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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 area of a sector?
x°/360 times (?r²) - where x is the degrees in the angle
(pi)r^2
½(base x height) [or (base x height)÷2]
(n degrees/360) * (pi)r^2

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

3. Rough est. of v1 =
1
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(x+y)(x-y)
x°/360 times (?r²) - where x is the degrees in the angle

4. Perimeter of a rectangle
(n/2) * (t1+tn)
4/3pir^3
2Length + 2width [or (length + width) x 2]
(a+b)(a²-ab+b²)

5. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
(x1+x2)/2 - (y1+y2)/2
Pir^2h
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.

6. How do you calculate the surface area of a rectangular box?
1/1
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.
(y2-y1)/(x2-x1)

7. What is inversely proportional?
(x+y)²
Number of desired outcomes/number of total outcomes
y = k/x
(n degrees/360) * 2(pi)r

8. In intersecting lines - opposite angles are _____.
Equal
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/2bh
The average - mean - median - or mode.

9. How do you find the midpoint?
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
y2-y1/x2-x1
(x1+x2)/2 - (y1+y2)/2

10. What is the factored version of (x+y)(x-y) ?
x²-y²
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.
Pir^2h
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

11. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.
1.4
(x1+x2)/2 - (y1+y2)/2

12. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Pi*d
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.
Probability A * Probability B

13. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
Ac+ad+bc+bd
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 average - mean - median - or mode.

14. (a+b)(c+d)
Order does matter for a permutation - but does not matter for a combination.
2x2x2x5x5
Ac+ad+bc+bd
The average - mean - median - or mode.

15. If x² = 144 - does v144 = x?
Opens up
Total distance/total time
Bh
Not necessarily. This is a trick question - because x could be either positive or negative.

16. What is the area of a solid rectangle?
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(lw+wh+lh)
Part of a circle connecting two points on the circle.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

17. How do you find the nth term of a geometric sequence?
y = k/x
T1 * r^(n-1)
Opens down
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

18. length of a sector
T1 * r^(n-1)/(r-1)
x°/360 times (2 pi r) - where x is the degrees in the angle
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
S*v2

19. a³-b³
(a-b)(a²+ab+b²)
(n degrees/360) * (pi)r^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.
Between 0 and 1.

20. What is the 'Third side' rule for triangles?
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 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.
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
Between 0 and 1.

21. How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2pir^2 + 2pir*h
2lw+2lh+2wh
Equal

22. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Groups - teams - or committees.
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.
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.

23. Volume of pyramid
1/3Bh
Opens up
2(pi)r
A=bh

24. a² - b² is equal to
(a+b)(a-b)
?d OR 2?r
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
Lw

25. Define the 'Third side' rule for triangles

26. Area of Trapezoid
Equal
1/2 h (b1 + b2)
b±[vb²-4ac]/2a
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

27. Area of a sector
2l+2w
x°/360 times (?r²) - where x is the degrees in the angle
T1 * r^(n-1)
1/x^a

28. What is the sum of the inside angles of an n-sided 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.
1/x^a
The set of points which are all the same distance (the radius) from a certain point (the center).
(n-2)180

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

30. Diameter
Groups - teams - or committees.
Bh
The distance across the circle through the center of the circle.The diameter is twice the radius.
2(pi)r

31. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

32. The probability of an event happening and the probability of an event NOT happening must add up to what number?
?d OR 2?r
2(pi)r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1. Given event A: A + notA = 1.

33. In a parabola - if the first term is negative - the parabola ________.
Opens down
(0 -0)
Opens up
S^2

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

35. Area of Rectangle
Lw
T1 + (n-1)d
2x2x2x5x5
Percentage Change = Difference/Original * 100

36. What is the average speed?
Total distance/total time
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
4pir^2
Number of desired outcomes/number of total outcomes

37. Does order matter for a permutation? How about for a combination?
x²-y²
Order does matter for a permutation - but does not matter for a combination.
Opens up
Percentage Change = Difference/Original * 100

38. What is the unfactored version of (x-y)² ?
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
x² -2xy + y²

39. What is the unfactored version of x²-y² ?
4s
(x+y)(x-y)
(x+y)²
N x M

40. Circumference of a 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.
N x M
?d OR 2?r
The distance from one point on the circle to another point on the circle.

41. What is a '30:60:90' triangle?
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
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.
T1 * r^(n-1)/(r-1)
(x+y)²

42. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
1/1
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'.
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.

43. How do you solve a permutation?
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
T1 * r^(n-1)
Lwh
(n degrees/360) * 2(pi)r

44. Volume of Cylinder
Between 0 and 1.
1.4
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.
Pir^2h

45. When you reverse FOIL - the term that needs to multiply out is the _____
(n degrees/360) * (pi)r^2
Pi*r^2
Last term
(a+b)(a²-ab+b²)

46. Surface Area of Sphere
1
1/x^a
b±[vb²-4ac]/2a
4pir^2

47. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
A+b
(n degrees/360) * 2(pi)r
N x M
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

48. Define a factorial of a number - and how it is written.
(x-y)²
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.
Opens down
Middle term

49. What is the factored version of x² -2xy + y² ?
Pi*d
(a-b)²
(x-y)²
Pi*r^2

50. Area of a triangle
½(base x height) [or (base x height)÷2]
2 pi r
2(pi)r(r+h)
(x1+x2)/2 - (y1+y2)/2