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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. perimeter of square
(n degrees/360) * (pi)r^2
T1 + (n-1)d
2(pi)r
4s

2. Area of a square
1.4
2x2x2x5x5
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
S² - where s = length of a side

3. Circumference of a circle
1.4
(x1+x2)/2 - (y1+y2)/2
Total distance/total time
?d OR 2?r

4. How do you multiply powers with the same base?
Number of desired outcomes/number of total outcomes
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A=bh
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.

5. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Pir^2h
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
b±[vb²-4ac]/2a
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.

6. Perimeter of a rectangle
y2-y1/x2-x1
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.
1/x^a
2Length + 2width [or (length + width) x 2]

7. What is the surface area of a cylinder?
2(pi)r(r+h)
1. Given event A: A + notA = 1.
Bh
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

8. What is the side ratio for a 30:60:90 triangle?
Sum of the lengths of the sides
Middle term
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.

9. Rough est. of v1 =
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
A+b

10. Volume of Cylinder
Pir^2h
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
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 distance across the circle through the center of the circle.The diameter is twice the radius.

11. a²+2ab+b²
(a+b)²
Opens up
Opens down
(n/2) * (t1+tn)

12. Diameter
(0 -0)
Lw
The distance across the circle through the center of the circle.The diameter is twice the radius.
Pir^2h

13. List two odd behaviors of exponents
½(base x height) [or (base x height)÷2]
2x2x2x5x5
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.
2 pi r

14. In a parabola - if the first term is negative - the parabola ________.
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.
Opens down
Equal
T1 * r^(n-1)/(r-1)

15. How do you find the midpoint?
Lw
(x1+x2)/2 - (y1+y2)/2
(pi)r^2
The distance from one point on the circle to another point on the circle.

16. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
2(pi)r(r+h)
T1 + (n-1)d
(x+y)(x-y)

17. a³+b³
(a+b)(a²-ab+b²)
A²-b²
2pir^2 + 2pir*h
1/3Bh

18. Rough est. of v2 =
(y2-y1)/(x2-x1)
Bh
S² - where s = length of a side
1.4

19. Explain the special properties of zero.
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
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.
(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.

20. What is the factored version of x² -2xy + y² ?
1/1
(x-y)²
1
2(pi)r

21. To divide powers with the same base...
(n/2) * (t1+tn)
1/x^a
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The set of points which are all the same distance (the radius) from a certain point (the center).

22. How do you calculate a diagonal inside a 3-dimensional rectangular box?
N x M
The four big angles are equal and the four small angles are equal
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1/1

23. How do you multiply and divide square roots?
Lw
A=bh
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A+b

24. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
N x M
2 pi r
(y2-y1)/(x2-x1)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

25. (a+b)(c+d)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Ac+ad+bc+bd
2pir^2 + 2pir*h
An ange whose vertex is the center of the circle

26. Sector
2pi*r
2(lw+wh+lh)
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.
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.

27. Surface Area of Cylinder
Lw
2pir^2 + 2pir*h
C =?d
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

28. a³-b³
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(a-b)(a²+ab+b²)
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.
?d OR 2?r

29. Surface Area of Sphere
4pir^2
x°/360 times (?r²) - where x is the degrees in the angle
b±[vb²-4ac]/2a
y2-y1/x2-x1

30. What is the average speed?
4/3pir^3
2(pi)r(r+h)
(n degrees/360) * 2(pi)r
Total distance/total time

31. Area of Triangle
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Ac+ad+bc+bd
2pir^2 + 2pir*h
1/2bh

32. What is the area of a triangle?
T1 * r^(n-1)/(r-1)
1/2bh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(x1+x2)/2 - (y1+y2)/2

33. What is the unfactored version of x²-y² ?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Last term
(a-b)(a+b)
(x+y)(x-y)

34. Surface Area of rectangular prism
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.
1/2 h (b1 + b2)
2lw+2lh+2wh

35. Central 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.
An ange whose vertex is the center of the circle
2x2x2x5x5
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

36. What do combination problems usually ask for?
Groups - teams - or committees.
(n degrees/360) * (pi)r^2
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
?d OR 2?r

37. 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.
x°/360 times (2 pi r) - where x is the degrees in the angle
1/3Bh
Sum of the lengths of the sides

38. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
?d OR 2?r
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.
C =?d

39. Slope
(a-b)²
2pir^2 + 2pir*h
(y2-y1)/(x2-x1)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

40. What is the side ratio for a Right Isosceles triangle?
(a+b)(a-b)
(x+y)(x-y)
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

41. What is the area of a circle?
(pi)r^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.
The four big angles are equal and the four small angles are equal
Pi*r^2

42. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
S^2
(x1+x2)/2 - (y1+y2)/2
x² -2xy + y²

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

44. What is the circumference of a circle?
2(pi)r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/2bh
Ac+ad+bc+bd

45. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Ac+ad+bc+bd
1/x^a
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

46. What must be true before a quadratic equation can be solved?

47. 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.
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.
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+b

48. Does order matter for a permutation? How about for a combination?
(y-y1)=m(x-x1)
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.
Negative
Order does matter for a permutation - but does not matter for a combination.

49. Perimeter of polygon
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(x+y)²
(pi)r^2(h)
Sum of the lengths of the sides

50. What is the factored version of (x+y)(x-y) ?
1/3pir^2*h
1/2bh
2(lw+wh+lh)
x²-y²