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GRE Math 2

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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 positive - the parabola ________.
1/1
2pi*r
x² -2xy + y²
Opens up

2. What is the unfactored version of (x+y)² ?
(a+b)(a-b)
Equal
4pir^2
x² + 2xy + y²

3. If something is certain to happen - how is the probability of this event expressed mathematically?
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
4s (where s = length of a side)
1/1
C =?d

4. a³-b³
Sum of terms/number of terms
(a-b)(a²+ab+b²)
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.
Total distance/total time

5. Radius (Radii)
1/1
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A segment connecting the center of a circle to any point on the circle
Last term

6. What is the surface area of a cylinder?
2x2x2x5x5
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2(pi)r(r+h)
(x+y)²

7. a²+2ab+b²
y-y1=m(x-x1)
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
(a+b)²
y = k/x

8. What is the unfactored version of x²-y² ?
Percentage Change = Difference/Original * 100
(x+y)(x-y)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1/3pir^2*h

9. Point-Slope form
b±[vb²-4ac]/2a
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.
y-y1=m(x-x1)
(y2-y1)/(x2-x1)

10. Sector
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
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 part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.

11. x^-a =
A²-b²
1/x^a
Bh
x°/360 times (?r²) - where x is the degrees in the angle

12. Define a factorial of a number - and how it is written.
Order does matter for a permutation - but does not matter for a combination.
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
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'.

13. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
C =?d
(x+y)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.
N x M

14. What'S the most important thing to remember about charts you'll see on the GRE?
(pi)r^2(h)
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.
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

15. How do you multiply powers with the same base?
1/2 h (b1 + b2)
An ange whose vertex is the center of the circle
Groups - teams - or committees.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

16. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
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
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.

17. How do you calculate the surface area of a rectangular box?
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.
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.
2 pi 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

18. x^a * x^b = x^__
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.
1/3Bh
A+b
?r²

19. Area of Square
Pir^2h
4s
S^2
2(pi)r

20. What is the formula for the diagonal of any square?
The distance across the circle through the center of the circle.The diameter is twice the radius.
Between 0 and 1.
S*v2
Lwh

21. 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.
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.
Arrangements - orders - schedules - or lists.
Probability A * Probability B

22. What is a '30:60:90' triangle?
Arrangements - orders - schedules - or lists.
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. 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.
2(pi)r

23. The length of one side of any triangle is ____ than the sum of the other two sides.
1/3Bh
Less
2lw+2lh+2wh
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.

24. Circumference of a circle using radius
Less
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.
2pi*r
Total distance/total time

25. Area of Circle
Pi*r^2
C =?d
(x+y)²
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

26. What is the area of a cylinder?
2(pi)r(r+h)
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.
(n degrees/360) * 2(pi)r
y-y1=m(x-x1)

27. Volume of Cone
1/3pir^2*h
Last term
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

28. What is the point-slope form?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(y-y1)=m(x-x1)
4pir^2
A=bh

29. What is the area of a triangle?
Percentage Change = Difference/Original * 100
Part of a circle connecting two points on the circle.
1/2bh
4s

30. Explain the special properties of zero.
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.
Ac+ad+bc+bd
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.
2pi*r

31. What is a 'Right isosceles' triangle?
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.
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.
(n-2)180
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

32. Area of rectangle - square - parallelogram
Pi*d
T1 * r^(n-1)
A=bh
x°/360 times (2 pi r) - where x is the degrees in the angle

33. What is the side ratio for a Right Isosceles triangle?
T1 * r^(n-1)
Opens up
Pir^2h
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

34. What is the area of a 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
(pi)r^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

35. Circumference of cirlce using diameter
Last term
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.
Pi*d
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

36. When you reverse FOIL - the term that needs to add out is the _____
Negative
2pir^2 + 2pir*h
Middle term
Pir^2h

37. Define 'proportionate' values
(n degrees/360) * 2(pi)r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(a-b)²
Not necessarily. This is a trick question - because x could be either positive or negative.

38. Surface Area of Cylinder
T1 + (n-1)d
2(pi)r
Equal
2pir^2 + 2pir*h

39. How do you find the sum of an arithmetic sequence?
(n/2) * (t1+tn)
y = k/x
The set of points which are all the same distance (the radius) from a certain point (the center).
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.

40. Does order matter for a permutation? How about for a combination?
x²-y²
Order does matter for a permutation - but does not matter for a combination.
A segment connecting the center of a circle to any point on the circle
1.4

41. How do you solve a permutation?
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
2(pi)r(r+h)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2x2x2x5x5

42. Surface Area of Sphere
(y-y1)=m(x-x1)
T1 * r^(n-1)/(r-1)
4pir^2
S*v2

43. Area of Triangle
1/2bh
N x M
Sum of terms/number of terms
Ac+ad+bc+bd

44. What is the prime factorization of 200?
Lw
(a+b)(a²-ab+b²)
?d OR 2?r
2x2x2x5x5

45. What is the 'Third side' rule for triangles?
A=bh
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.
4s
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.

46. Area of a triangle
½(base x height) [or (base x height)÷2]
1/3pir^2*h
1/2bh
Equal

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

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48. In a parabola - if the first term is negative - the parabola ________.
(x+y)(x-y)
Pir^2h
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.
Opens down

49. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
2l+2w
1.4
S^2

50. Chord
The distance from one point on the circle to another point on the circle.
y = kx
Opens up
2 pi r

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GRE Math 2

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