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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 prime factorization of 200?
2x2x2x5x5
Between 0 and 1.
2pi*r
4s (where s = length of a side)

2. How do you find the sum of a geometric sequence?
A=?r2
T1 * r^(n-1)/(r-1)
Bh
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

3. How do you find the nth term of a geometric sequence?
x² + 2xy + y²
2(pi)r
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
T1 * r^(n-1)

4. Define 'proportionate' values
Ac+ad+bc+bd
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
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.

5. In intersecting lines - opposite angles are _____.
Pir^2h
Equal
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

6. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
1/3pir^2*h
T1 * r^(n-1)/(r-1)
Number of desired outcomes/number of total outcomes

7. (a+b)(c+d)
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.
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.
Part of a circle connecting two points on the circle.
Ac+ad+bc+bd

8. What do combination problems usually ask for?
Groups - teams - or committees.
1.4
x°/360 times (2 pi r) - where x is the degrees in the angle
(n degrees/360) * 2(pi)r

9. Explain the special properties of zero.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Opens up
4/3pir^3

10. How do you calculate the surface area of a rectangular box?
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.
Bh
Equal
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.

11. What is the area of a solid rectangle?
2(pi)r(r+h)
½(base x height) [or (base x height)÷2]
2(lw+wh+lh)
(0 -0)

12. Define a factorial of a number - and how it is written.
Ac+ad+bc+bd
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.
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.

13. Volume of Cone
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'.
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.
A=?r2
1/3pir^2*h

14. Area of Triangle
2x2x2x5x5
(n degrees/360) * (pi)r^2
1/2bh
S^2

15. Area of a square
Opens down
2(pi)r
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
S² - where s = length of a side

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

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17. What is an 'equilateral' triangle?
1.7
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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)

18. If x² = 144 - does v144 = x?
4s (where s = length of a side)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Not necessarily. This is a trick question - because x could be either positive or negative.
½(base x height) [or (base x height)÷2]

19. Rough est. of v2 =
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Bh
4s
1.4

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

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21. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
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
4s
Equal

22. What is the factored version of x² -2xy + y² ?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(x-y)²
Between 0 and 1.

23. What is the factored version of (x+y)(x-y) ?
S^2
x² -2xy + y²
x²-y²
C =?d

24. What is the area of a cylinder?
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
2(pi)r(r+h)
(a-b)(a²+ab+b²)
4s (where s = length of a side)

25. x^-a =
T1 + (n-1)d
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.
An ange whose vertex is the center of the circle
1/x^a

26. Chord
The distance from one point on the circle to another point on the circle.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Last term

27. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
2x2x2x5x5
Probability A * Probability B
1/2bh

28. What is the volume of a solid rectangle?
Bh
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.
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.
Lwh

29. Volume of pyramid
1/3Bh
2(pi)r
(x-y)²
Less

30. Circumference of cirlce using diameter
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'.
Pi*d
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.
(n/2) * (t1+tn)

31. Arc
Part of a circle connecting two points on the circle.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Order does matter for a permutation - but does not matter for a combination.

32. Circumference of a circle using radius
Opens down
2pi*r
4s (where s = length of a side)
The distance from one point on the circle to another point on the circle.

33. What is the point-slope form?
y = kx
(y-y1)=m(x-x1)
x²-y²
T1 * r^(n-1)

34. If something is certain to happen - how is the probability of this event expressed mathematically?
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
1/1
Percentage Change = Difference/Original * 100
(a+b)(a²-ab+b²)

35. What do permutation problems often ask for?
1/2bh
S*v2
Arrangements - orders - schedules - or lists.
C =?d

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

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37. What is the unfactored version of (x+y)² ?
½(base x height) [or (base x height)÷2]
1.4
x² + 2xy + y²
2pir^2 + 2pir*h

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

39. Surface Area of rectangular prism
(pi)r^2(h)
2lw+2lh+2wh
(a+b)(a²-ab+b²)
2x2x2x5x5

40. What are the side ratios for a 30:60:90 triangle?
An ange whose vertex is the center of the circle
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4s
x²-y²

41. Volume of Cylinder
Pir^2h
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.
S*v2
(a+b)(a²-ab+b²)

42. Perimeter of rectangle
?r²
Sum of the lengths of the sides
2l+2w
2(pi)r

43. Area of Circles
A=?r2
2lw+2lh+2wh
½(base x height) [or (base x height)÷2]
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.

44. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
S² - where s = length of a side
2x2x2x5x5
Sum of the lengths of the sides

45. 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.
4/3pir^3
x°/360 times (2 pi r) - where x is the degrees in the angle
Sqr( x2 -x1) + (y2- y1)

46. Area of Trapezoid
x°/360 times (?r²) - where x is the degrees in the angle
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/2bh
1/2 h (b1 + b2)

47. Area of Square
(n degrees/360) * 2(pi)r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
S^2
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.

48. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
½(base x height) [or (base x height)÷2]
Sqr( x2 -x1) + (y2- y1)
(n-2)180
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.

49. 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.
Pi*r^2
A²-b²
x°/360 times (?r²) - where x is the degrees in the angle

50. When a line crosses two parallel lines - ________.
x²-y²
Total distance/total time
(x+y)(x-y)
The four big angles are equal and the four small angles are equal