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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. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
(n degrees/360) * (pi)r^2
y2-y1/x2-x1
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.
1. Factored: x - y Unfactored: (x+y)(x-y) 2. Factored: (x+y) Unfactored: x + 2xy + y 3. Factored: (x-y) Unfactored: x - 2xy + y

2. Sector
1.7
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.
x/360 times (?r) - where x is the degrees in the angle
4s (where s = length of a side)

3. What is the 'Third side' rule for triangles?
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.
The total # of possible outcomes.
Sum of terms/number of terms
Part of a circle connecting two points on the circle.

4. If x = 144 - does v144 = x?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
Sum of terms/number of terms

5. What is the surface area of a cylinder?
(y-y1)=m(x-x1)
1/2 h (b1 + b2)
2(pi)r(r+h)
An ange whose vertex is the center of the circle

6. Quadratic Formula
Sum of terms/number of terms
x-y
Part of a circle connecting two points on the circle.
b[vb-4ac]/2a

7. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? x4 = x?-4 = x5
4pir^2
1/2 h (b1 + b2)
2(pi)r(r+h)

8. What is the 'distributive law'?
2(pi)r(r+h)
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.
(x1+x2)/2 - (y1+y2)/2
2(pi)r(r+h)

9. What are the side ratios for a 30:60:90 triangle?
S*v2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Negative
A-b

10. Volume of Cone
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/3pir^2*h
(n-2)180
4s

11. Rough est. of v2 =
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1.4
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.
T1 * r^(n-1)

12. Point-Slope form
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.
Less
Sqr( x2 -x1) + (y2- y1)
y-y1=m(x-x1)

13. Diameter
Lwh
2(lw+wh+lh)
The distance across the circle through the center of the circle.The diameter is twice the radius.
Opens up

14. Perimeter of polygon
Opens down
Opens up
Sum of the lengths of the sides
2 pi r

15. a - b is equal to
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.
2(lw+wh+lh)
(a+b)(a-b)

16. How do you calculate a diagonal inside a 3-dimensional rectangular box?
T1 + (n-1)d
1. Given event A: A + notA = 1.
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.
T1 * r^(n-1)/(r-1)

17. x^-a =
Pir^2h
1/x^a
The formula is a + b + c = d where a - b - c are the dimensions of the figure and d is the diagonal.
Lw

18. Area of Trapezoid
(x+y)(x-y)
x -2xy + y
1/2 h (b1 + b2)
(y2-y1)/(x2-x1)

19. What is the prime factorization of 200?
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
2x2x2x5x5
(a-b)(a+b)

20. How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
T1 * r^(n-1)
Bh

21. What is the probability?
Number of desired outcomes/number of total outcomes
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Total distance/total time
Add the exponents - retain the base. for example - x + x5 = x+5 = x7

22. In a coordinate system - what is the origin?
1/x^a
(0 -0)
Percentage Change = Difference/Original * 100
A=bh

23. Perimeter of a square
x-y
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.
4s (where s = length of a side)
(x-y)

24. What is the volume of a cylinder?
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.
(pi)r^2(h)
Lw

25. What is the equation of a line?
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'.
The distance from one point on the circle to another point on the circle.
2pir^2 + 2pir*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.

26. Area of rectangle - square - parallelogram
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.
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
A=bh

27. Area of a circle
An ange whose vertex is the center of the circle
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(a-b)(a+b)
?r

28. What is the average speed?
Total distance/total time
A=?r2
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

29. What is directly proportional?
That they often have not just one answer - but two. For example - solving x -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
y = kx
1. Given event A: A + notA = 1.
Bh

30. a-2ab+b
Probability A + Probability B
Equal
(a-b)
2pi*r

31. Area of Circles
(a+b)(a-ab+b)
The four big angles are equal and the four small angles are equal
A=?r2
Arrangements - orders - schedules - or lists.

32. Lines reflected over the x or y axis have ____ slopes.
1.4
(y2-y1)/(x2-x1)
A=bh
Negative

33. What must be true before a quadratic equation can be solved?
1/1
2 pi r
(y2-y1)/(x2-x1)
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.

34. What is the factored version of x + 2xy + y ?
(x+y)
(y2-y1)/(x2-x1)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Total distance/total time

35. Area of Square
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.
(x1+x2)/2 - (y1+y2)/2
S^2
(n-2)180

36. How do you find the slope?
(n degrees/360) * 2(pi)r
N x M
Groups - teams - or committees.
y2-y1/x2-x1

37. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
A=bh
N x M
2x2x2x5x5
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.

38. Define 'proportionate' values
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.
y2-y1/x2-x1
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(y-y1)=m(x-x1)

39. Area of Circle
y2-y1/x2-x1
(n/2) * (t1+tn)
Pi*r^2
T1 + (n-1)d

40. What is the area of a cylinder?
2(pi)r(r+h)
Opens down
Pi*r^2
4/3pir^3

41. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(base x height) [or (base x height)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.
Opens up

42. a-b
(a-b)(a+ab+b)
The total # of possible outcomes.
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.
T1 + (n-1)d

43. How do you find the midpoint?
(base x height) [or (base x height)2]
1/3pir^2*h
(x1+x2)/2 - (y1+y2)/2
(a-b)(a+ab+b)

44. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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.
4/3pir^3
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Part of a circle connecting two points on the circle.

45. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.
A segment connecting the center of a circle to any point on the circle
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.
1/2bh
Lwh

46. Volume of prism
Bh
1. Factored: x - y Unfactored: (x+y)(x-y) 2. Factored: (x+y) Unfactored: x + 2xy + y 3. Factored: (x-y) Unfactored: x - 2xy + y
x-y
The total # of possible outcomes.

47. What is the volume of a solid rectangle?
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.
(0 -0)
Lwh
Arrangements - orders - schedules - or lists.

48. When you reverse FOIL - the term that needs to add out is the _____
(y-y1)=m(x-x1)
Middle term
2(pi)r(r+h)
S - where s = length of a side

49. Define the range of a set of numbers.
Opens up
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.
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.
x -2xy + y

50. The length of one side of any triangle is ____ than the sum of the other two sides.
x/360 times (?r) - where x is the degrees in the angle
S^2
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Less

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