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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. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Total distance/total time
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Part of a circle connecting two points on the circle.

2. Area of Trapezoid
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
(x1+x2)/2 - (y1+y2)/2
1/2 h (b1 + b2)
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.

3. Circumference of a circle using radius
1/3pir^2*h
Pir^2h
T1 * r^(n-1)
2pi*r

4. Define a factorial of a number - and how it is written.
(n-2)180
2x2x2x5x5
Pir^2h
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.

5. What do permutation problems often ask for?
The distance from one point on the circle to another point on the circle.
1/2bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Arrangements - orders - schedules - or lists.

6. a²-2ab+b²
½(base x height) [or (base x height)÷2]
Arrangements - orders - schedules - or lists.
(a-b)²
S*v2

7. What is the probability?
2(pi)r
Number of desired outcomes/number of total outcomes
2 pi r
T1 * r^(n-1)/(r-1)

8. Radius (Radii)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Groups - teams - or committees.
Opens down
A segment connecting the center of a circle to any point on the circle

9. To divide powers with the same base...
1. Given event A: A + notA = 1.
1/3pir^2*h
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The distance from one point on the circle to another point on the circle.

10. What is the unfactored version of x²-y² ?
Last term
(x+y)(x-y)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

11. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
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.
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.
Part of a circle connecting two points on the circle.

12. Circumference of a circle
?d OR 2?r
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
b±[vb²-4ac]/2a
A=?r2

13. What is the distance formula?
y2-y1/x2-x1
Sum of terms/number of terms
Sqr( x2 -x1) + (y2- y1)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

14. How do you multiply and divide square roots?
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. 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 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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

15. What is the length of an arc?
1/x^a
1.7
(n degrees/360) * 2(pi)r
1.4

16. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
A=?r2
Probability A + Probability B
Pi*r^2
x²-y²

17. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Middle term
Last term

18. What is a 'Right isosceles' triangle?
2pir^2 + 2pir*h
Sum of terms/number of terms
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.
Equal

19. What is an 'equilateral' triangle?
Pi*r^2
Opens up
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
A=?r2

20. Chord
A²-b²
Sum of the lengths of the sides
(a+b)²
The distance from one point on the circle to another point on the circle.

21. Quadratic Formula
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.
Pi*r^2
b±[vb²-4ac]/2a
2x2x2x5x5

22. How do you find the sum of an arithmetic sequence?
(a-b)(a²+ab+b²)
1.4
T1 + (n-1)d
(n/2) * (t1+tn)

23. Circumference of cirlce using diameter
1/1
x°/360 times (?r²) - where x is the degrees in the angle
A segment connecting the center of a circle to any point on the circle
Pi*d

24. Lines reflected over the x or y axis have ____ slopes.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
Negative
4s

25. What is the volume of a cylinder?
?r²
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)
(pi)r^2(h)

26. What is the 'Third side' rule for triangles?
Bh
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
T1 + (n-1)d

27. Surface Area of rectangular prism
Number of desired outcomes/number of total outcomes
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.
2lw+2lh+2wh

28. Perimeter of polygon
A+b
x°/360 times (?r²) - where x is the degrees in the angle
?r²
Sum of the lengths of the sides

29. Area of a circle
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.
?r²
x°/360 times (2 pi r) - where x is the degrees in the angle
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.

30. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
A²-b²
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.
(x1+x2)/2 - (y1+y2)/2
y2-y1/x2-x1

31. Circumference Formula
Less
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.
A+b
C =?d

32. 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.
x²-y²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A=?r2

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

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34. x^-a =
1/x^a
Equal
1. Given event A: A + notA = 1.
Lw

35. How do you calculate the percentage of change?
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2 pi r
Percentage Change = Difference/Original * 100
A segment connecting the center of a circle to any point on the circle

36. perimeter of square
N x M
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.
4s
2x2x2x5x5

37. What is the area of a circle?
(pi)r^2
A+b
1/2bh
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.

38. 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
(n degrees/360) * 2(pi)r
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.
T1 + (n-1)d

39. a³-b³
(a-b)(a²+ab+b²)
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.
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

40. Define the mode of a set of numbers.
½(base x height) [or (base x height)÷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 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.
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.

41. a²-b²
y-y1=m(x-x1)
(a+b)(a²-ab+b²)
Pi*r^2
(a-b)(a+b)

42. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-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.
(a-b)(a+b)
Less

43. What is the 'distributive law'?
Pi*d
x² + 2xy + y²
Negative
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.

44. What is the area of a triangle?
(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.
(a-b)(a+b)
1/2bh

45. Central Angle
2(lw+wh+lh)
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.
1/2bh
An ange whose vertex is the center of the circle

46. (a+b)(c+d)
(a+b)(a-b)
2pi*r
x² + 2xy + y²
Ac+ad+bc+bd

47. Area of Square
S^2
2l+2w
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

48. Volume of prism
The four big angles are equal and the four small angles are equal
(a+b)²
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

49. Rough est. of v3 =
1.7
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(y2-y1)/(x2-x1)
(n degrees/360) * 2(pi)r

50. What is the area of a solid rectangle?
1/2bh
(n/2) * (t1+tn)
2(lw+wh+lh)
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.