y)

29. What is the length of an arc?
(n degrees/360) * (pi)r^2
x²-y²
(n degrees/360) * 2(pi)r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

30. What is the area of a sector?
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.
b±[vb²-4ac]/2a
(a+b)²
(n degrees/360) * (pi)r^2

31. What is the factored version of x² -2xy + y² ?
(x-y)²
Equal
(y2-y1)/(x2-x1)
The distance from one point on the circle to another point on the circle.

32. What is the factored version of x² + 2xy + y² ?
Pi*d
1/2bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(x+y)²

33. Perimeter of a rectangle
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
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.
1/2 h (b1 + b2)
2Length + 2width [or (length + width) x 2]

34. What is the prime factorization of 200?
2x2x2x5x5
T1 * r^(n-1)
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.
?d OR 2?r

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

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36. What number goes on the bottom of a probability fraction?
(a-b)(a²+ab+b²)
The distance across the circle through the center of the circle.The diameter is twice the radius.
S*v2
The total # of possible outcomes.

37. Chord
2lw+2lh+2wh
The distance from one point on the circle to another point on the circle.
2pi*r
Pir^2h

38. 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.
T1 + (n-1)d
(n-2)180
x²-y²

39. What is the circumference of a circle?
The distance from one point on the circle to another point on the circle.
2(pi)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.
Bh

40. x^-a =
Probability A * Probability B
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
1/x^a

41. Explain the special properties of zero.
(n degrees/360) * (pi)r^2
Number of desired outcomes/number of total outcomes
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.
2pi*r

42. How do you find the midpoint?
(a-b)(a²+ab+b²)
T1 * r^(n-1)
(n-2)180
(x1+x2)/2 - (y1+y2)/2

43. If x² = 144 - does v144 = x?
S² - where s = length of a side
Not necessarily. This is a trick question - because x could be either positive or negative.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Opens down

44. Volume of pyramid
N x M
1/3Bh
y = k/x
(y2-y1)/(x2-x1)

45. Lines reflected over the x or y axis have ____ slopes.
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.
Order does matter for a permutation - but does not matter for a combination.
T1 * r^(n-1)/(r-1)
Negative

46. What is a '30:60:90' triangle?
(n-2)180
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
Pir^2h
½(b1 +b2) x h [or (b1 +b2) x h÷2]

47. Point-Slope form
Less
y-y1=m(x-x1)
2lw+2lh+2wh
x°/360 times (?r²) - where x is the degrees in the angle

48. Define the mode of a set of numbers.
Sum of the lengths of the sides
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.
x°/360 times (?r²) - where x is the degrees in the angle
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

49. Surface Area of Sphere
A+b
4pir^2
A=bh
2(pi)r

50. Slope
(y2-y1)/(x2-x1)
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.
1/3Bh
?r²