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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.
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. Surface Area of Cylinder
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
S*v2
2(pi)r(r+h)
2pir^2 + 2pir*h

2. Central Angle
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.
An ange whose vertex is the center of the circle
2 pi r
2Length + 2width [or (length + width) x 2]

3. Circumference of a circle using radius
y2-y1/x2-x1
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2pi*r

4. 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.
1.7
(0 -0)
(a-b)(a+b)

5. How do you find the sum of an arithmetic sequence?
(n/2) * (t1+tn)
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.
2(pi)r(r+h)
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.

6. Rough est. of v1 =
1
1/x^a
Less
The distance across the circle through the center of the circle.The diameter is twice the radius.

7. Area of a trapezoid
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Number of desired outcomes/number of total outcomes
Pir^2h

8. What is the unfactored version of x²-y² ?
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.
Middle term
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)(x-y)

9. How do you find the slope?
Sum of terms/number of terms
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.
y2-y1/x2-x1
x² + 2xy + y²

10. What is the average speed?
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.
2lw+2lh+2wh
(a-b)²
Total distance/total time

11. What is an 'equilateral' triangle?
Bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(n degrees/360) * (pi)r^2
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.

12. How do you multiply and divide square roots?
4s (where s = length of a side)
2Length + 2width [or (length + width) x 2]
(a+b)²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

13. If something is certain to happen - how is the probability of this event expressed mathematically?
(y2-y1)/(x2-x1)
(a+b)(a²-ab+b²)
1/1
(a-b)(a²+ab+b²)

14. What'S the most important thing to remember about charts you'll see on the GRE?
Sqr( x2 -x1) + (y2- y1)
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.
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.

15. What is the factored version of x² -2xy + y² ?
(x-y)²
2 pi r
(y2-y1)/(x2-x1)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

16. Volume of Cylinder
Pir^2h
x°/360 times (2 pi r) - where x is the degrees in the angle
½(b1 +b2) x h [or (b1 +b2) x h÷2]
1/2 h (b1 + b2)

17. When you reverse FOIL - the term that needs to multiply out is the _____
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.
Last term
1/2 h (b1 + b2)
2 pi r

18. What is the equation of a line?

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19. Area of a square
Equal
S² - where s = length of a side
1/3pir^2*h
Opens up

20. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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. 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
1/1
Pi*r^2

21. When a line crosses two parallel lines - ________.
2l+2w
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.
The four big angles are equal and the four small angles are equal
S^2

22. Surface Area of rectangular prism
Pi*r^2
(a-b)(a²+ab+b²)
2lw+2lh+2wh
(a+b)²

23. What is a 'Right isosceles' triangle?
2pir^2 + 2pir*h
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
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.

24. In a parabola - if the first term is positive - 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.
Opens up
1/2bh
?d OR 2?r

25. Area of Trapezoid
x² + 2xy + y²
S^2
Probability A + Probability B
1/2 h (b1 + b2)

26. Rough est. of v3 =
1.7
(y2-y1)/(x2-x1)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(a+b)²

27. Area of Circles
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.
A=?r2
Sqr( x2 -x1) + (y2- y1)
Order does matter for a permutation - but does not matter for a combination.

28. How do you find the nth term of an arithmetic sequence?
Opens down
T1 + (n-1)d
Less
(pi)r^2(h)

29. Perimeter of a rectangle
Last term
The distance from one point on the circle to another point on the circle.
2Length + 2width [or (length + width) x 2]
4/3pir^3

30. Define the 'Third side' rule for triangles

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31. If something is possible but not certain - what is the numeric range of probability of it happening?
x²-y²
Between 0 and 1.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.

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

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33. Radius (Radii)
Pi*r^2
A segment connecting the center of a circle to any point on 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.
T1 + (n-1)d

34. What is directly proportional?
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
y = kx
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.
A²-b²

35. What is the formula for the diagonal of any square?
Pi*d
Less
S*v2
The four big angles are equal and the four small angles are equal

36. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Part of a circle connecting two points on the circle.
y-y1=m(x-x1)
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.
(n-2)180

37. Define 'proportionate' values
(a+b)(a-b)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1. Given event A: A + notA = 1.
1.4

38. What is the circumference of a circle?
1/3pir^2*h
2(pi)r
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

39. Quadratic Formula
2(pi)r(r+h)
2(pi)r
b±[vb²-4ac]/2a
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.

40. How do you calculate a diagonal inside a 3-dimensional rectangular box?
(x+y)(x-y)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(x+y)²
2pir^2 + 2pir*h

41. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
N x M
The four big angles are equal and the four small angles are equal
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

42. In a parabola - if the first term is negative - the parabola ________.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Opens down
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.
A=?r2

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

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44. To divide powers with the same base...
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
x°/360 times (2 pi r) - where x is the degrees in the angle
2pir^2 + 2pir*h

45. What is the prime factorization of 200?
2x2x2x5x5
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.
The distance from one point on the circle to another point on the circle.
(pi)r^2

46. Area of a circle
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.
T1 * r^(n-1)
?r²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

47. What is the length of an arc?
y = k/x
(n degrees/360) * 2(pi)r
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Not necessarily. This is a trick question - because x could be either positive or negative.

48. What is the 'Third side' rule for triangles?
2(lw+wh+lh)
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.
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.
(y2-y1)/(x2-x1)

49. List two odd behaviors of exponents
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.
2Length + 2width [or (length + width) x 2]
2(lw+wh+lh)
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.

50. a³+b³
x² -2xy + y²
(a-b)(a²+ab+b²)
(a+b)(a²-ab+b²)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

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GRE Math 2

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