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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. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
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
x² -2xy + y²

2. In a parabola - if the first term is positive - the parabola ________.
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.
The set of points which are all the same distance (the radius) from a certain point (the center).
Opens up

3. What is the area of a triangle?
1/2bh
2pir^2 + 2pir*h
The distance across the circle through the center of the circle.The diameter is twice the radius.
y = kx

4. What is the area of a solid rectangle?
2(lw+wh+lh)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Order does matter for a permutation - but does not matter for a combination.
1/2bh

5. What is the volume of a solid rectangle?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Ac+ad+bc+bd
1
Lwh

6. What is the unfactored version of (x+y)² ?
2(pi)r(r+h)
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.
x² + 2xy + y²
1/2bh

7. What is the volume of a cylinder?
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.
(n degrees/360) * (pi)r^2
Bh
(pi)r^2(h)

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

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9. What do combination problems usually ask for?
2(pi)r
?d OR 2?r
1. Given event A: A + notA = 1.
Groups - teams - or committees.

10. (a+b)(a-b)=
2 pi r
S*v2
1/3Bh
A²-b²

11. What is the average speed?
2l+2w
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'.
Negative
Total distance/total time

12. Area of a circle
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
Pir^2h
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'.
?r²

13. How do you calculate the surface area of a rectangular box?
Part of a circle connecting two points on the circle.
S^2
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.
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.

14. How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
T1 + (n-1)d
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.
(x-y)²

15. What is the area of a cylinder?
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
(a-b)(a²+ab+b²)
2(pi)r(r+h)
Equal

16. Sector
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.
S*v2
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.
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.

17. perimeter of square
½(base x height) [or (base x height)÷2]
1. Given event A: A + notA = 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.
4s

18. Area of a sector
The total # of possible outcomes.
x°/360 times (?r²) - where x is the degrees in the angle
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 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.

19. Rough est. of v2 =
S² - where s = length of a side
y = k/x
Opens up
1.4

20. What are the side ratios for a 30:60:90 triangle?
1/2 h (b1 + b2)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A=?r2
y = kx

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

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22. Volume of prism
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 four big angles are equal and the four small angles are equal
T1 * r^(n-1)
Bh

23. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
1.7
Probability A * Probability B
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.

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

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25. Area of a triangle
Order does matter for a permutation - but does not matter for a combination.
(x+y)²
Total distance/total time
½(base x height) [or (base x height)÷2]

26. Circumference of a circle
?d OR 2?r
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
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

27. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
1/x^a
Probability A + Probability B
A+b
The set of points which are all the same distance (the radius) from a certain point (the center).

28. How do you find the nth term of a geometric sequence?
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.
S² - where s = length of a side
T1 * r^(n-1)
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

29. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The four big angles are equal and the four small angles are equal
2pi*r
Groups - teams - or committees.

30. What is a '30:60:90' triangle?
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
4s
y2-y1/x2-x1
x°/360 times (?r²) - where x is the degrees in the angle

31. Area of Circle
Pi*r^2
y2-y1/x2-x1
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(n degrees/360) * (pi)r^2

32. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
(pi)r^2
Lw
T1 + (n-1)d

33. Volume of Cone
1/3pir^2*h
Less
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(pi)r^2(h)

34. What is the area of a circle?
A=bh
(pi)r^2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The total # of possible outcomes.

35. Area of rectangle - square - parallelogram
The distance across the circle through the center of the circle.The diameter is twice the radius.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A=bh
Sqr( x2 -x1) + (y2- y1)

36. Perimeter of polygon
x² -2xy + y²
Sum of the lengths of the sides
A+b
Pir^2h

37. Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
A+b
?r²
Percentage Change = Difference/Original * 100

38. What is the unfactored version of x²-y² ?
(x+y)(x-y)
1/2bh
2pir^2 + 2pir*h
An ange whose vertex is the center of the circle

39. Area of a square
The four big angles are equal and the four small angles are equal
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
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

40. What is the area of a sector?
(n degrees/360) * (pi)r^2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2(pi)r(r+h)
1.7

41. Define a factorial of a number - and how it is written.
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.
1/1
Pi*r^2
2pir^2 + 2pir*h

42. What is an 'equilateral' triangle?
(a+b)(a²-ab+b²)
(a+b)(a-b)
2pir^2 + 2pir*h
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

43. Lines reflected over the x or y axis have ____ slopes.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
1/3Bh
Negative
A=?r2

44. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
T1 * r^(n-1)/(r-1)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
(a+b)(a²-ab+b²)

45. How do you find the slope?
y2-y1/x2-x1
1/3Bh
The distance across the circle through the center of the circle.The diameter is twice the radius.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

46. Rough est. of v1 =
1
Order does matter for a permutation - but does not matter for a combination.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

47. (a+b)(c+d)
Lwh
T1 * r^(n-1)/(r-1)
Ac+ad+bc+bd
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.

48. What is the surface area of a cylinder?
1/3pir^2*h
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.
2(pi)r(r+h)

49. x^a * x^b = x^__
A+b
½(base x height) [or (base x height)÷2]
(a+b)(a²-ab+b²)
(a-b)(a+b)

50. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
y2-y1/x2-x1
b±[vb²-4ac]/2a
4s (where s = length of a side)