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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. What is the area of a solid rectangle?
Pi*d
2(lw+wh+lh)
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 from one point on the circle to another point on the circle.

2. If something is possible but not certain - what is the numeric range of probability of it happening?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Between 0 and 1.
2(pi)r
2(lw+wh+lh)

3. Circumference of a 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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
?d OR 2?r

4. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
Last term
Sqr( x2 -x1) + (y2- y1)
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

5. x^-a =
1/x^a
(a-b)(a+b)
Pir^2h
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.

6. Circumference of cirlce using diameter
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.
Pi*d
Bh
1/2bh

7. Volume of pyramid
1/3Bh
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 degrees/360) * 2(pi)r
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.

8. Define a factorial of a number - and how it is written.
(n-2)180
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.
1.4
y-y1=m(x-x1)

9. How do you find the sum of an arithmetic sequence?
1
(y-y1)=m(x-x1)
(n/2) * (t1+tn)
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. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
C =?d
(a-b)(a+b)
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. a³+b³
(a+b)(a²-ab+b²)
Last term
y2-y1/x2-x1
S*v2

12. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Probability A + Probability B
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.
1. Given event A: A + notA = 1.

13. (a+b)(a-b)=
(x+y)(x-y)
A²-b²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

14. The length of one side of any triangle is ____ than the sum of the other two sides.
(a+b)(a-b)
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.
Less
2pi*r

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

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16. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

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17. If something is certain to happen - how is the probability of this event expressed mathematically?
(pi)r^2
1
(x-y)²
1/1

18. List two odd behaviors of exponents
Equal
Pi*r^2
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

19. How do you find the nth term of an arithmetic sequence?
2pir^2 + 2pir*h
Arrangements - orders - schedules - or lists.
(x+y)(x-y)
T1 + (n-1)d

20. Perimeter (circumference) of a circle
A=?r2
2l+2w
2 pi r
The average - mean - median - or mode.

21. Area of Circle
Number of desired outcomes/number of total outcomes
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2(pi)r(r+h)
Pi*r^2

22. Area of Triangle
1/2bh
y2-y1/x2-x1
y = kx
Last term

23. If x² = 144 - does v144 = x?
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.
(a+b)(a-b)
Lw
Not necessarily. This is a trick question - because x could be either positive or negative.

24. What do combination problems usually ask for?
2Length + 2width [or (length + width) x 2]
Lw
Less
Groups - teams - or committees.

25. Lines reflected over the x or y axis have ____ slopes.
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.
S^2
4pir^2
Negative

26. What is the point-slope form?
S*v2
(y-y1)=m(x-x1)
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.

27. How do you calculate the surface area of a rectangular box?
T1 * r^(n-1)
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4pir^2

28. perimeter of square
(n degrees/360) * 2(pi)r
4s
Groups - teams - or committees.
S*v2

29. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
b±[vb²-4ac]/2a
Bh
1/3pir^2*h
N x M

30. What is the average?
y-y1=m(x-x1)
4pir^2
S^2
Sum of terms/number of terms

31. Perimeter of polygon
(a+b)(a²-ab+b²)
The four big angles are equal and the four small angles are equal
Sum of the lengths of the sides
A=bh

32. When a line crosses two parallel lines - ________.
The four big angles are equal and the four small angles are equal
An ange whose vertex is the center of the circle
1
Probability A + Probability B

33. Quadratic Formula
b±[vb²-4ac]/2a
Pir^2h
(a+b)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.

34. a²+2ab+b²
(a+b)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.
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
Not necessarily. This is a trick question - because x could be either positive or negative.

35. What is the 'distributive law'?
(pi)r^2(h)
2l+2w
(a+b)²
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.

36. Chord
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
N x M
The distance from one point on the circle to another point on the circle.
x°/360 times (2 pi r) - where x is the degrees in the angle

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

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38. 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.
(a+b)(a-b)
2(pi)r(r+h)

39. What must be true before a quadratic equation can be solved?

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40. Area of a square
(a-b)(a+b)
S² - where s = length of a side
2 pi r
A²-b²

41. Area of Parallelogram
Probability A * Probability B
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Bh

42. 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.
T1 * r^(n-1)/(r-1)
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.
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.

43. Circle
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'.
?d OR 2?r
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 set of points which are all the same distance (the radius) from a certain point (the center).

44. Area of Rectangle
Lw
(0 -0)
4/3pir^3
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.

45. What is the sum of the inside angles of an n-sided polygon?
S² - where s = length of a side
y = kx
T1 + (n-1)d
(n-2)180

46. What is the area of a circle?
(pi)r^2
The total # of possible outcomes.
A²-b²
(n/2) * (t1+tn)

47. When you reverse FOIL - the term that needs to multiply out is the _____
Not necessarily. This is a trick question - because x could be either positive or negative.
Order does matter for a permutation - but does not matter for a combination.
T1 * r^(n-1)
Last term

48. What is the area of a triangle?
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.
T1 * r^(n-1)
1/2bh
Opens down

49. How do you find the slope?
Part of a circle connecting two points on the circle.
The distance from one point on the circle to another point on 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.
y2-y1/x2-x1

50. Volume of Cone
Groups - teams - or committees.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Part of a circle connecting two points on the circle.
1/3pir^2*h