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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 find the sum of an arithmetic sequence?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(n/2) * (t1+tn)
A=?r2
2pi*r

2. How do you calculate the surface area of a rectangular box?
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.
Equal
2(lw+wh+lh)
x² + 2xy + y²

3. What is the surface area of a cylinder?
4s
Sum of the lengths of the sides
2l+2w
2(pi)r(r+h)

4. Surface Area of rectangular prism
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
2lw+2lh+2wh
T1 * r^(n-1)/(r-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.

5. In a parabola - if the first term is negative - the parabola ________.
1
Opens down
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.

6. The length of one side of any triangle is ____ than the sum of the other two sides.
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.
Less
(pi)r^2(h)
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.

7. Diameter
Opens down
2 pi r
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The distance across the circle through the center of the circle.The diameter is twice the radius.

8. What is 'absolute value' - and how is it represented?

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9. (a+b)(a-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.
Order does matter for a permutation - but does not matter for a combination.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
A²-b²

10. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
A=?r2
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.

11. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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
2(pi)r(r+h)
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.
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.

12. What is the formula for the diagonal of any square?
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a-b)(a+b)
S*v2

13. Central Angle
A segment connecting the center of a circle to any point on the circle
x²-y²
An ange whose vertex is the center of the circle
(x+y)²

14. Area of Triangle
Not necessarily. This is a trick question - because x could be either positive or negative.
1/2bh
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.
Sqr( x2 -x1) + (y2- y1)

15. Circle
The set of points which are all the same distance (the radius) from a certain point (the center).
(x+y)(x-y)
4s (where s = length of a side)
(y2-y1)/(x2-x1)

16. What is the unfactored version of (x-y)² ?
The average - mean - median - or mode.
1/1
x² -2xy + y²
Bh

17. What is the volume of a cylinder?
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
Middle term
(pi)r^2(h)
The total # of possible outcomes.

18. What is the prime factorization of 200?
2x2x2x5x5
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
(pi)r^2(h)

19. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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=?r2
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.

20. Define 'proportionate' values
T1 * r^(n-1)/(r-1)
1/x^a
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1/1

21. How do you find the sum of a geometric sequence?
Sum of terms/number of terms
(a+b)(a²-ab+b²)
T1 * r^(n-1)/(r-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.

22. For a bell curve - what three terms might be used to describe the number in the middle?
2pi*r
Pi*d
The distance from one point on the circle to another point on the circle.
The average - mean - median - or mode.

23. What is the area of a sector?
(n degrees/360) * (pi)r^2
2l+2w
1/x^a
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

24. The probability of an event happening and the probability of an event NOT happening must add up to what number?
(y-y1)=m(x-x1)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2Length + 2width [or (length + width) x 2]
1. Given event A: A + notA = 1.

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

26. Define a factorial of a number - and how it is written.
The set of points which are all the same distance (the radius) from a certain point (the center).
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.
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

27. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
2x2x2x5x5
1.7
(n-2)180

28. How do you solve a permutation?
2(lw+wh+lh)
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
2(pi)r
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.

29. Circumference of a circle
?d OR 2?r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1. Given event A: A + notA = 1.
The distance from one point on the circle to another point on the circle.

30. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2(pi)r(r+h)
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

31. To divide powers with the same base...
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Lwh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Part of a circle connecting two points on the circle.

32. What is the factored version of (x+y)(x-y) ?
x°/360 times (2 pi r) - where x is the degrees in the angle
Equal
(a+b)(a-b)
x²-y²

33. What is the area of a solid rectangle?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1/3Bh
2(lw+wh+lh)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

34. What is the area of a triangle?
x² + 2xy + y²
The distance across the circle through the center of the circle.The diameter is twice the radius.
(a-b)²
1/2bh

35. What is the average speed?
x² + 2xy + y²
Percentage Change = Difference/Original * 100
Total distance/total time
C =?d

36. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
(0 -0)
Sum of terms/number of terms
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
y-y1=m(x-x1)

37. How do you find the midpoint?
Opens up
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.
(x1+x2)/2 - (y1+y2)/2
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.

38. When you reverse FOIL - the term that needs to multiply out is the _____
1.7
Last term
Equal
The distance across the circle through the center of the circle.The diameter is twice the radius.

39. Surface Area of Sphere
(a+b)(a-b)
4s
4pir^2
b±[vb²-4ac]/2a

40. Area of Circle
Middle term
4/3pir^3
A+b
Pi*r^2

41. How do you find the slope?
x²-y²
C =?d
y2-y1/x2-x1
Less

42. 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.
(a+b)²
1.7
Opens up

43. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
1/2bh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.

44. a² - b² is equal to
1/2bh
x² + 2xy + y²
(a+b)(a-b)
Bh

45. What'S the most important thing to remember about charts you'll see on the GRE?
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.
(n-2)180
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Middle term

46. What is the volume of a solid rectangle?
Lwh
1/x^a
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.
2Length + 2width [or (length + width) x 2]

47. What is the side ratio 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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
y2-y1/x2-x1
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

48. a³-b³
Probability A * Probability B
4s (where s = length of a side)
(x+y)²
(a-b)(a²+ab+b²)

49. Area of a square
S² - where s = length of a side
4pir^2
(a-b)²
A=bh

50. When a line crosses two parallel lines - ________.
T1 + (n-1)d
The four big angles are equal and the four small angles are equal
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2(pi)r