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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. Explain the difference between a digit and a number.

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2. Area of a triangle
½(base x height) [or (base x height)÷2]
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.
Order does matter for a permutation - but does not matter for a combination.
S² - where s = length of a side

3. What is the point-slope form?
(y-y1)=m(x-x1)
2x2x2x5x5
x²-y²
1/3pir^2*h

4. Perimeter of a square
Pi*d
1. Given event A: A + notA = 1.
4s (where s = length of a side)
(x1+x2)/2 - (y1+y2)/2

5. In a coordinate system - identify the quadrants and describe their location.
y = kx
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(x+y)(x-y)

6. Area of Circle
Pi*r^2
y = k/x
Negative
Last term

7. Rough est. of v2 =
Bh
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.
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.
1.4

8. Volume of prism
The total # of possible outcomes.
Probability A * Probability B
x² + 2xy + y²
Bh

9. Area of Trapezoid
Bh
1/2 h (b1 + b2)
S^2
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.

10. When a line crosses two parallel lines - ________.
The four big angles are equal and the four small angles are equal
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
2Length + 2width [or (length + width) x 2]
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

11. Volume of Cylinder
(a-b)(a+b)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
Pir^2h

12. Slope
(y2-y1)/(x2-x1)
S^2
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 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.

13. (a+b)(c+d)
Sum of terms/number of terms
(x-y)²
Ac+ad+bc+bd
2(pi)r

14. How do you solve a permutation?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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
1/1
Probability A * Probability B

15. Quadratic Formula
2Length + 2width [or (length + width) x 2]
1.7
The distance from one point on the circle to another point on the circle.
b±[vb²-4ac]/2a

16. Perimeter of rectangle
Negative
2l+2w
2(pi)r(r+h)
y = k/x

17. What is the area of a triangle?
1/3Bh
1/2bh
1
Pi*r^2

18. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or 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'.
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.
Probability A + Probability B
x² -2xy + y²

19. What is the factored version of (x+y)(x-y) ?
(x+y)²
2(pi)r(r+h)
2x2x2x5x5
x²-y²

20. a³-b³
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(x-y)²
(a-b)(a²+ab+b²)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

21. What is the area of a circle?
(pi)r^2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

22. What is the area of a sector?
2(pi)r(r+h)
(y2-y1)/(x2-x1)
(n degrees/360) * (pi)r^2
1

23. What is the formula for the diagonal of any square?
x² + 2xy + y²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
S*v2
Part of a circle connecting two points on the circle.

24. Area of a square
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
S² - where s = length of a side
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.
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.

25. Define a factorial of a number - and how it is written.
?d OR 2?r
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(n-2)180

26. Volume of pyramid
Sum of terms/number of terms
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
1/3Bh

27. How do you calculate the probability of two events in a row? (Probability of A and B)
Percentage Change = Difference/Original * 100
Probability A * Probability B
(n-2)180
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.

28. When you reverse FOIL - the term that needs to multiply out is the _____
4s (where s = length of a side)
(n degrees/360) * (pi)r^2
1/1
Last term

29. What is the volume of a cylinder?
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.
?r²
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.
(pi)r^2(h)

30. How do you calculate the percentage of change?
A²-b²
Order does matter for a permutation - but does not matter for a combination.
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.
Percentage Change = Difference/Original * 100

31. What is the average speed?
2(pi)r(r+h)
(a-b)(a+b)
Total distance/total time
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.

32. Define the mode of a set of numbers.
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=bh
(x-y)²

33. 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)² = 1/4.2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
Equal

34. Point-Slope form
y-y1=m(x-x1)
x°/360 times (?r²) - where x is the degrees in the angle
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]

35. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Lw
x°/360 times (?r²) - where x is the degrees in the angle
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

36. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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
A+b
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.
S^2

37. Circumference Formula
Pir^2h
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
C =?d
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

38. Perimeter of a rectangle
Opens up
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.
4s (where s = length of a side)

39. What is the average?
Sum of terms/number of terms
4s (where s = length of a side)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Total distance/total time

40. Area of Circles
(x-y)²
1.4
4s
A=?r2

41. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

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42. What is the volume of a solid rectangle?
y2-y1/x2-x1
1/3pir^2*h
Lwh
Between 0 and 1.

43. The length of one side of any triangle is ____ than the sum of the other two sides.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
Less
The four big angles are equal and the four small angles are equal

44. What is directly proportional?
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+y)(x-y)
y = kx
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.

45. Perimeter (circumference) of a circle
2 pi r
4s
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2lw+2lh+2wh

46. How do you multiply powers with the same base?
y-y1=m(x-x1)
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(a-b)(a²+ab+b²)

47. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A+b
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.
Probability A * Probability B

48. x^a * x^b = x^__
A+b
Bh
?d OR 2?r
Groups - teams - or committees.

49. Define the range of a set of numbers.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
Number of desired outcomes/number of total outcomes
(a+b)(a²-ab+b²)

50. What number goes on the bottom of a probability fraction?
An ange whose vertex is the center of the circle
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 total # of possible outcomes.
Lw