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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 nth term of a geometric sequence?
T1 * r^(n-1)
Between 0 and 1.
The set of points which are all the same distance (the radius) from a certain point (the center).
?r²

2. What is inversely proportional?
y = k/x
1/3Bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

3. Volume of pyramid
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(x-y)²
1/3Bh
Bh

4. a²-b²
(a-b)(a+b)
Negative
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.
Middle term

5. How do you calculate a diagonal inside a 3-dimensional rectangular box?
½(b1 +b2) x h [or (b1 +b2) x h÷2]
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
Opens down

6. How do you calculate the percentage of change?
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.
Percentage Change = Difference/Original * 100
T1 * r^(n-1)/(r-1)
S² - where s = length of a side

7. Define a factorial of a number - and how it is written.
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.
An ange whose vertex is the center of the circle
The four big angles are equal and the four small angles are equal
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.

8. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
Pir^2h
(n degrees/360) * (pi)r^2
The set of points which are all the same distance (the radius) from a certain point (the center).

9. Area of Parallelogram
4pir^2
y2-y1/x2-x1
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.
Bh

10. How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
4s (where s = length of a side)
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.

11. What is the side ratio for a 30:60:90 triangle?
(a-b)²
S*v2
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

12. Circumference of a circle using radius
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
2pi*r
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.
?r²

13. When you reverse FOIL - the term that needs to add out is the _____
(x-y)²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A=?r2
Middle term

14. What is the circumference of a circle?
The distance across the circle through the center of the circle.The diameter is twice the radius.
2(pi)r
Part of a circle connecting two points on the circle.
The set of points which are all the same distance (the radius) from a certain point (the center).

15. How do you find the nth term of an arithmetic sequence?
(n-2)180
1
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
T1 + (n-1)d

16. Circle
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 set of points which are all the same distance (the radius) from a certain point (the center).
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.
Opens up

17. Area of a square
(a+b)(a-b)
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.
S² - where s = length of a side
(x+y)(x-y)

18. a³-b³
Middle term
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'.
x°/360 times (?r²) - where x is the degrees in the angle
(a-b)(a²+ab+b²)

19. What is the area of a sector?
The distance from one point on the circle to another point on the circle.
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.
A²-b²
(n degrees/360) * (pi)r^2

20. How do you find the slope?
y2-y1/x2-x1
Order does matter for a permutation - but does not matter for a combination.
Between 0 and 1.
2(pi)r(r+h)

21. For a bell curve - what three terms might be used to describe the number in the middle?
Less
1/2bh
y = kx
The average - mean - median - or mode.

22. What is the unfactored version of x²-y² ?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1. Given event A: A + notA = 1.
(x+y)(x-y)
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'.

23. What is the factored version of x² + 2xy + y² ?
Pi*r^2
1/2bh
(x+y)²
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.

24. What is the 'distributive law'?
Groups - teams - or committees.
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)
The average - mean - median - or mode.

25. What is the equation of a line?

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26. The length of one side of any triangle is ____ than the sum of the other two sides.
A²-b²
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
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.

27. Area of a trapezoid
2pi*r
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.
T1 * r^(n-1)/(r-1)

28. List two odd behaviors of exponents
1. Given event A: A + notA = 1.
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.
y2-y1/x2-x1
Probability A + Probability B

29. 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.
x°/360 times (2 pi r) - where x is the degrees in the angle
Lw
(a+b)²

30. To divide powers with the same base...
T1 * r^(n-1)
y2-y1/x2-x1
2l+2w
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

31. a²-2ab+b²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4/3pir^3
(a-b)²
T1 + (n-1)d

32. What is the volume of a solid rectangle?
Lwh
y = k/x
(n/2) * (t1+tn)
y-y1=m(x-x1)

33. What is a '30:60:90' triangle?
A=bh
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
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.
1/2bh

34. x^-a =
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
4/3pir^3
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.
1/x^a

35. Radius (Radii)
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.
A segment connecting the center of a circle to any point 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
Equal

36. Circumference of a circle
S² - where s = length of a side
?d OR 2?r
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
1/1

37. In a parabola - if the first term is positive - the parabola ________.
Sqr( x2 -x1) + (y2- y1)
Opens up
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.
x² + 2xy + y²

38. Define the formula for calculating slope.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
T1 * r^(n-1)/(r-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.

39. Arc
Opens up
Part of a circle connecting two points on the circle.
A+b
(n degrees/360) * 2(pi)r

40. Sector
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.
(a-b)(a+b)
(y2-y1)/(x2-x1)
A²-b²

41. Volume of prism
Bh
A=?r2
An ange whose vertex is the center of the circle
2pi*r

42. If something is possible but not certain - what is the numeric range of probability of it happening?
(n degrees/360) * 2(pi)r
T1 + (n-1)d
Opens down
Between 0 and 1.

43. Define 'proportionate' values
Ac+ad+bc+bd
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
4s
2(pi)r

44. Perimeter of rectangle
Groups - teams - or committees.
2l+2w
(a+b)(a²-ab+b²)
Percentage Change = Difference/Original * 100

45. Perimeter (circumference) of a circle
(n-2)180
(0 -0)
2 pi r
(a+b)(a²-ab+b²)

46. What is the length of an arc?
(a-b)²
The set of points which are all the same distance (the radius) from a certain point (the center).
(n degrees/360) * 2(pi)r
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

47. What is the area of a cylinder?
?d OR 2?r
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.
2(pi)r(r+h)
(a-b)²

48. How do you calculate the probability of two events in a row? (Probability of A and B)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
S^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.
Probability A * Probability B

49. Rough est. of v3 =
A=bh
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.
1.7
y = k/x

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

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