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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. a² - b² is equal to
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).
(a+b)(a-b)
(a-b)(a+b)

2. What is the area of a circle?
(x+y)(x-y)
Sum of terms/number of terms
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
(pi)r^2

3. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
Sum of terms/number of terms
4s (where s = length of a side)
Arrangements - orders - schedules - or lists.

4. What is the length of an arc?
(n degrees/360) * 2(pi)r
Lw
Lwh
(x-y)²

5. x^a * x^b = x^__
A+b
The set of points which are all the same distance (the radius) from a certain point (the center).
Total distance/total time
(a-b)²

6. Chord
(a-b)(a+b)
The total # of possible outcomes.
The distance from one point on the circle to another point on the circle.
Order does matter for a permutation - but does not matter for a combination.

7. Area of a trapezoid
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
An ange whose vertex is the center of the circle

8. To divide powers with the same base...
?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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Ac+ad+bc+bd

9. What is the unfactored version of x²-y² ?
(x+y)(x-y)
The total # of possible outcomes.
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.
Bh

10. 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.
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
(x+y)(x-y)
(n-2)180

11. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
1/2bh
Sqr( x2 -x1) + (y2- y1)
A=bh

12. What is the factored version of x² -2xy + y² ?
A²-b²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(x-y)²
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.

13. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
Equal
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Arrangements - orders - schedules - or lists.

14. Area of Circle
Pi*r^2
(pi)r^2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.

15. a²+2ab+b²
A=?r2
(a+b)²
?d OR 2?r
T1 * r^(n-1)

16. How do you calculate the percentage of change?
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.
2(pi)r(r+h)
Percentage Change = Difference/Original * 100
?d OR 2?r

17. Perimeter (circumference) of a circle
2 pi r
2pir^2 + 2pir*h
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.
1

18. Slope
A+b
Bh
(y2-y1)/(x2-x1)
2pir^2 + 2pir*h

19. Rough est. of v1 =
1
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Ac+ad+bc+bd
(a+b)(a²-ab+b²)

20. What is directly proportional?
T1 * r^(n-1)
y2-y1/x2-x1
?d OR 2?r
y = kx

21. What is the volume of a solid rectangle?
(n degrees/360) * 2(pi)r
Opens up
Lwh
x°/360 times (2 pi r) - where x is the degrees in the angle

22. What are the side ratios for a 30:60:90 triangle?
1/2 h (b1 + b2)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(n/2) * (t1+tn)
1/3pir^2*h

23. Quadratic Formula
x²-y²
b±[vb²-4ac]/2a
½(base x height) [or (base x height)÷2]
1/3pir^2*h

24. What is the area of a solid rectangle?
Probability A + Probability B
Groups - teams - or committees.
(n degrees/360) * 2(pi)r
2(lw+wh+lh)

25. a³-b³
(a-b)(a²+ab+b²)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Opens down
Sum of the lengths of the sides

26. perimeter of square
4s
The average - mean - median - or mode.
2Length + 2width [or (length + width) x 2]
2pi*r

27. Perimeter of rectangle
Sum of terms/number of terms
(x-y)²
2l+2w
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

28. What is inversely proportional?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A=bh
Bh
y = k/x

29. Define the range of a set of numbers.
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.
The set of points which are all the same distance (the radius) from a certain point (the center).
(x+y)(x-y)
Arrangements - orders - schedules - or lists.

30. Define a factorial of a number - and how it is written.
The distance from one point on the circle to another point on the circle.
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-y²
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.

31. Area of rectangle - square - parallelogram
Arrangements - orders - schedules - or lists.
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=bh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

32. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
(a-b)²
1/3pir^2*h
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

33. Volume of sphere
Part of a circle connecting two points on the circle.
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
x²-y²
4/3pir^3

34. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
2lw+2lh+2wh
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.
2x2x2x5x5

35. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
Probability A + Probability B
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

36. Circumference of a circle using radius
2pi*r
½(base x height) [or (base x height)÷2]
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.
Equal

37. Point-Slope form
b±[vb²-4ac]/2a
x²-y²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
y-y1=m(x-x1)

38. What is the unfactored version of (x-y)² ?
2l+2w
x°/360 times (2 pi r) - where x is the degrees in the angle
x² -2xy + y²
Sqr( x2 -x1) + (y2- y1)

39. What is the factored version of x² + 2xy + y² ?
(x+y)²
?r²
x² -2xy + y²
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.

40. How do you solve a permutation?
(a-b)(a+b)
N x M
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
Sqr( x2 -x1) + (y2- y1)

41. What is the prime factorization of 200?
2x2x2x5x5
A²-b²
The total # of possible outcomes.
1

42. What is the side ratio for a Right Isosceles triangle?
Middle term
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.
(pi)r^2(h)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

43. Diameter
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.
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.
(n/2) * (t1+tn)

44. Volume of Cylinder
Bh
Lw
The distance across the circle through the center of the circle.The diameter is twice the radius.
Pir^2h

45. Area of a circle
x°/360 times (?r²) - where x is the degrees in the angle
S*v2
?r²
An ange whose vertex is the center of the circle

46. If x² = 144 - does v144 = x?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
y2-y1/x2-x1
Not necessarily. This is a trick question - because x could be either positive or negative.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

47. What is the unfactored version of (x+y)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.
Last term
x² + 2xy + y²
2(lw+wh+lh)

48. How do you find the sum of an arithmetic sequence?
2 pi r
(n/2) * (t1+tn)
C =?d
2lw+2lh+2wh

49. Does order matter for a permutation? How about for a combination?
?r²
Not necessarily. This is a trick question - because x could be either positive or negative.
Less
Order does matter for a permutation - but does not matter for a combination.

50. 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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
4/3pir^3
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.