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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 probability?
?r²
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.
Number of desired outcomes/number of total outcomes
1/3pir^2*h

2. What is the unfactored version of (x-y)² ?
1/3Bh
x² -2xy + y²
Between 0 and 1.
A+b

3. What is the volume of a cylinder?
Opens down
x²-y²
(pi)r^2(h)
?d OR 2?r

4. How do you calculate the surface area of a rectangular box?
(pi)r^2(h)
Percentage Change = Difference/Original * 100
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.
(x-y)²

5. What is the 'Third side' rule for triangles?
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.
T1 * r^(n-1)
x°/360 times (2 pi r) - where x is the degrees in the angle
A segment connecting the center of a circle to any point on the circle

6. Area of Square
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
S^2
A segment connecting the center of a circle to any point on the circle
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

7. Define the 'Third side' rule for triangles

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8. What is the factored version of (x+y)(x-y) ?
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.
S^2
x²-y²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

9. Area of Rectangle
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Lw
The average - mean - median - or mode.
x²-y²

10. Area of a sector
A=?r2
(pi)r^2(h)
x°/360 times (?r²) - where x is the degrees in the angle
Pir^2h

11. What is the area of a sector?
b±[vb²-4ac]/2a
2 pi r
(n degrees/360) * (pi)r^2
Total distance/total time

12. Quadratic Formula
x°/360 times (?r²) - where x is the degrees in the angle
Not necessarily. This is a trick question - because x could be either positive or negative.
b±[vb²-4ac]/2a
(n degrees/360) * 2(pi)r

13. Volume of pyramid
2(lw+wh+lh)
1/3Bh
(pi)r^2(h)
(n degrees/360) * 2(pi)r

14. Arc
(n/2) * (t1+tn)
Part of a circle connecting two points on the circle.
Percentage Change = Difference/Original * 100
1

15. What number goes on the bottom of a probability fraction?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Total distance/total time
(x-y)²
The total # of possible outcomes.

16. Explain the special properties of zero.
N x M
Between 0 and 1.
x²-y²
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.

17. Perimeter (circumference) of a circle
1/3Bh
4s (where s = length of a side)
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'.
2 pi r

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

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19. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
A segment connecting the center of a circle to any point on the circle
Number of desired outcomes/number of total outcomes
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
(0 -0)

20. In a parabola - if the first term is negative - the parabola ________.
The distance from one point on the circle to another point on the circle.
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.
Opens down

21. Point-Slope form
Middle term
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Equal
y-y1=m(x-x1)

22. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
Arrangements - orders - schedules - or lists.
Sum of the lengths of the sides
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
N x M

23. What is the point-slope form?
(n degrees/360) * (pi)r^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.
2lw+2lh+2wh
(y-y1)=m(x-x1)

24. What is the area of a triangle?
A+b
Not necessarily. This is a trick question - because x could be either positive or negative.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/2bh

25. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
4pir^2
Probability A + Probability B
4/3pir^3
Total distance/total time

26. Perimeter of a square
2Length + 2width [or (length + width) x 2]
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4s (where s = length of a side)
Sum of terms/number of terms

27. Define the formula for calculating slope.
b±[vb²-4ac]/2a
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2Length + 2width [or (length + width) x 2]
T1 * r^(n-1)

28. In intersecting lines - opposite angles are _____.
Equal
Number of desired outcomes/number of total outcomes
(a-b)(a²+ab+b²)
(y-y1)=m(x-x1)

29. How do you find the sum of a geometric sequence?
Opens down
(n/2) * (t1+tn)
1.7
T1 * r^(n-1)/(r-1)

30. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
1/1
y = kx
Bh

31. Volume of Cone
Between 0 and 1.
?d OR 2?r
1/3pir^2*h
Sum of terms/number of terms

32. perimeter of square
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.
(x-y)²
4s
y2-y1/x2-x1

33. Surface Area of Sphere
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.
4pir^2
Total distance/total time
An ange whose vertex is the center of the circle

34. The length of one side of any triangle is ____ than the sum of the other two sides.
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.
(pi)r^2(h)
Bh
Less

35. To divide powers with the same base...
4pir^2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
N x M

36. What is the average?
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Sum of terms/number of terms
1. Given event A: A + notA = 1.
T1 + (n-1)d

37. (a+b)(a-b)=
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.
A²-b²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(a+b)(a-b)

38. If x² = 144 - does v144 = x?
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.
S² - where s = length of a side
Not necessarily. This is a trick question - because x could be either positive or 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

39. List two odd behaviors of exponents
Pi*d
Bh
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.
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.

40. a² - b² is equal to
Percentage Change = Difference/Original * 100
Between 0 and 1.
(x1+x2)/2 - (y1+y2)/2
(a+b)(a-b)

41. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
4s
2pi*r

42. For a bell curve - what three terms might be used to describe the number in the middle?
Probability A + Probability B
The average - mean - median - or mode.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1/3pir^2*h

43. What is the factored version of x² + 2xy + y² ?
(a-b)²
(x+y)²
(n-2)180
Between 0 and 1.

44. What is the unfactored version of (x+y)² ?
x² + 2xy + y²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Probability A * Probability B
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

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

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46. Volume of prism
(a-b)²
(0 -0)
Bh
1

47. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
Sqr( x2 -x1) + (y2- y1)
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.
Between 0 and 1.

48. What is the area of a cylinder?
2(pi)r(r+h)
A segment connecting the center of a circle to any point on the circle
C =?d
A²-b²

49. What is the side ratio for a 30:60:90 triangle?
(y-y1)=m(x-x1)
1. Given event A: A + notA = 1.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x² + 2xy + y²

50. Area of a square
S² - where s = length of a side
2(lw+wh+lh)
Between 0 and 1.
(x+y)²