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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 special properties of zero.
A=bh
(n-2)180
Sum of terms/number of terms
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.

2. What is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
S² - where s = length of a side
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Pir^2h

3. What is the length of an arc?
(n degrees/360) * 2(pi)r
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Order does matter for a permutation - but does not matter for a combination.
(y-y1)=m(x-x1)

4. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
1
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.
1/1
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

5. For a bell curve - what three terms might be used to describe the number in the middle?
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 average - mean - median - or mode.
Negative
(pi)r^2(h)

6. Circumference of a circle using radius
2pi*r
(a-b)(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.
1/1

7. What is the sum of the inside angles of an n-sided polygon?
2lw+2lh+2wh
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.
Equal
(n-2)180

8. Area of a triangle
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
N x M
?r²
½(base x height) [or (base x height)÷2]

9. What do combination problems usually ask for?
Groups - teams - or committees.
1/2 h (b1 + b2)
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

10. What is the unfactored version of x²-y² ?
4s (where s = length of a side)
(x+y)(x-y)
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.
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.

11. Circumference Formula
Probability A + Probability B
C =?d
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.
Ac+ad+bc+bd

12. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
Less
The set of points which are all the same distance (the radius) from a certain point (the center).
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

13. If x² = 144 - does v144 = x?
Ac+ad+bc+bd
4pir^2
Not necessarily. This is a trick question - because x could be either positive or negative.
(n degrees/360) * (pi)r^2

14. x^-a =
An ange whose vertex is the center of the circle
T1 * r^(n-1)/(r-1)
4pir^2
1/x^a

15. Circumference of a circle
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(a+b)(a-b)
?d OR 2?r
Opens up

16. What is the surface area of a cylinder?
2(pi)r(r+h)
Less
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.
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.

17. In a coordinate system - what is the origin?
(n-2)180
2 pi r
(0 -0)
(n degrees/360) * 2(pi)r

18. Define 'proportionate' values
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)²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Pi*r^2

19. Slope
The set of points which are all the same distance (the radius) from a certain point (the center).
(n degrees/360) * 2(pi)r
(y2-y1)/(x2-x1)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

20. a² - b² is equal to
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(a+b)(a-b)
1/2bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

21. What is the side ratio for a 30:60:90 triangle?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2l+2w
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
½(b1 +b2) x h [or (b1 +b2) x h÷2]

22. What is the area of a circle?
Opens up
(pi)r^2
S*v2
A=bh

23. The length of one side of any triangle is ____ than the sum of the other two sides.
2 pi r
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.
Less
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.

24. Rough est. of v3 =
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1.7
?d OR 2?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.

25. How do you find the slope?
y2-y1/x2-x1
Lw
2 pi r
x²-y²

26. What is an 'equilateral' triangle?
Sqr( x2 -x1) + (y2- y1)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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
½(b1 +b2) x h [or (b1 +b2) x h÷2]

27. What is the point-slope form?
The distance from one point on the circle to another point on the circle.
b±[vb²-4ac]/2a
(y-y1)=m(x-x1)
(x1+x2)/2 - (y1+y2)/2

28. How do you calculate the percentage of change?
2Length + 2width [or (length + width) x 2]
S^2
2 pi r
Percentage Change = Difference/Original * 100

29. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
y2-y1/x2-x1
(n-2)180
?r²

30. a³+b³
Sum of terms/number of terms
(a+b)(a²-ab+b²)
S^2
y2-y1/x2-x1

31. In a parabola - if the first term is negative - the parabola ________.
Opens down
2(lw+wh+lh)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.

32. What is the area of a sector?
Number of desired outcomes/number of total outcomes
1/1
C =?d
(n degrees/360) * (pi)r^2

33. What is a '30:60:90' triangle?
?d OR 2?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
4s
(x+y)(x-y)

34. What is the formula for the diagonal of any square?
(pi)r^2
S*v2
1/2bh
(a+b)(a-b)

35. What is the 'distributive law'?
x² -2xy + y²
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.
(x1+x2)/2 - (y1+y2)/2
A+b

36. What is the distance formula?
2pir^2 + 2pir*h
(a-b)(a+b)
Sqr( x2 -x1) + (y2- y1)
Less

37. Surface Area of Sphere
4pir^2
2(lw+wh+lh)
1/1
The set of points which are all the same distance (the radius) from a certain point (the center).

38. What is the factored version of x² -2xy + y² ?
A²-b²
1. Given event A: A + notA = 1.
(0 -0)
(x-y)²

39. What is the equation of a line?

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40. What is the volume 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.
Percentage Change = Difference/Original * 100
(pi)r^2(h)
Sum of the lengths of the sides

41. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

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42. Area of rectangle - square - parallelogram
A=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.
Part of a circle connecting two points on the circle.
1/2bh

43. When you reverse FOIL - the term that needs to add out is the _____
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
S² - where s = length of a side
Middle term
Bh

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

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45. What is the factored version of x² + 2xy + y² ?
(n degrees/360) * (pi)r^2
(x+y)²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.

46. What is the circumference of a circle?
A+b
2(pi)r
4s
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.

47. What number goes on the bottom of a probability fraction?
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(a+b)²
The total # of possible outcomes.

48. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
4s
1/3Bh
(a+b)(a-b)

49. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
1/1
1/3pir^2*h
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

50. How do you find the sum of a geometric sequence?
Less
Sqr( x2 -x1) + (y2- y1)
Sum of terms/number of terms
T1 * r^(n-1)/(r-1)