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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. x^-a =
(x-y)²
(n degrees/360) * 2(pi)r
S² - where s = length of a side
1/x^a

2. Perimeter of a square
(n degrees/360) * 2(pi)r
Last term
Total distance/total time
4s (where s = length of a side)

3. 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.
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.
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.

4. When you reverse FOIL - the term that needs to add out is the _____
Middle term
y2-y1/x2-x1
2pir^2 + 2pir*h
(x+y)(x-y)

5. How do you multiply and divide square roots?
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
T1 * r^(n-1)/(r-1)
y2-y1/x2-x1

6. Arc
A+b
Part of a circle connecting two points on the circle.
Sqr( x2 -x1) + (y2- y1)
A²-b²

7. (a+b)(a-b)=
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.
A²-b²
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.

8. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
y = kx
Pi*r^2
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.
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.

9. What is the formula for the diagonal of any square?
S*v2
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.
2lw+2lh+2wh
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.

10. Does order matter for a permutation? How about for a combination?
2Length + 2width [or (length + width) x 2]
x°/360 times (2 pi r) - where x is the degrees in the angle
Order does matter for a permutation - but does not matter for a combination.
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.

11. How do you calculate the probability of two events in a row? (Probability of A and B)
Pir^2h
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.
Pi*d
Probability A * Probability B

12. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
Ac+ad+bc+bd
1/2bh
Bh

13. 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.
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 degrees/360) * (pi)r^2
Sqr( x2 -x1) + (y2- y1)

14. What is the 'Third side' rule for triangles?
Probability A + Probability B
(x+y)(x-y)
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(h)

15. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
x²-y²
2(pi)r(r+h)
A²-b²

16. Area of Circles
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/x^a
A=?r2

17. What is the area of a sector?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(n degrees/360) * (pi)r^2
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Opens down

18. Area of Parallelogram
Bh
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
C =?d
(x+y)(x-y)

19. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
4s (where s = length of a side)
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.
Probability A + Probability B
(x-y)²

20. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(pi)r^2(h)
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.

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.
½(base x height) [or (base x height)÷2]
1/3Bh
4pir^2

22. How do you find the midpoint?
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.
1/2bh
(x1+x2)/2 - (y1+y2)/2
Middle term

23. Sector
x² -2xy + y²
S*v2
(x+y)(x-y)
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.

24. Perimeter of a rectangle
(a+b)(a²-ab+b²)
Less
x² + 2xy + y²
2Length + 2width [or (length + width) x 2]

25. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

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26. What is the length of an arc?
4/3pir^3
(n degrees/360) * 2(pi)r
Less
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

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

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28. In a coordinate system - what is the origin?
A+b
(0 -0)
Probability A * Probability B
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.

29. What is the area of a triangle?
Sqr( x2 -x1) + (y2- y1)
A²-b²
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.
1/2bh

30. perimeter of square
Opens down
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.
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

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

32. Chord
(a+b)(a²-ab+b²)
The distance from one point on the circle to another point on the circle.
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.
Between 0 and 1.

33. Volume of Cone
1/3pir^2*h
Probability A + Probability B
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
1/2 h (b1 + b2)

34. The length of one side of any triangle is ____ than the sum of the other two sides.
Pi*r^2
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
The average - mean - median - or mode.
Less

35. What do combination problems usually ask for?
Groups - teams - or committees.
Pi*r^2
(a+b)²
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.

36. When you reverse FOIL - the term that needs to multiply out is the _____
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 four big angles are equal and the four small angles are equal
Last term
Negative

37. Area of a circle
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(y-y1)=m(x-x1)
T1 * r^(n-1)
?r²

38. What is the equation of a line?

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39. Surface Area of Sphere
2(pi)r
1/3pir^2*h
4pir^2
(x+y)²

40. What is the volume of a solid rectangle?
Lwh
(a-b)(a+b)
(n-2)180
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

41. Circumference of a circle using radius
(y-y1)=m(x-x1)
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.
2pi*r
2(pi)r

42. Area of a square
Between 0 and 1.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Pi*d
S² - where s = length of a side

43. Area of Trapezoid
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.
1/2 h (b1 + b2)
Last term
x² + 2xy + y²

44. When a line crosses two parallel lines - ________.
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.
2lw+2lh+2wh
The four big angles are equal and the four small angles are equal
(a-b)²

45. Define a factorial of a number - and how it is written.
The distance across the circle through the center of the circle.The diameter is twice the radius.
(y-y1)=m(x-x1)
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

46. a²+2ab+b²
(a-b)(a+b)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Pi*d
(a+b)²

47. What is the average?
(a-b)²
4s (where s = length of a side)
Sum of terms/number of terms
T1 * r^(n-1)/(r-1)

48. Circle
The set of points which are all the same distance (the radius) from a certain point (the center).
An ange whose vertex is the center 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.
(a+b)(a-b)

49. Area of a sector
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x°/360 times (2 pi r) - where x is the degrees in the angle
2pir^2 + 2pir*h
x°/360 times (?r²) - where x is the degrees in the angle

50. How do you find the nth term of a geometric sequence?
2(pi)r(r+h)
T1 * r^(n-1)
(pi)r^2(h)
(0 -0)

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GRE Math 2

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