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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. Rough est. of v3 =
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2pi*r
The distance from one point on the circle to another point on the circle.
1.7

2. Define the mode of a set of numbers.
x² -2xy + y²
(a+b)(a²-ab+b²)
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.
Opens up

3. Surface Area of rectangular prism
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.
4/3pir^3
2lw+2lh+2wh
(n-2)180

4. What is the sum of the inside angles of an n-sided polygon?
The set of points which are all the same distance (the radius) from a certain point (the center).
Sum of the lengths of the sides
(n-2)180
(0 -0)

5. Area of rectangle - square - parallelogram
(n/2) * (t1+tn)
A=bh
Last term
1/2bh

6. What is the unfactored version of (x-y)² ?
x² -2xy + y²
(a+b)(a²-ab+b²)
Order does matter for a permutation - but does not matter for a combination.
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

7. a³-b³
½(base x height) [or (base x height)÷2]
(0 -0)
(a-b)(a²+ab+b²)
Total distance/total time

8. Explain the difference between a digit and a number.

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9. How do you calculate the surface area of a rectangular box?
(a+b)²
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

10. What is the area of a cylinder?
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.
2(pi)r(r+h)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/x^a

11. When you reverse FOIL - the term that needs to add out is the _____
Middle term
Equal
Total distance/total time
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.

12. Diameter
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
T1 + (n-1)d
The distance across the circle through the center of the circle.The diameter is twice the radius.

13. Perimeter of a square
4s (where s = length of a side)
(y-y1)=m(x-x1)
y2-y1/x2-x1
Number of desired outcomes/number of total outcomes

14. Circumference of a circle using radius
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
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(y-y1)=m(x-x1)
2pi*r

15. Explain the special properties of zero.
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.
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.
y2-y1/x2-x1
A²-b²

16. What is the average?
(n degrees/360) * (pi)r^2
Sum of terms/number of terms
A=bh
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.

17. 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.
(x-y)²
(n degrees/360) * 2(pi)r
(n/2) * (t1+tn)

18. What is inversely proportional?
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.
2(pi)r(r+h)
y = k/x
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

19. To divide powers with the same base...
An ange whose vertex is the center of the circle
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
Probability A * Probability B

20. What is the 'distributive law'?
(pi)r^2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
T1 * r^(n-1)/(r-1)

21. What is the circumference of a circle?
Arrangements - orders - schedules - or lists.
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.
2(pi)r
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

22. What do permutation problems often ask for?
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.
Arrangements - orders - schedules - or lists.
T1 * r^(n-1)
T1 * r^(n-1)/(r-1)

23. a²+2ab+b²
(y-y1)=m(x-x1)
A segment connecting the center of a circle to any point on the circle
1/3pir^2*h
(a+b)²

24. What is the factored version of (x+y)(x-y) ?
(pi)r^2
x²-y²
The average - mean - median - or mode.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

25. What do combination problems usually ask for?
Groups - teams - or committees.
(a-b)(a+b)
1/3pir^2*h
Number of desired outcomes/number of total outcomes

26. Perimeter of rectangle
2l+2w
Part of a circle connecting two points on the circle.
Total distance/total time
The total # of possible outcomes.

27. What is an 'equilateral' triangle?
(a+b)(a²-ab+b²)
Part of a circle connecting two points on the circle.
Negative
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

28. What is the formula for the diagonal of any square?
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.
S*v2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Negative

29. What'S the most important thing to remember about charts you'll see on the GRE?
T1 * r^(n-1)/(r-1)
Part of a circle connecting two points on 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.
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.

30. The length of one side of any triangle is ____ than the sum of the other two sides.
Lw
(x-y)²
x°/360 times (?r²) - where x is the degrees in the angle
Less

31. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Percentage Change = Difference/Original * 100
2 pi r
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.
Probability A + Probability B

32. For a bell curve - what three terms might be used to describe the number in the middle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The average - mean - median - or mode.
(y2-y1)/(x2-x1)
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.

33. If x² = 144 - does v144 = x?
y = kx
Not necessarily. This is a trick question - because x could be either positive or negative.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

34. Area of a triangle
x²-y²
1.7
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.
½(base x height) [or (base x height)÷2]

35. Rough est. of v1 =
1/2 h (b1 + b2)
(a+b)²
Opens down
1

36. Radius (Radii)
4/3pir^3
1.7
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A segment connecting the center of a circle to any point on the circle

37. Area of Triangle
1/2bh
y2-y1/x2-x1
(n degrees/360) * 2(pi)r
1.7

38. What is directly proportional?
y = kx
Opens down
(n degrees/360) * 2(pi)r
1/1

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

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

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41. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
(a+b)²
(x1+x2)/2 - (y1+y2)/2
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

42. In intersecting lines - opposite angles are _____.
Equal
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
Sqr( x2 -x1) + (y2- y1)
1/x^a

43. How do you calculate a diagonal inside a 3-dimensional rectangular box?
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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(0 -0)

44. a² - b² is equal to
(n-2)180
Percentage Change = Difference/Original * 100
(pi)r^2(h)
(a+b)(a-b)

45. a²-2ab+b²
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.
y2-y1/x2-x1
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a-b)²

46. Area of Circle
Number of desired outcomes/number of total outcomes
Pi*r^2
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. 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.

47. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Pir^2h
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.
(n/2) * (t1+tn)
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.

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

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49. What is the area of a triangle?
1/2bh
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Lw
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'.

50. What is the 'Third side' rule for triangles?
Negative
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.
Number of desired outcomes/number of total outcomes
1/3pir^2*h