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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. Lines reflected over the x or y axis have ____ slopes.
(a+b)(a²-ab+b²)
Between 0 and 1.
Negative
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

2. Volume of Cone
4s (where s = length of a side)
x°/360 times (?r²) - where x is the degrees in the angle
1/3pir^2*h
Part of a circle connecting two points on the circle.

3. Volume of sphere
4/3pir^3
2(pi)r
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.
1/2bh

4. What is an 'equilateral' triangle?
1. Given event A: A + notA = 1.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Pi*d
(n-2)180

5. What is the equation of a line?

6. What is directly proportional?
An ange whose vertex is the center of the circle
1/3pir^2*h
y = kx
The distance across the circle through the center of the circle.The diameter is twice the radius.

7. How do you calculate the probability of two events in a row? (Probability of A and B)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
4s (where s = length of a side)
Probability A * Probability B
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.

8. Perimeter of rectangle
2l+2w
(y-y1)=m(x-x1)
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.
1

9. If something is certain to happen - how is the probability of this event expressed mathematically?
2pir^2 + 2pir*h
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Probability A * Probability B
1/1

10. What is the formula for the diagonal of any square?
Ac+ad+bc+bd
The set of points which are all the same distance (the radius) from a certain point (the center).
Sum of the lengths of the sides
S*v2

11. Define the mode of a set of numbers.
(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.
The total # of possible outcomes.
Pir^2h

12. What is the area of a circle?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Lwh
(pi)r^2
y = k/x

13. What is the factored version of x² -2xy + y² ?
1/x^a
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(x-y)²
S² - where s = length of a side

14. What are the side ratios for a 30:60:90 triangle?
(a-b)(a²+ab+b²)
Opens down
2x2x2x5x5
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

15. What is the 'Third side' rule for triangles?
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

16. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A+b
Probability A + Probability B

17. Surface Area of rectangular prism
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
2lw+2lh+2wh
Bh

18. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
?d OR 2?r
(0 -0)
2pi*r

19. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
Negative
Lwh
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

20. What is the factored version of (x+y)(x-y) ?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x²-y²
Ac+ad+bc+bd
y2-y1/x2-x1

21. Arc
S^2
2 pi r
Middle term
Part of a circle connecting two points on the circle.

22. How do you multiply powers with the same base?
2Length + 2width [or (length + width) x 2]
Less
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.

23. Area of a square
(n-2)180
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
4s
S² - where s = length of a side

24. a³-b³
(a-b)(a²+ab+b²)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2(pi)r(r+h)
Equal

25. perimeter of square
(x+y)²
4s
The set of points which are all the same distance (the radius) from a certain point (the center).
The average - mean - median - or mode.

26. What is inversely proportional?
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.
y = k/x
(n degrees/360) * 2(pi)r
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.

27. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(x+y)²
(y2-y1)/(x2-x1)
Probability A + Probability B

28. What is the area of a sector?
(n degrees/360) * (pi)r^2
(a+b)²
x²-y²
A=bh

29. In a parabola - if the first term is negative - the parabola ________.
Sum of the lengths of the sides
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Opens down
y2-y1/x2-x1

30. What is the average speed?
2pi*r
?d OR 2?r
Total distance/total time
(pi)r^2(h)

31. 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.
Percentage Change = Difference/Original * 100
Part of a circle connecting two points on the circle.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

32. Perimeter of a rectangle
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.
Arrangements - orders - schedules - or lists.
2Length + 2width [or (length + width) x 2]
Negative

33. Area of a trapezoid
Pi*d
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a-b)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.

34. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
(a-b)(a²+ab+b²)
The four big angles are equal and the four small angles are equal
x² + 2xy + y²

35. What is the point-slope form?
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.
(y-y1)=m(x-x1)
Bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

36. Chord
The distance from one point on the circle to another point on the circle.
T1 + (n-1)d
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2(lw+wh+lh)

37. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Pir^2h
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
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.

38. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Part of a circle connecting two points on the circle.
x² + 2xy + y²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(a+b)(a²-ab+b²)

39. x^a * x^b = x^__
x²-y²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A+b
Opens up

40. What is the area of a cylinder?
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Opens down
2(pi)r(r+h)

41. Volume of pyramid
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'.
1/3Bh
1/2 h (b1 + b2)
(n degrees/360) * 2(pi)r

42. What is the area of a solid rectangle?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2(lw+wh+lh)
S² - where s = length of a side

43. Area of a triangle
½(base x height) [or (base x height)÷2]
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
The average - mean - median - or mode.
y = k/x

44. Define the range of a set of numbers.
(y2-y1)/(x2-x1)
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.
2pir^2 + 2pir*h
(n/2) * (t1+tn)

45. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
1/3Bh
Number of desired outcomes/number of total outcomes
Order does matter for a permutation - but does not matter for a combination.

46. Perimeter (circumference) of a circle
Bh
2 pi r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

47. Perimeter of polygon
Sum of the lengths of the sides
(a-b)(a²+ab+b²)
An ange whose vertex is the center of the circle
?r²

48. How do you find the sum of a geometric sequence?
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.
T1 * r^(n-1)/(r-1)
2(pi)r(r+h)
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. What is a 'Right isosceles' triangle?
1/2 h (b1 + b2)
C =?d
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.
2(pi)r

50. Surface Area of Sphere
4pir^2
2(pi)r
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.
Pi*d