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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 an 'equilateral' triangle?
(pi)r^2
Bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(x1+x2)/2 - (y1+y2)/2

2. 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.
y = k/x
Sum of terms/number of terms

3. List two odd behaviors of exponents
Pi*r^2
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.
2(pi)r(r+h)

4. Volume of prism
The average - mean - median - or mode.
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.
2l+2w

5. Area of a square
y2-y1/x2-x1
S² - where s = length of a side
The total # of possible outcomes.
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

6. What is the area of a sector?
(n degrees/360) * (pi)r^2
T1 * r^(n-1)
1.4
Part of a circle connecting two points on the circle.

7. What is the 'Third side' rule for triangles?
(y-y1)=m(x-x1)
2lw+2lh+2wh
T1 * r^(n-1)/(r-1)
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.

8. Volume of Cone
1/1
1/3pir^2*h
4s
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.

9. In a parabola - if the first term is negative - the parabola ________.
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.
2(pi)r
Opens down
T1 + (n-1)d

10. Circle
1/2 h (b1 + b2)
The set of points which are all the same distance (the radius) from a certain point (the center).
Sum of the lengths of the sides
x² -2xy + y²

11. a³+b³
Middle term
(a+b)(a²-ab+b²)
N x M
1.4

12. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
Between 0 and 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.
y2-y1/x2-x1

13. 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.
Part of a circle connecting two points on the circle.
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.
(n degrees/360) * (pi)r^2

14. Circumference of a circle using radius
2pi*r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
b±[vb²-4ac]/2a
(x+y)(x-y)

15. What is the area of a triangle?
Negative
(a-b)(a+b)
1/2bh
?d OR 2?r

16. What'S the most important thing to remember about charts you'll see on the GRE?
An ange whose vertex is the center of the circle
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.
(n degrees/360) * (pi)r^2
A=?r2

17. In a coordinate system - identify the quadrants and describe their location.
2(pi)r(r+h)
(y2-y1)/(x2-x1)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(a+b)(a²-ab+b²)

18. How do you find the sum of an arithmetic sequence?
2(pi)r
x² + 2xy + y²
(a+b)(a²-ab+b²)
(n/2) * (t1+tn)

19. Circumference of a circle
Pir^2h
An ange whose vertex is the center of the circle
?d OR 2?r
Last term

20. In a parabola - if the first term is positive - the parabola ________.
A=?r2
A=bh
Opens up
The four big angles are equal and the four small angles are equal

21. What is the 'distributive law'?
A segment connecting the center of a circle to any point on the circle
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.
x²-y²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

22. Volume of sphere
(x1+x2)/2 - (y1+y2)/2
(a-b)²
Probability A * Probability B
4/3pir^3

23. How do you find the midpoint?
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
Sqr( x2 -x1) + (y2- y1)
Pir^2h
(x1+x2)/2 - (y1+y2)/2

24. Volume of Cylinder
The set of points which are all the same distance (the radius) from a certain point (the center).
x²-y²
Pir^2h
Ac+ad+bc+bd

25. How do you find the slope?
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
Number of desired outcomes/number of total outcomes
y2-y1/x2-x1

26. When a line crosses two parallel lines - ________.
The four big angles are equal and the four small angles are equal
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
T1 * r^(n-1)
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

27. a²+2ab+b²
Number of desired outcomes/number of total outcomes
(a+b)²
½(base x height) [or (base x height)÷2]
A+b

28. Area of Triangle
(x-y)²
Bh
1/2bh
A²-b²

29. Area of Square
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
S^2

30. Define a factorial of a number - and how it is written.
Probability A + Probability B
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
2(pi)r

31. What is the length of an arc?
The distance from one point on the circle to another point on the circle.
2Length + 2width [or (length + width) x 2]
(n degrees/360) * 2(pi)r
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

32. a³-b³
T1 * r^(n-1)/(r-1)
Middle term
(a-b)(a²+ab+b²)
4/3pir^3

33. Rough est. of v1 =
T1 + (n-1)d
(n degrees/360) * 2(pi)r
y = kx
1

34. Sector
Not necessarily. This is a trick question - because x could be either positive or negative.
S² - where s = length of a side
?d OR 2?r
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.

35. Area of a circle
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
?r²
Pir^2h
The set of points which are all the same distance (the radius) from a certain point (the center).

36. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
N x M
(0 -0)
Number of desired outcomes/number of total outcomes

37. If x² = 144 - does v144 = x?
x² -2xy + y²
Pi*d
1. Given event A: A + notA = 1.
Not necessarily. This is a trick question - because x could be either positive or negative.

38. In intersecting lines - opposite angles are _____.
Lwh
Equal
1/2 h (b1 + b2)
(x1+x2)/2 - (y1+y2)/2

39. In a coordinate system - what is the origin?
(0 -0)
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.
(pi)r^2
1/x^a

40. What is the prime factorization of 200?
(y2-y1)/(x2-x1)
2x2x2x5x5
(a-b)²
x² + 2xy + y²

41. Area of Rectangle
Lw
An ange whose vertex is the center of the circle
x²-y²
(pi)r^2(h)

42. What is the probability?
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.
Lwh
An ange whose vertex is the center of the circle

43. Circumference Formula
2lw+2lh+2wh
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.
C =?d

44. 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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4/3pir^3
?d OR 2?r

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

46. What is the average?
Number of desired outcomes/number of total outcomes
Sum of terms/number of terms
T1 + (n-1)d
A²-b²

47. Diameter
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.
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 distance across the circle through the center of the circle.The diameter is twice the radius.
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.

48. Perimeter (circumference) of a circle
2 pi r
Probability A + Probability B
Pi*r^2
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.

49. Area of Trapezoid
1/2 h (b1 + b2)
An ange whose vertex is the center of the circle
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.

50. Perimeter of a square
2(pi)r(r+h)
A segment connecting the center of a circle to any point on the circle
Not necessarily. This is a trick question - because x could be either positive or negative.
4s (where s = length of a side)