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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. In a parabola - if the first term is negative - the parabola ________.
(a-b)(a+b)
Opens down
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

2. Perimeter of polygon
Ac+ad+bc+bd
Sum of the lengths of the sides
Order does matter for a permutation - but does not matter for a combination.
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.

3. What is the circumference of a circle?
S*v2
2(pi)r
(0 -0)
Part of a circle connecting two points on the circle.

4. Area of a circle
1/3Bh
?r²
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.
4s (where s = length of a side)

5. Circumference of a circle
?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.
(n degrees/360) * (pi)r^2
Groups - teams - or committees.

6. Area of Circles
x² + 2xy + y²
A=?r2
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

7. Rough est. of v1 =
?d OR 2?r
2x2x2x5x5
1
1/2bh

8. What is the area of a cylinder?
y2-y1/x2-x1
2(pi)r(r+h)
(a+b)(a-b)
Part of a circle connecting two points on the circle.

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

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10. Area of Square
Total distance/total time
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.
S^2
4s

11. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
S^2
2lw+2lh+2wh
Pi*r^2
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.

12. What is the unfactored version of x²-y² ?
(pi)r^2(h)
(x+y)(x-y)
Opens up
Pi*r^2

13. What is the length of an arc?
y2-y1/x2-x1
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
(n degrees/360) * 2(pi)r

14. How do you calculate the percentage of change?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
Percentage Change = Difference/Original * 100
Less

15. How do you multiply powers with the same base?
2pi*r
2l+2w
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Ac+ad+bc+bd

16. a²-b²
(a-b)(a+b)
S² - where s = length of a side
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
Sum of the lengths of the sides

17. 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.
A=bh
1.4
The distance across the circle through the center of the circle.The diameter is twice the radius.

18. How do you calculate the probability of two events in a row? (Probability of A and B)
The distance across the circle through the center of the circle.The diameter is twice the radius.
Middle term
Bh
Probability A * Probability B

19. Define the mode of a set of numbers.
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.
Sqr( x2 -x1) + (y2- y1)
1.7
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

20. When you reverse FOIL - the term that needs to multiply out is the _____
4pir^2
Last term
Between 0 and 1.
(a-b)(a²+ab+b²)

21. 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.
(x1+x2)/2 - (y1+y2)/2
Opens up
T1 * r^(n-1)/(r-1)

22. How do you multiply and divide square roots?
N x M
Arrangements - orders - schedules - or lists.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(a-b)²

23. Circumference of cirlce using diameter
Pi*d
Pi*r^2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Arrangements - orders - schedules - or lists.

24. What is the area of a triangle?
y = kx
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1/2bh
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

25. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
Number of desired outcomes/number of total outcomes
N x M
A²-b²
Last term

26. In a coordinate system - identify the quadrants and describe their location.
Percentage Change = Difference/Original * 100
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Sqr( x2 -x1) + (y2- y1)
?r²

27. What is directly proportional?
A=bh
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.
y = kx
The set of points which are all the same distance (the radius) from a certain point (the center).

28. Rough est. of v2 =
Ac+ad+bc+bd
1.4
A²-b²
C =?d

29. Circle
½(base x height) [or (base x height)÷2]
x² -2xy + y²
The set of points which are all the same distance (the radius) from a certain point (the center).
1/3pir^2*h

30. How do you calculate a diagonal inside a 3-dimensional rectangular box?
(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.
x°/360 times (2 pi r) - where x is the degrees in the angle
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. How do you solve a permutation?
Number of desired outcomes/number of total outcomes
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
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.
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'.

32. length of a sector
(x+y)(x-y)
x°/360 times (2 pi r) - where x is the degrees in the angle
1/2bh
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.

33. What is the side ratio for a Right Isosceles triangle?
The four big angles are equal and the four small angles are equal
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.
The average - mean - median - or mode.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

34. Define 'proportionate' values
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 part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of 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.

35. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
(a-b)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.
4s (where s = length of a side)

36. In a parabola - if the first term is positive - the parabola ________.
Opens up
(n/2) * (t1+tn)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.

37. Area of a trapezoid
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The total # of possible outcomes.
S^2
½(b1 +b2) x h [or (b1 +b2) x h÷2]

38. Volume of pyramid
An ange whose vertex is the center of the circle
1/3Bh
A segment connecting the center of a circle to any point on the circle
1.7

39. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
1/3pir^2*h
1/2bh
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.

40. Area of a sector
The distance from one point on the circle to another point on the circle.
4pir^2
x°/360 times (?r²) - where x is the degrees in the angle
(n-2)180

41. Volume of Cylinder
(a-b)²
2(pi)r(r+h)
Pir^2h
An ange whose vertex is the center of the circle

42. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
1.7
The distance from one point on the circle to another point on the circle.
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
½(b1 +b2) x h [or (b1 +b2) x h÷2]

43. What is the volume of a cylinder?
Pi*r^2
b±[vb²-4ac]/2a
4s (where s = length of a side)
(pi)r^2(h)

44. What is the factored version of x² + 2xy + y² ?
Lw
Total distance/total time
1
(x+y)²

45. What is the volume of a solid rectangle?
Lwh
A=bh
2(lw+wh+lh)
2 pi r

46. How do you find the sum of an arithmetic sequence?
Lwh
Not necessarily. This is a trick question - because x could be either positive or negative.
T1 * r^(n-1)
(n/2) * (t1+tn)

47. Surface Area of Cylinder
Not necessarily. This is a trick question - because x could be either positive or negative.
2pir^2 + 2pir*h
Middle term
(a+b)(a-b)

48. a³-b³
C =?d
2pir^2 + 2pir*h
(a-b)(a²+ab+b²)
1/x^a

49. Radius (Radii)
2(pi)r(r+h)
A segment connecting the center of a circle to any point on the circle
(pi)r^2(h)
2x2x2x5x5

50. Lines reflected over the x or y axis have ____ slopes.
Negative
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.
b±[vb²-4ac]/2a
1