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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. The length of one side of any triangle is ____ than the sum of the other two sides.
x°/360 times (?r²) - where x is the degrees in the angle
Bh
(n degrees/360) * (pi)r^2
Less

2. a²-b²
(a-b)(a+b)
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)
Bh

3. (a+b)(c+d)
Number of desired outcomes/number of total outcomes
Ac+ad+bc+bd
Pi*r^2
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.

4. What is the area of a sector?
(n degrees/360) * (pi)r^2
An ange whose vertex is the center of the circle
Bh
Ac+ad+bc+bd

5. Area of rectangle - square - parallelogram
A=bh
A+b
1/3pir^2*h
4s (where s = length of a side)

6. 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.
b±[vb²-4ac]/2a
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Bh

7. Area of a square
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
S² - where s = length of a side
2lw+2lh+2wh

8. Define the range of a set of numbers.
Ac+ad+bc+bd
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.
Pir^2h
y-y1=m(x-x1)

9. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
Equal
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.

10. When a line crosses two parallel lines - ________.
Last term
1/2bh
(a-b)²
The four big angles are equal and the four small angles are equal

11. What is the 'distributive law'?
x°/360 times (?r²) - where x is the degrees in the angle
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.
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.
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.

12. What is the prime factorization of 200?
2x2x2x5x5
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/2bh
(x-y)²

13. Rough est. of v2 =
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1.4
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.

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

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15. What is the unfactored version of (x-y)² ?
Pi*r^2
(n degrees/360) * (pi)r^2
A segment connecting the center of a circle to any point on the circle
x² -2xy + y²

16. In a coordinate system - identify the quadrants and describe their location.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
S*v2
(a+b)(a-b)

17. Area of a trapezoid
(x1+x2)/2 - (y1+y2)/2
Total distance/total time
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(y2-y1)/(x2-x1)

18. What is an 'equilateral' triangle?
Pi*r^2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Pi*d
?r²

19. Area of Parallelogram
2lw+2lh+2wh
(pi)r^2(h)
Arrangements - orders - schedules - or lists.
Bh

20. What is the unfactored version of x²-y² ?
(x+y)(x-y)
1/2bh
(x-y)²
Arrangements - orders - schedules - or lists.

21. What is the area of a cylinder?
The four big angles are equal and the four small angles are equal
2(pi)r(r+h)
2(lw+wh+lh)
(pi)r^2(h)

22. What is the area of a circle?
(pi)r^2
1
y2-y1/x2-x1
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

23. Does order matter for a permutation? How about for a combination?
Bh
1.7
The distance across the circle through the center of the circle.The diameter is twice the radius.
Order does matter for a permutation - but does not matter for a combination.

24. Central Angle
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
4s (where s = length of a side)
An ange whose vertex is the center of the circle
C =?d

25. a² - b² is equal to
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.
?d OR 2?r
(a+b)(a-b)
(a+b)²

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

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27. Point-Slope form
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
y-y1=m(x-x1)
Between 0 and 1.

28. In intersecting lines - opposite angles are _____.
Equal
1. Given event A: A + notA = 1.
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.
2pir^2 + 2pir*h

29. Circumference of a circle
Pi*d
4/3pir^3
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.
?d OR 2?r

30. Volume of Cone
Middle term
1/2 h (b1 + b2)
2x2x2x5x5
1/3pir^2*h

31. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
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
Probability A + Probability B
x°/360 times (2 pi r) - where x is the degrees in the angle
Probability A * Probability B

32. What is the distance formula?
T1 + (n-1)d
Sqr( x2 -x1) + (y2- y1)
(n-2)180
Sum of terms/number of terms

33. perimeter of square
Middle term
4s
(a+b)(a²-ab+b²)
(x+y)²

34. 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
?r²
?d OR 2?r
4pir^2

35. What is the formula for the diagonal of any square?
2(lw+wh+lh)
S*v2
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

36. What are the side ratios for a 30:60:90 triangle?
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.
2(pi)r
(pi)r^2(h)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

37. Perimeter of a rectangle
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
y2-y1/x2-x1
2Length + 2width [or (length + width) x 2]
An ange whose vertex is the center of the circle

38. What is the average?
Sum of terms/number of terms
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1.4
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.

39. Rough est. of v1 =
1
1/3Bh
T1 + (n-1)d
Arrangements - orders - schedules - or lists.

40. Quadratic Formula
Groups - teams - or committees.
Lw
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.
b±[vb²-4ac]/2a

41. 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.
Probability A * Probability B
(a+b)²
1/3pir^2*h

42. To divide powers with the same base...
(a-b)²
Between 0 and 1.
½(base x height) [or (base x height)÷2]
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

43. How do you find the nth term of an arithmetic sequence?
The distance from one point on the circle to another point on the circle.
(a-b)(a+b)
(n degrees/360) * (pi)r^2
T1 + (n-1)d

44. x^-a =
T1 * r^(n-1)
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.
1/x^a
1/3Bh

45. How do you find the midpoint?
Between 0 and 1.
(x1+x2)/2 - (y1+y2)/2
N x M
(a-b)(a+b)

46. length of a sector
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x 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.
x°/360 times (2 pi r) - where x is the degrees in the angle

47. In a parabola - if the first term is negative - the parabola ________.
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.
(a-b)(a+b)
Opens down
(n degrees/360) * 2(pi)r

48. What is the volume of a solid rectangle?
Lwh
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Between 0 and 1.
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.

49. What'S the most important thing to remember about charts you'll see on the GRE?
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'.
(x+y)²
Number of desired outcomes/number of total outcomes
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.

50. What do combination problems usually ask for?
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.
N x M
Groups - teams - or committees.
Opens down

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GRE Math 2

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