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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. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
Groups - teams - or committees.
The four big angles are equal and the four small angles are equal
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

2. Define the range of a set of numbers.
Multiply each numerator by the other fraction'S denominator. Example: 3/7 and 7/12. Multiply 312 = 36 - and 77 = 49. If you completed the full calculation - you'd also cross-multiply the denominators - but you don'T have to in order to compare values
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.
Pi*d
Arrangements - orders - schedules - or lists.

3. In intersecting lines - opposite angles are _____.
Equal
N x M
Sum of terms/number of terms
Number of desired outcomes/number of total outcomes

4. In a coordinate system - identify the quadrants and describe their location.
2 pi r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(a-b)(a+b)
The total # of possible outcomes.

5. What is the factored version of x² + 2xy + y² ?
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.
(x+y)²
S² - where s = length of a side
1/x^a

6. For a bell curve - what three terms might be used to describe the number in the middle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Number of desired outcomes/number of total outcomes
T1 + (n-1)d
The average - mean - median - or mode.

7. What is the area of a cylinder?
(pi)r^2(h)
1
Total distance/total time
2(pi)r(r+h)

8. List two odd behaviors of exponents
1
1/3pir^2*h
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.
(x+y)(x-y)

9. Area of rectangle - square - parallelogram
2x2x2x5x5
Middle term
A=bh
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.

10. Perimeter of rectangle
(a-b)(a²+ab+b²)
2l+2w
?d OR 2?r
Multiply each numerator by the other fraction'S denominator. Example: 3/7 and 7/12. Multiply 312 = 36 - and 77 = 49. If you completed the full calculation - you'd also cross-multiply the denominators - but you don'T have to in order to compare values

11. What is an 'equilateral' triangle?
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
b±[vb²-4ac]/2a
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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'.

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

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

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14. 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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15. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
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.
N x M
(x-y)²
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

16. length of a sector
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x°/360 times (2 pi r) - where x is the degrees in the angle
The distance across the circle through the center of the circle.The diameter is twice the radius.
Total distance/total time

17. Volume of pyramid
Arrangements - orders - schedules - or lists.
y = k/x
1/3Bh
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

18. Area of Parallelogram
y = k/x
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.
1.7
Bh

19. What is the surface area of a cylinder?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2(pi)r(r+h)
(0 -0)
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.

20. Area of a trapezoid
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
1
(pi)r^2

21. Perimeter of a rectangle
2Length + 2width [or (length + width) x 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.
(n degrees/360) * 2(pi)r
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.

22. Slope
(y2-y1)/(x2-x1)
(x-y)²
Part of a circle connecting two points on the 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.

23. What is the area of a sector?
T1 * r^(n-1)/(r-1)
(n degrees/360) * (pi)r^2
Bh
2Length + 2width [or (length + width) x 2]

24. What is the equation of a line?

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25. Area of a triangle
Total distance/total time
Pi*r^2
½(base x height) [or (base x height)÷2]
(x1+x2)/2 - (y1+y2)/2

26. What is the 'Third side' rule for triangles?
?r²
x°/360 times (?r²) - where x is the degrees in the angle
Arrangements - orders - schedules - or lists.
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.

27. What is the point-slope form?
1/x^a
(y-y1)=m(x-x1)
2x2x2x5x5
A segment connecting the center of a circle to any point on the circle

28. Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
4s
Equal
Middle term

29. Circumference of cirlce using diameter
Pi*d
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.
(n-2)180
2lw+2lh+2wh

30. Area of Circle
Pi*r^2
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.
S² - where s = length of a side
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.

31. Perimeter (circumference) of a circle
C =?d
A²-b²
The set of points which are all the same distance (the radius) from a certain point (the center).
2 pi r

32. Sector
½(base x height) [or (base x height)÷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.
Lw
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.

33. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Number of desired outcomes/number of total outcomes
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
x² + 2xy + y²
Less

34. Chord
(x1+x2)/2 - (y1+y2)/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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The distance from one point on the circle to another point on the circle.

35. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
The four big angles are equal and the four small angles are equal
N x M
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.
Negative

36. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Equal
Pi*r^2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

37. What number goes on the bottom of a probability fraction?
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.
Total distance/total time
The total # of possible outcomes.
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.

38. Area of a square
(n degrees/360) * 2(pi)r
Sum of the lengths of the sides
S² - where s = length of a side
Arrangements - orders - schedules - or lists.

39. What is directly proportional?
Order does matter for a permutation - but does not matter for a combination.
A²-b²
y = kx
(pi)r^2(h)

40. Rough est. of v2 =
1.4
Less
(x1+x2)/2 - (y1+y2)/2
(n degrees/360) * 2(pi)r

41. The length of one side of any triangle is ____ than the sum of the other two sides.
Pir^2h
Less
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'.
N x M

42. What is the sum of the inside angles of an n-sided polygon?
Equal
2lw+2lh+2wh
(n-2)180
x²-y²

43. In a parabola - if the first term is negative - the parabola ________.
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.
Opens down
1.4
Number of desired outcomes/number of total outcomes

44. What is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(y-y1)=m(x-x1)
T1 + (n-1)d
x²-y²

45. What is the 'distributive law'?
y-y1=m(x-x1)
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.
S² - where s = length of a side
(y-y1)=m(x-x1)

46. Circumference 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.
Probability A * Probability B
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.
C =?d

47. Central Angle
Pi*d
Not necessarily. This is a trick question - because x could be either positive or negative.
An ange whose vertex is the center of the circle
1.4

48. In a coordinate system - what is the origin?
x°/360 times (2 pi r) - where x is the degrees in the angle
T1 * r^(n-1)/(r-1)
1
(0 -0)

49. What do permutation problems often ask for?
4pir^2
Arrangements - orders - schedules - or lists.
2(pi)r(r+h)
(n-2)180

50. Perimeter of a square
Less
x² -2xy + y²
4s (where s = length of a side)
x² + 2xy + y²