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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. a² - b² is equal to
Negative
(a+b)(a-b)
T1 * r^(n-1)
x°/360 times (2 pi r) - where x is the degrees in the angle

2. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Negative
Arrangements - orders - schedules - or lists.
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.
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.

3. What is the average speed?
Total distance/total time
2pi*r
(y-y1)=m(x-x1)
2Length + 2width [or (length + width) x 2]

4. If something is certain to happen - how is the probability of this event expressed mathematically?
(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.
1/1
(pi)r^2(h)

5. Surface Area of Sphere
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
y2-y1/x2-x1
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
4pir^2

6. Area of a square
T1 + (n-1)d
4pir^2
The distance from one point on the circle to another point on the circle.
S² - where s = length of a side

7. What is the factored version of x² + 2xy + y² ?
(0 -0)
(x+y)²
x°/360 times (2 pi r) - where x is the degrees in the angle
1/2bh

8. Area of Parallelogram
S*v2
Bh
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.

9. If something is possible but not certain - what is the numeric range of probability of it happening?
Last term
Percentage Change = Difference/Original * 100
1/3pir^2*h
Between 0 and 1.

10. (a+b)(c+d)
A+b
x²-y²
(x-y)²
Ac+ad+bc+bd

11. What is the distance formula?
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.
Order does matter for a permutation - but does not matter for a combination.
Probability A + Probability B
Sqr( x2 -x1) + (y2- y1)

12. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A segment connecting the center of a circle to any point on the circle
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.
y2-y1/x2-x1

13. Quadratic Formula
b±[vb²-4ac]/2a
The four big angles are equal and the four small angles are equal
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

14. Define the 'Third side' rule for triangles

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15. Perimeter of polygon
The average - mean - median - or mode.
(y-y1)=m(x-x1)
Sum of the lengths of the sides
4/3pir^3

16. Area of Circles
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.
Pir^2h
2(pi)r(r+h)
A=?r2

17. Lines reflected over the x or y axis have ____ slopes.
Negative
2pi*r
T1 * r^(n-1)
Order does matter for a permutation - but does not matter for a combination.

18. The length of one side of any triangle is ____ than the sum of the other two sides.
4s
An ange whose vertex is the center of the circle
1/1
Less

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

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20. Circumference Formula
1.4
C =?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.
Negative

21. What is the average?
Bh
Sum of terms/number of terms
T1 * r^(n-1)
2(pi)r(r+h)

22. How do you find the slope?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(n degrees/360) * 2(pi)r
y2-y1/x2-x1
Opens up

23. What is the unfactored version of (x-y)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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Bh
x² -2xy + y²

24. What is the area of a solid rectangle?
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)
1.7
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.

25. How do you multiply powers with the same base?
2(lw+wh+lh)
x°/360 times (2 pi r) - where x is the degrees in the angle
4/3pir^3
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

26. Area of 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
1/2bh
(a+b)²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

27. Chord
A²-b²
The distance from one point on the circle to another point on the circle.
2Length + 2width [or (length + width) x 2]
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.

28. Perimeter of rectangle
(x+y)(x-y)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
2l+2w

29. What do combination problems usually ask for?
Groups - teams - or committees.
A=?r2
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 total # of possible outcomes.

30. What is the volume of a cylinder?
x°/360 times (?r²) - where x is the degrees in the angle
(pi)r^2(h)
Opens down
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.

31. What number goes on the bottom of a probability fraction?
2pi*r
(pi)r^2(h)
The total # of possible outcomes.
N x M

32. Volume of Cone
1/3pir^2*h
N x M
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A=?r2

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

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34. Area of a trapezoid
T1 * r^(n-1)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Not necessarily. This is a trick question - because x could be either positive or negative.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

35. a³-b³
?d OR 2?r
(a-b)(a²+ab+b²)
(a+b)²
A=?r2

36. What is the side ratio for a 30:60:90 triangle?
?d OR 2?r
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/1
2(pi)r

37. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
?d OR 2?r
The four big angles are equal and the four small angles are equal
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.
1/3Bh

38. Define a factorial of a number - and how it is written.
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.
(0 -0)
S² - where s = length of a side
A=bh

39. If x² = 144 - does v144 = x?
x²-y²
(n-2)180
(y-y1)=m(x-x1)
Not necessarily. This is a trick question - because x could be either positive or negative.

40. What is the point-slope form?
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.
(y-y1)=m(x-x1)
2lw+2lh+2wh
T1 * r^(n-1)

41. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The total # of possible outcomes.
The distance from one point on the circle to another point on the circle.
(a-b)²

42. Area of Square
S^2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(x+y)²
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

43. What is the 'distributive law'?
?d OR 2?r
1.4
Opens down
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. a³+b³
(a+b)(a²-ab+b²)
(x+y)(x-y)
Order does matter for a permutation - but does not matter for a combination.
½(base x height) [or (base x height)÷2]

45. What is inversely proportional?
T1 + (n-1)d
y = k/x
(y2-y1)/(x2-x1)
½(base x height) [or (base x height)÷2]

46. Slope
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(y2-y1)/(x2-x1)
(pi)r^2(h)
(x+y)(x-y)

47. What is a 'Right isosceles' triangle?
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.
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.
Probability A + Probability B
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.

48. Circumference of cirlce using diameter
x² -2xy + y²
Sum of the lengths of the sides
Pi*d
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

49. Area of Circle
2x2x2x5x5
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Pi*r^2

50. What is the probability?
(pi)r^2(h)
4/3pir^3
Last term
Number of desired outcomes/number of total outcomes