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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. a²+2ab+b²
(a+b)²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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(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.

2. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
(0 -0)
Probability A + Probability B
A=bh

3. What number goes on the bottom of a probability fraction?
Less
Lw
x°/360 times (2 pi r) - where x is the degrees in the angle
The total # of possible outcomes.

4. Rough est. of v1 =
4s
Pi*r^2
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.

5. What is the 'Third side' rule for triangles?
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
Lw
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 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.

6. perimeter of square
(y-y1)=m(x-x1)
S^2
Bh
4s

7. What is inversely proportional?
Opens down
y = k/x
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.
Order does matter for a permutation - but does not matter for a combination.

8. Volume of prism
Probability A * Probability B
(x-y)²
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.
Bh

9. What is the circumference of a circle?
4s
1. Given event A: A + notA = 1.
2(pi)r
Sum of terms/number of terms

10. What is the area of a solid rectangle?
2(lw+wh+lh)
Opens down
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
(n degrees/360) * (pi)r^2

11. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Pi*d
2lw+2lh+2wh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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

12. What is the area of a cylinder?
2(pi)r(r+h)
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
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.
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. What is the probability?
Number of desired outcomes/number of total outcomes
Probability A * Probability B
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.
S^2

14. Surface Area of rectangular prism
(a+b)(a-b)
1
2lw+2lh+2wh
4/3pir^3

15. Central Angle
(n-2)180
Last term
An ange whose vertex is the center of the circle
A²-b²

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

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17. Area of Trapezoid
(n-2)180
1/2 h (b1 + b2)
(a+b)(a²-ab+b²)
x²-y²

18. What is the area of a sector?
(n degrees/360) * (pi)r^2
A segment connecting the center of a circle to any point on the circle
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The distance from one point on the circle to another point on the circle.

19. Area of rectangle - square - parallelogram
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
A segment connecting the center of a circle to any point on the circle
(a+b)(a²-ab+b²)
A=bh

20. Area of Circle
x² + 2xy + y²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Pi*r^2
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.

21. a³-b³
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
1.4
(a-b)(a+b)
(a-b)(a²+ab+b²)

22. What is directly proportional?
y = kx
Lw
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
Probability A + Probability B

23. Circumference of a circle
A segment connecting the center of a circle to any point on the circle
?d OR 2?r
2(pi)r(r+h)
The four big angles are equal and the four small angles are equal

24. Circumference of cirlce using diameter
Order does matter for a permutation - but does not matter for a combination.
Ac+ad+bc+bd
Pi*d
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.

25. How do you calculate the probability of two events in a row? (Probability of A and B)
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.
Probability A * Probability B
4/3pir^3
Sqr( x2 -x1) + (y2- y1)

26. Define the 'Third side' rule for triangles

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27. List two odd behaviors of exponents
(n-2)180
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.
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

28. x^-a =
1/x^a
1.7
Not necessarily. This is a trick question - because x could be either positive or negative.
x² -2xy + y²

29. What is an 'equilateral' triangle?
(x+y)(x-y)
x°/360 times (2 pi r) - where x is the degrees in the angle
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1/1

30. What is the area of a circle?
A=bh
(pi)r^2
x°/360 times (2 pi r) - where x is the degrees in the angle
x² + 2xy + y²

31. What are the side ratios for a 30:60:90 triangle?
2 pi r
(y2-y1)/(x2-x1)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/x^a

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

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33. How do you multiply and divide square roots?
N x M
1/1
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.

34. What is the unfactored version of x²-y² ?
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.
Bh
(x+y)(x-y)
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.

35. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
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
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
?r²
N x M

36. Area of a circle
?r²
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
The average - mean - median - or mode.
Part of a circle connecting two points on the circle.

37. How do you multiply powers with the same base?
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.
(a+b)(a-b)
1/1
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

38. What is the area of a triangle?
Bh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2lw+2lh+2wh
1/2bh

39. Define the range of a set of numbers.
y-y1=m(x-x1)
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 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(lw+wh+lh)

40. a³+b³
(a-b)(a²+ab+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.
1/1
(a+b)(a²-ab+b²)

41. How do you find the nth term of a geometric sequence?
(n-2)180
(x+y)²
2pir^2 + 2pir*h
T1 * r^(n-1)

42. Volume of pyramid
A=bh
1/3Bh
(n/2) * (t1+tn)
b±[vb²-4ac]/2a

43. Perimeter of rectangle
Sum of the lengths of the sides
2l+2w
2lw+2lh+2wh
T1 * r^(n-1)/(r-1)

44. What is a '30:60:90' triangle?
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2(pi)r
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
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.

45. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
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.
Middle term
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

46. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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.
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.
Negative

47. What is the average?
Negative
2Length + 2width [or (length + width) x 2]
1/1
Sum of terms/number of terms

48. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
(pi)r^2
S*v2
1. Given event A: A + notA = 1.

49. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

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50. 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.
4s (where s = length of a side)
2Length + 2width [or (length + width) x 2]
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.