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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. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
S*v2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
T1 * r^(n-1)/(r-1)

2. Define the formula for calculating slope.
(x+y)(x-y)
S² - where s = length of a side
(a-b)(a²+ab+b²)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

3. Perimeter of a rectangle
x°/360 times (2 pi r) - where x is the degrees in the angle
T1 * r^(n-1)/(r-1)
2 pi r
2Length + 2width [or (length + width) x 2]

4. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A=bh
Groups - teams - or committees.
1. Given event A: A + notA = 1.

5. (a+b)(a-b)=
(a+b)²
A²-b²
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.
Between 0 and 1.

6. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Less
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Middle term

7. Diameter
Between 0 and 1.
A=?r2
Not necessarily. This is a trick question - because x could be either positive or negative.
The distance across the circle through the center of the circle.The diameter is twice the radius.

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

9. When you reverse FOIL - the term that needs to add out is the _____
Negative
(n-2)180
1.7
Middle term

10. What is the factored version of x² -2xy + y² ?
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
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-y)²

11. Area of rectangle - square - parallelogram
A=bh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(n-2)180
2pi*r

12. What is the length of an arc?
(n degrees/360) * 2(pi)r
Order does matter for a permutation - but does not matter for a combination.
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
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.

13. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
T1 + (n-1)d
4s
1/1
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.

14. Area of Square
?d OR 2?r
Arrangements - orders - schedules - or lists.
The average - mean - median - or mode.
S^2

15. Volume of Cylinder
(y2-y1)/(x2-x1)
1/1
Pir^2h
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.

16. Circumference of cirlce using diameter
Pi*d
(a+b)²
1/x^a
1/2bh

17. What is the equation of a line?

18. Circumference of a circle
(a-b)(a²+ab+b²)
A²-b²
Number of desired outcomes/number of total outcomes
?d OR 2?r

19. length of a sector
Less
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.
(n/2) * (t1+tn)

20. Area of Triangle
(a-b)²
1/2bh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(x1+x2)/2 - (y1+y2)/2

21. How do you find the nth term of a geometric sequence?
C =?d
T1 * r^(n-1)
Not necessarily. This is a trick question - because x could be either positive or negative.
A+b

22. What is the area of a cylinder?
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.
2(pi)r(r+h)
4/3pir^3
Arrangements - orders - schedules - or lists.

23. Circumference of a circle using radius
2pi*r
1/2 h (b1 + b2)
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.
(n/2) * (t1+tn)

24. What is the formula for the diagonal of any square?
A²-b²
S*v2
C =?d
Less

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

26. Rough est. of v1 =
Lwh
1
x²-y²
Groups - teams - or committees.

27. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
(x+y)(x-y)
x²-y²
Opens up

28. What is directly proportional?
Total distance/total time
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 x M
y = kx

29. Area of a trapezoid
Probability A * Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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'.

30. What is the factored version of (x+y)(x-y) ?
x²-y²
1/1
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.
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.

31. Arc
Probability A * Probability B
2lw+2lh+2wh
Part of a circle connecting two points on the circle.
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

32. Volume of prism
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.
Pi*d
1/2bh
Bh

33. What is the circumference of a circle?
T1 * r^(n-1)/(r-1)
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 (?r²) - where x is the degrees in the angle
2(pi)r

34. (a+b)(c+d)
Ac+ad+bc+bd
?r²
1. Given event A: A + notA = 1.
(a+b)(a-b)

35. What is 'absolute value' - and how is it represented?

36. What is the 'distributive law'?
Total distance/total time
x°/360 times (?r²) - where x is the degrees in the angle
A²-b²
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.

37. In a coordinate system - identify the quadrants and describe their location.
(x+y)(x-y)
(x+y)²
An ange whose vertex is the center of the circle
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

38. How do you solve a permutation?
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.
The four big angles are equal and the four small angles are equal
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

39. What'S the most important thing to remember about charts you'll see on the GRE?
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+b)(a-b)
The four big angles are equal and the four small angles are equal
The total # of possible outcomes.

40. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/1
Bh
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.

41. Radius (Radii)
1
1/3Bh
Part of a circle connecting two points on the circle.
A segment connecting the center of a circle to any point on the circle

42. How do you calculate the probability of two events in a row? (Probability of A and B)
x°/360 times (?r²) - where x is the degrees in the angle
Probability A * Probability B
2l+2w
2x2x2x5x5

43. Surface Area of rectangular prism
Total distance/total time
(n degrees/360) * 2(pi)r
2lw+2lh+2wh
(a-b)²

44. Area of a circle
The set of points which are all the same distance (the radius) from a certain point (the center).
?r²
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+b)²

45. Rough est. of v3 =
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
1.7
x°/360 times (?r²) - where x is the degrees in the angle
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.

46. Explain the special properties of zero.
(a-b)²
Probability A * Probability B
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.
(y-y1)=m(x-x1)

47. Area of a sector
A²-b²
A=bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
x°/360 times (?r²) - where x is the degrees in the angle

48. Define the 'Third side' rule for triangles

49. Central Angle
4s
An ange whose vertex is the center of the circle
Equal
Groups - teams - or committees.

50. a²-2ab+b²
Ac+ad+bc+bd
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.
(x1+x2)/2 - (y1+y2)/2
(a-b)²