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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. Surface Area of Sphere
Pi*d
Middle term
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.
4pir^2

2. Sector
S² - where s = length of a side
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.
(n-2)180
1/2 h (b1 + b2)

3. Does order matter for a permutation? How about for a combination?
S^2
Probability A + Probability B
Order does matter for a permutation - but does not matter for a combination.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

4. Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The average - mean - median - or mode.
(n-2)180
Pir^2h

5. (a+b)(c+d)
Last term
Ac+ad+bc+bd
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.
2pir^2 + 2pir*h

6. 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.
A=bh
Equal
Pi*d

7. How do you solve a permutation?
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
(a+b)(a-b)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a+b)²

8. Perimeter of a rectangle
4s
Pi*r^2
A segment connecting the center of a circle to any point on the circle
2Length + 2width [or (length + width) x 2]

9. Volume of Cylinder
Pir^2h
2lw+2lh+2wh
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

10. perimeter of square
4s (where s = length of a side)
A+b
4s
(x1+x2)/2 - (y1+y2)/2

11. What is the factored version of x² -2xy + y² ?
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.
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.
(x-y)²
2pir^2 + 2pir*h

12. What is directly proportional?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
N x M
y = kx
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.

13. Volume of sphere
4/3pir^3
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x² -2xy + y²
1/2bh

14. Define the mode of a set of numbers.
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.
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.
(y-y1)=m(x-x1)
Pi*d

15. What do permutation problems often ask for?
2(lw+wh+lh)
Sum of the lengths of the sides
(x+y)(x-y)
Arrangements - orders - schedules - or lists.

16. Slope
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a+b)(a-b)
Pi*d
(y2-y1)/(x2-x1)

17. What is a 'Right isosceles' triangle?
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.
(pi)r^2
S^2
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

18. In intersecting lines - opposite angles are _____.
Equal
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.
(0 -0)
The distance from one point on the circle to another point on the circle.

19. The probability of an event happening and the probability of an event NOT happening must add up to what number?
2(pi)r(r+h)
1. Given event A: A + notA = 1.
?r²
½(base x height) [or (base x height)÷2]

20. a²-2ab+b²
4/3pir^3
S*v2
(a-b)²
(a+b)²

21. Area of Parallelogram
Bh
Part of a circle connecting two points on the circle.
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+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.

22. Area of Trapezoid
1/2 h (b1 + b2)
A=bh
2(pi)r(r+h)
(a-b)(a+b)

23. 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.
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
Part of a circle connecting two points on the circle.
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.

24. Volume of Cone
A+b
The four big angles are equal and the four small angles are equal
(n/2) * (t1+tn)
1/3pir^2*h

25. (a+b)(a-b)=
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2x2x2x5x5
A²-b²

26. How do you find the midpoint?
C =?d
(x1+x2)/2 - (y1+y2)/2
S*v2
The distance across the circle through the center of the circle.The diameter is twice the radius.

27. Explain the special properties of zero.
Middle term
x² + 2xy + y²
Opens down
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.

28. Area of rectangle - square - parallelogram
A=bh
(a+b)²
Bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

29. What is the factored version of (x+y)(x-y) ?
N x M
(x+y)²
1/3Bh
x²-y²

30. List two odd behaviors of exponents
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. 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.
(pi)r^2
(0 -0)

31. 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.
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.
N x M
2(lw+wh+lh)

32. Rough est. of v1 =
(n-2)180
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.
Ac+ad+bc+bd

33. Area of Circles
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.
2l+2w
(n/2) * (t1+tn)
A=?r2

34. Perimeter of rectangle
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.
(n degrees/360) * (pi)r^2
2l+2w
Equal

35. a² - b² is equal to
1. Given event A: A + notA = 1.
Probability A * Probability B
(a+b)(a-b)
Opens up

36. Arc
Part of a circle connecting two points on the circle.
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.
A=?r2
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.

37. When you reverse FOIL - the term that needs to multiply out is the _____
x°/360 times (?r²) - where x is the degrees in the angle
The four big angles are equal and the four small angles are equal
x² + 2xy + y²
Last term

38. What is the formula for the diagonal of any square?
1.7
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.
y = kx
S*v2

39. In a coordinate system - what is the origin?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(0 -0)
4pir^2
y = k/x

40. What is the area of a circle?
Negative
The set of points which are all the same distance (the radius) from a certain point (the center).
(pi)r^2
(x+y)²

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

42. Central Angle
An ange whose vertex is the center of the circle
A²-b²
Pi*r^2
x²-y²

43. What is a '30:60:90' triangle?
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
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
x°/360 times (2 pi r) - where x is the degrees in the angle
1/2bh

44. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
x² -2xy + y²
2pir^2 + 2pir*h
1

45. x^-a =
1/x^a
2lw+2lh+2wh
x² -2xy + y²
(n degrees/360) * 2(pi)r

46. In a coordinate system - identify the quadrants and describe their location.
Number of desired outcomes/number of total outcomes
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
½(base x height) [or (base x height)÷2]
1/3pir^2*h

47. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
1/2bh
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
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.

48. What is the area of a sector?
(n degrees/360) * (pi)r^2
Less
y = kx
The total # of possible outcomes.

49. 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
T1 + (n-1)d
Groups - teams - or committees.
y = k/x

50. Perimeter of a square
The distance from one point on the circle to another point on the circle.
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.
4s (where s = length of a side)
(pi)r^2(h)