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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. length of a sector
2pir^2 + 2pir*h
T1 + (n-1)d
x°/360 times (2 pi r) - where x is the degrees in the angle
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.

2. What is the average speed?
N x M
Total distance/total time
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4s (where s = length of a side)

3. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
(x1+x2)/2 - (y1+y2)/2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/3pir^2*h
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.

4. Circumference of a circle using radius
2pi*r
y = k/x
N x M
?r²

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

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6. Area of a triangle
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
?r²
Pir^2h
½(base x height) [or (base x height)÷2]

7. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
S^2
2(pi)r(r+h)
x² -2xy + y²

8. What is the surface area of a cylinder?
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'.
x²-y²
2(pi)r(r+h)
(a-b)(a+b)

9. How do you multiply powers with the same base?
(x1+x2)/2 - (y1+y2)/2
Pi*d
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(0 -0)

10. What number goes on the bottom of a probability fraction?
(n/2) * (t1+tn)
(a+b)²
The total # of possible outcomes.
An ange whose vertex is the center of the circle

11. Area of Rectangle
Less
C =?d
Lw
(a+b)(a²-ab+b²)

12. (a+b)(a-b)=
A²-b²
2l+2w
1/3pir^2*h
T1 * r^(n-1)/(r-1)

13. Does order matter for a permutation? How about for a combination?
Between 0 and 1.
A=?r2
1/2bh
Order does matter for a permutation - but does not matter for a combination.

14. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
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)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

15. What is the formula for the diagonal of any square?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Lwh
1.4
S*v2

16. How do you find the slope?
y2-y1/x2-x1
2(pi)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.
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.

17. Surface Area of rectangular prism
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
2lw+2lh+2wh
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/2) * (t1+tn)

18. What is the factored version of x² + 2xy + y² ?
Sqr( x2 -x1) + (y2- y1)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
y = kx
(x+y)²

19. How do you calculate the percentage of change?
Bh
Percentage Change = Difference/Original * 100
Total distance/total time
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.

20. What is the 'distributive law'?
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The set of points which are all the same distance (the radius) from a certain point (the center).
Total distance/total time

21. How do you multiply and divide square roots?
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.
(pi)r^2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
b±[vb²-4ac]/2a

22. What is the factored version of (x+y)(x-y) ?
x²-y²
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.
2pi*r
?r²

23. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
(pi)r^2(h)
(n/2) * (t1+tn)
(y2-y1)/(x2-x1)

24. In a parabola - if the first term is negative - the parabola ________.
Opens down
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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 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.

25. Rough est. of v3 =
Between 0 and 1.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
A²-b²
1.7

26. What is the probability?
(y-y1)=m(x-x1)
Percentage Change = Difference/Original * 100
Number of desired outcomes/number of total outcomes
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.

27. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
Sum of terms/number of terms
(n/2) * (t1+tn)
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'.

28. Area of a circle
?r²
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.

29. What is directly proportional?
The total # of possible outcomes.
y = kx
Lw
(y2-y1)/(x2-x1)

30. What is the sum of the inside angles of an n-sided polygon?
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-2)180
A=?r2
Pi*r^2

31. What is the unfactored version of (x-y)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.
1/x^a
The total # of possible outcomes.
x² -2xy + y²

32. If x² = 144 - does v144 = x?
(n/2) * (t1+tn)
Not necessarily. This is a trick question - because x could be either positive or negative.
½(base x height) [or (base x height)÷2]
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

33. Area of Circle
Pi*r^2
(x+y)²
(a+b)²
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.

34. x^-a =
4/3pir^3
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
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.
1/x^a

35. If something is certain to happen - how is the probability of this event expressed mathematically?
Probability A + Probability B
(a+b)²
b±[vb²-4ac]/2a
1/1

36. 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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(n/2) * (t1+tn)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

37. What is the factored version of x² -2xy + y² ?
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.
1.4
(x-y)²
Total distance/total time

38. What do permutation problems often ask for?
Probability A * Probability B
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.
A²-b²

39. When a line crosses two parallel lines - ________.
The four big angles are equal and the four small angles are equal
Bh
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2(lw+wh+lh)

40. perimeter of square
1/1
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
4s

41. Perimeter of a rectangle
Not necessarily. This is a trick question - because x could be either positive or negative.
2Length + 2width [or (length + width) x 2]
4s
(a+b)(a-b)

42. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
Last term
1/3Bh
1/2bh

43. What is the length of an arc?
(a+b)(a-b)
(n degrees/360) * 2(pi)r
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
y = k/x

44. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
?d OR 2?r
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
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.

45. Explain the special properties of zero.
(pi)r^2
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.
Groups - teams - or committees.
Lwh

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

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47. Circumference Formula
2pir^2 + 2pir*h
C =?d
Total distance/total time
Probability A * Probability B

48. Area of Circles
1/2bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A=?r2
Sqr( x2 -x1) + (y2- y1)

49. What is the circumference of a circle?
2(pi)r
N x M
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
1/x^a

50. The length of one side of any triangle is ____ than the sum of the other two sides.
N x M
Less
?r²
A segment connecting the center of a circle to any point on the circle

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