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GRE Math 2

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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

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2. Define the 'Third side' rule for triangles

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3. 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.
4/3pir^3
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.
Negative

4. Perimeter of a square
4s (where s = length of a side)
Percentage Change = Difference/Original * 100
(n-2)180
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.

5. In a parabola - if the first term is negative - the parabola ________.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Opens down
1/2bh
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.

6. Circle
(n/2) * (t1+tn)
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.
4s (where s = length of a side)
The set of points which are all the same distance (the radius) from a certain point (the center).

7. Area of Square
S^2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1. Given event A: A + notA = 1.
(n degrees/360) * 2(pi)r

8. Area of a triangle
y-y1=m(x-x1)
½(base x height) [or (base x height)÷2]
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.
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

9. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
4s (where s = length of a side)
x² + 2xy + y²
S² - where s = length of a side

10. Quadratic Formula
b±[vb²-4ac]/2a
(a+b)(a²-ab+b²)
Not necessarily. This is a trick question - because x could be either positive or negative.
4/3pir^3

11. (a+b)(c+d)
Ac+ad+bc+bd
x² -2xy + y²
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.
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.

12. What is the factored version of (x+y)(x-y) ?
Total distance/total time
The four big angles are equal and the four small angles are equal
x²-y²
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

13. What is the point-slope form?
T1 * r^(n-1)/(r-1)
x² -2xy + y²
(y-y1)=m(x-x1)
4pir^2

14. Define 'proportionate' values
Number of desired outcomes/number of total outcomes
1/3Bh
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2lw+2lh+2wh

15. How do you calculate the surface area of a rectangular box?
T1 * r^(n-1)
2pir^2 + 2pir*h
1. Given event A: A + notA = 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.

16. What is the unfactored version of (x+y)² ?
x² + 2xy + y²
Total distance/total time
x°/360 times (2 pi r) - where x is the degrees in the angle
Middle term

17. perimeter of square
4s
2pir^2 + 2pir*h
A²-b²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

18. How do you find the midpoint?
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.
(x1+x2)/2 - (y1+y2)/2
T1 + (n-1)d
(pi)r^2(h)

19. Surface Area of rectangular prism
?d OR 2?r
(0 -0)
2lw+2lh+2wh
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'.

20. What is the formula for the diagonal of any square?
S*v2
S^2
Less
(pi)r^2

21. Explain the special properties of zero.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
(n/2) * (t1+tn)
(y-y1)=m(x-x1)

22. Volume of pyramid
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(r+h)
1/3Bh
Not necessarily. This is a trick question - because x could be either positive or negative.

23. What is the side ratio for a Right Isosceles triangle?
N x M
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
Sum of terms/number of terms

24. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
(a+b)(a²-ab+b²)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Between 0 and 1.

25. What number goes on the bottom of a probability fraction?
(pi)r^2(h)
Number of desired outcomes/number of total outcomes
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.
The total # of possible outcomes.

26. Area of Circles
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
b±[vb²-4ac]/2a
Ac+ad+bc+bd
A=?r2

27. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
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
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.

28. a³+b³
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x°/360 times (?r²) - where x is the degrees in the angle
1.7
(a+b)(a²-ab+b²)

29. a²-b²
Last term
(a-b)(a+b)
1. Given event A: A + notA = 1.
Pi*d

30. How do you find the nth term of a geometric sequence?
(a+b)²
T1 * r^(n-1)
Lw
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.

31. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
N x M
Negative
(0 -0)
Probability A + Probability B

32. Central Angle
2 pi r
An ange whose vertex is the center of the circle
(a-b)²
(a+b)(a-b)

33. What is the side ratio for a 30:60:90 triangle?
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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2l+2w
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.

34. What is the volume of a cylinder?
x°/360 times (?r²) - where x is the degrees in the angle
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
(pi)r^2(h)

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

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36. How do you find the slope?
?d OR 2?r
Last term
y2-y1/x2-x1
(pi)r^2

37. What is the unfactored version of x²-y² ?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
S^2
(x+y)(x-y)
A segment connecting the center of a circle to any point on the circle

38. Area of a square
Groups - teams - or committees.
Percentage Change = Difference/Original * 100
2x2x2x5x5
S² - where s = length of a side

39. If something is possible but not certain - what is the numeric range of probability of it happening?
(a+b)(a²-ab+b²)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Between 0 and 1.
(0 -0)

40. How do you find the nth term of an arithmetic sequence?
The distance across the circle through the center of the circle.The diameter is twice the radius.
T1 + (n-1)d
(pi)r^2(h)
2Length + 2width [or (length + width) x 2]

41. What is the length of an arc?
A²-b²
Less
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.
(n degrees/360) * 2(pi)r

42. 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.
Total distance/total time
Pi*r^2
1/3pir^2*h

43. What is the prime factorization of 200?
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.
1/3Bh
2x2x2x5x5
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.

44. What is the factored version of x² + 2xy + y² ?
Probability A * Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(x+y)²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

45. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
(a+b)²
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.
Between 0 and 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.

46. What is the 'Third side' rule for triangles?
Part of a circle connecting two points on the circle.
(pi)r^2(h)
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.
S*v2

47. Perimeter of rectangle
2l+2w
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
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
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

48. To divide powers with the same base...
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.
Percentage Change = Difference/Original * 100
1/2 h (b1 + b2)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

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

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50. What is the probability?
Number of desired outcomes/number of total outcomes
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.
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.