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GRE Math 2

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. If something is certain to happen - how is the probability of this event expressed mathematically?
(y2-y1)/(x2-x1)
x² + 2xy + y²
2(pi)r
1/1

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

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3. Area of Parallelogram
2lw+2lh+2wh
x² + 2xy + y²
Equal
Bh

4. What is the factored version of x² + 2xy + y² ?
(x+y)²
Last term
(x1+x2)/2 - (y1+y2)/2
Sum of terms/number of terms

5. What is the area of a triangle?
½(base x height) [or (base x height)÷2]
Sum of the lengths of the sides
T1 * r^(n-1)/(r-1)
1/2bh

6. Define the formula for calculating slope.
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
1. Given event A: A + notA = 1.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

7. How do you find the nth term of a geometric sequence?
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.
y = k/x
Pir^2h
T1 * r^(n-1)

8. 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.
S^2
(a-b)(a+b)
A²-b²

9. What is the distance formula?
T1 * r^(n-1)/(r-1)
Sqr( x2 -x1) + (y2- y1)
Total distance/total time
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.

10. 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.
1/x^a
The average - mean - median - or mode.
2pi*r

11. What is the 'Third side' rule for triangles?
1/2 h (b1 + b2)
2pir^2 + 2pir*h
(x1+x2)/2 - (y1+y2)/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.

12. What is the side ratio for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
T1 * r^(n-1)
Less

13. What is the probability?
The distance across the circle through the center of the circle.The diameter is twice the radius.
(y-y1)=m(x-x1)
1/x^a
Number of desired outcomes/number of total outcomes

14. Define a factorial of a number - and how it is written.
2pir^2 + 2pir*h
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 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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

15. In a coordinate system - identify the quadrants and describe their location.
x°/360 times (?r²) - where x is the degrees in the angle
Probability A + Probability B
?d OR 2?r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

16. Quadratic Formula
b±[vb²-4ac]/2a
(a+b)(a²-ab+b²)
x² -2xy + y²
Less

17. What is the unfactored version of x²-y² ?
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.
(n/2) * (t1+tn)
(x1+x2)/2 - (y1+y2)/2
(x+y)(x-y)

18. Volume of prism
y2-y1/x2-x1
2lw+2lh+2wh
Pi*r^2
Bh

19. How do you find the nth term of an arithmetic sequence?
(x+y)²
Lwh
T1 + (n-1)d
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.

20. (a+b)(a-b)=
A²-b²
(n/2) * (t1+tn)
4pir^2
Equal

21. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
2lw+2lh+2wh
Not necessarily. This is a trick question - because x could be either positive or negative.
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.

22. Area of Trapezoid
1/3pir^2*h
Number of desired outcomes/number of total outcomes
(a+b)(a²-ab+b²)
1/2 h (b1 + b2)

23. Perimeter of polygon
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.
The set of points which are all the same distance (the radius) from a certain point (the center).
4pir^2
Sum of the lengths of the sides

24. perimeter of square
S^2
1. Given event A: A + notA = 1.
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
4s

25. What is the factored version of (x+y)(x-y) ?
4pir^2
1/2 h (b1 + b2)
x²-y²
T1 * r^(n-1)

26. Volume of sphere
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.
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.
4/3pir^3

27. What is the point-slope form?
Number of desired outcomes/number of total outcomes
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.
Middle term
(y-y1)=m(x-x1)

28. What is the prime factorization of 200?
(a+b)(a-b)
1/3pir^2*h
Number of desired outcomes/number of total outcomes
2x2x2x5x5

29. Area of Triangle
1/2bh
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
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(a-b)(a²+ab+b²)

30. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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+b)²
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.
y = k/x

31. Rough est. of v3 =
1.7
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.
½(base x height) [or (base x height)÷2]
Pi*d

32. Define the 'Third side' rule for triangles

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33. Volume of Cylinder
Pir^2h
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
4pir^2
1/x^a

34. What do combination problems usually ask for?
(y2-y1)/(x2-x1)
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.
Groups - teams - or committees.
(n-2)180

35. What are the side ratios for a 30:60:90 triangle?
1/x^a
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/3pir^2*h
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.

36. Lines reflected over the x or y axis have ____ slopes.
A=?r2
Negative
The set of points which are all the same distance (the radius) from a certain point (the center).
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

37. What is the volume of a solid rectangle?
A segment connecting the center of a circle to any point on the circle
The distance across the circle through the center of the circle.The diameter is twice the radius.
1/3pir^2*h
Lwh

38. Area of a sector
(y-y1)=m(x-x1)
(n degrees/360) * 2(pi)r
(a-b)(a²+ab+b²)
x°/360 times (?r²) - where x is the degrees in the angle

39. Surface Area of Cylinder
2pir^2 + 2pir*h
(x+y)(x-y)
Pi*d
S^2

40. What is the average speed?
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
(a+b)(a²-ab+b²)
The four big angles are equal and the four small angles are equal
Total distance/total time

41. Area of Square
S^2
Between 0 and 1.
The distance across the circle through the center of the circle.The diameter is twice the radius.
x² -2xy + y²

42. Rough est. of v2 =
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.
1.4
Probability A * Probability B
1/x^a

43. Area of Circle
Pi*r^2
The total # of possible outcomes.
Groups - teams - or committees.
The average - mean - median - or mode.

44. 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.
Arrangements - orders - schedules - or lists.
?r²
1/2bh

45. What is the length of an arc?
(pi)r^2
Ac+ad+bc+bd
(n degrees/360) * 2(pi)r
1.4

46. In a parabola - if the first term is positive - the parabola ________.
Less
x°/360 times (?r²) - where x is the degrees in the angle
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.

47. a³-b³
1/2bh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(n degrees/360) * (pi)r^2
(a-b)(a²+ab+b²)

48. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
A=bh
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
S^2

49. Define 'proportionate' values
An ange whose vertex is the center of the circle
½(b1 +b2) x h [or (b1 +b2) x h÷2]
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

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

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GRE Math 2

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