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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.
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.
(x+y)²
Pi*d
b±[vb²-4ac]/2a

2. Quadratic Formula
b±[vb²-4ac]/2a
2(pi)r(r+h)
An ange whose vertex is the center of the circle
Bh

3. a² - b² is equal to
Lwh
(a+b)(a-b)
(x+y)²
(a-b)²

4. What is the volume of a cylinder?
Sum of the lengths of the sides
b±[vb²-4ac]/2a
(pi)r^2(h)
2x2x2x5x5

5. In intersecting lines - opposite angles are _____.
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.
Equal
S² - where s = length of a side
Pi*d

6. What is the area of a cylinder?
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 degrees/360) * 2(pi)r
?r²
2(pi)r(r+h)

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.
Equal
2lw+2lh+2wh
2pir^2 + 2pir*h

8. What is the equation of a line?

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9. 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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The average - mean - median - or mode.
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.

10. When you reverse FOIL - the term that needs to add out is the _____
(x1+x2)/2 - (y1+y2)/2
y = kx
2 pi r
Middle term

11. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
(a-b)(a+b)
x°/360 times (2 pi r) - where x is the degrees in the angle
Bh
N x M

12. What is the surface area of a cylinder?
2(pi)r(r+h)
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.
2Length + 2width [or (length + width) x 2]
Sqr( x2 -x1) + (y2- y1)

13. Perimeter of rectangle
2l+2w
1/x^a
Opens up
Probability A * Probability B

14. 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.
The set of points which are all the same distance (the radius) from a certain point (the center).
1.7
x°/360 times (2 pi r) - where x is the degrees in the angle

15. Surface Area of Sphere
N x M
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
4pir^2
An ange whose vertex is the center of the circle

16. Area of a square
Not necessarily. This is a trick question - because x could be either positive or negative.
4/3pir^3
S² - where s = length of a side
Less

17. Volume of prism
Bh
Negative
Opens down
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

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

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19. Area of Triangle
S^2
y = k/x
1/2bh
(x+y)²

20. Define the range of a set of numbers.
2(pi)r
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
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.
1/2bh

21. Volume of sphere
Last term
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
4/3pir^3
T1 * r^(n-1)

22. Rough est. of v1 =
Lwh
Pi*d
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

23. Slope
(x1+x2)/2 - (y1+y2)/2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(y2-y1)/(x2-x1)
2pir^2 + 2pir*h

24. Sector
A=bh
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.
x² + 2xy + y²
A segment connecting the center of a circle to any point on the circle

25. What is the average speed?
Total distance/total time
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x°/360 times (2 pi r) - where x is the degrees in the angle
4pir^2

26. What is the factored version of x² + 2xy + y² ?
Pir^2h
Part of a circle connecting two points on the circle.
(a-b)²
(x+y)²

27. Circumference Formula
Sqr( x2 -x1) + (y2- y1)
Sum of the lengths of the sides
C =?d
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.

28. 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.
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)(a-b)
2pir^2 + 2pir*h

29. How do you multiply and divide square roots?
y-y1=m(x-x1)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The distance from one point on the circle to another point on the circle.
y = k/x

30. length of a sector
2Length + 2width [or (length + width) x 2]
x°/360 times (2 pi r) - where x is the degrees in the angle
Lwh
A=?r2

31. perimeter of square
A²-b²
Negative
4s
1/2bh

32. Central Angle
Last term
An ange whose vertex is the center of the circle
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

33. How do you calculate the percentage of change?
(a-b)(a²+ab+b²)
Percentage Change = Difference/Original * 100
2(lw+wh+lh)
(a+b)(a-b)

34. Area of a circle
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
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
2Length + 2width [or (length + width) x 2]

35. How do you calculate the probability of two events in a row? (Probability of A and B)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Groups - teams - or committees.
(n degrees/360) * (pi)r^2
Probability A * Probability B

36. 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.
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.
Groups - teams - or committees.
Sum of terms/number of terms

37. What is the unfactored version of (x+y)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.
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.
Negative
x² + 2xy + y²

38. Area of Rectangle
Lw
2lw+2lh+2wh
y2-y1/x2-x1
Groups - teams - or committees.

39. Define the 'Third side' rule for triangles

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40. What is the point-slope form?
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1/x^a
(y-y1)=m(x-x1)

41. What is an 'equilateral' triangle?
The average - mean - median - or mode.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
x²-y²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

42. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
4pir^2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1. Given event A: A + notA = 1.

43. What is the area of a 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.
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
(x1+x2)/2 - (y1+y2)/2

44. Area of Circles
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
y = k/x
A=?r2
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

45. What is a '30:60:90' triangle?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
Opens up

46. Point-Slope form
y-y1=m(x-x1)
N x M
?r²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

47. What is the unfactored version of (x-y)² ?
x² -2xy + y²
The distance from one point on the circle to another point on the circle.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(pi)r^2

48. Area of Square
Between 0 and 1.
Equal
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
S^2

49. If something is possible but not certain - what is the numeric range of probability of it happening?
x² -2xy + y²
Between 0 and 1.
T1 * r^(n-1)
A²-b²

50. What is the average?
Sum of terms/number of terms
Negative
x°/360 times (2 pi r) - where x is the degrees in the angle
Part of a circle connecting two points on the circle.