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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. 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.
Probability A * Probability B
T1 * r^(n-1)/(r-1)
x°/360 times (2 pi r) - where x is the degrees in the angle

2. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-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
y = k/x
Probability A + Probability B

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

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4. What is the volume of a cylinder?
2l+2w
Bh
An ange whose vertex is the center of the circle
(pi)r^2(h)

5. Volume of Cylinder
Pir^2h
(a-b)(a+b)
2lw+2lh+2wh
2 pi r

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

7. What is a '30:60:90' triangle?
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.
(n/2) * (t1+tn)
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
A²-b²

8. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
Last term
Lw
(a+b)(a²-ab+b²)
N x M

9. In intersecting lines - opposite angles are _____.
x² -2xy + y²
x²-y²
An ange whose vertex is the center of the circle
Equal

10. Define the range of a set of numbers.
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.
4pir^2
Opens up
The distance across the circle through the center of the circle.The diameter is twice the radius.

11. What is the area of a triangle?
Groups - teams - or committees.
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
1/2bh
1/x^a

12. What is the length of an arc?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(n degrees/360) * 2(pi)r
4pir^2
x°/360 times (?r²) - where x is the degrees in the angle

13. Point-Slope form
Between 0 and 1.
(a+b)(a-b)
y-y1=m(x-x1)
A=bh

14. If x² = 144 - does v144 = x?
T1 * r^(n-1)
Not necessarily. This is a trick question - because x could be either positive or negative.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
x² + 2xy + y²

15. What is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1/2bh
Ac+ad+bc+bd
Lw

16. How do you multiply powers with the same base?
S² - where s = length of a side
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(x+y)²
Groups - teams - or committees.

17. Rough est. of v3 =
1.7
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'.
(x+y)²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

18. Surface Area of Cylinder
Between 0 and 1.
y = k/x
2pir^2 + 2pir*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

19. What is the area of a circle?
S² - where s = length of a side
2lw+2lh+2wh
Bh
(pi)r^2

20. What is the unfactored version of x²-y² ?
(x+y)(x-y)
A=bh
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.
Ac+ad+bc+bd

21. What is the probability?
Number of desired outcomes/number of total outcomes
1/3Bh
Total distance/total time
S^2

22. Perimeter of rectangle
2l+2w
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
y2-y1/x2-x1
2(lw+wh+lh)

23. Chord
1/x^a
The distance from one point on the circle to another point on the circle.
The total # of possible outcomes.
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.

24. In a coordinate system - what is the origin?
Sum of terms/number of terms
(pi)r^2
(0 -0)
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.

25. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Probability A * Probability B
(x1+x2)/2 - (y1+y2)/2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Opens down

26. Arc
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The distance from one point on the circle to another point on the circle.
Part of a circle connecting two points on the 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

27. Rough est. of v1 =
(a+b)²
1.4
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.

28. What is the area of a solid rectangle?
S^2
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2(lw+wh+lh)
(x1+x2)/2 - (y1+y2)/2

29. How do you find the slope?
y2-y1/x2-x1
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Pi*r^2

30. How do you calculate the percentage of change?
(a+b)(a-b)
C =?d
A+b
Percentage Change = Difference/Original * 100

31. x^-a =
(a-b)²
1/x^a
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
(x+y)²

32. Volume of prism
(a-b)(a+b)
Bh
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
b±[vb²-4ac]/2a

33. When you reverse FOIL - the term that needs to add out is the _____
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
Middle term
b±[vb²-4ac]/2a
S² - where s = length of a side

34. If something is certain to happen - how is the probability of this event expressed mathematically?
(a+b)(a-b)
1/1
A+b
2 pi r

35. Circumference of a circle
(a+b)²
?d OR 2?r
(n degrees/360) * 2(pi)r
2lw+2lh+2wh

36. To divide powers with the same base...
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.
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.
(a-b)(a²+ab+b²)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

37. 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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38. Define a factorial of a number - and how it is written.
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
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.
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.

39. Lines reflected over the x or y axis have ____ slopes.
A=?r2
?r²
Negative
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.

40. What is the side ratio for a 30:60:90 triangle?
Part of a circle connecting two points on the circle.
Sqr( x2 -x1) + (y2- y1)
Groups - teams - or committees.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

41. The length of one side of any triangle is ____ than the sum of the other two sides.
Probability A * Probability B
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.
Less
Sum of terms/number of terms

42. Circumference Formula
1/3Bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
A+b
C =?d

43. What is directly proportional?
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'.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(0 -0)
y = kx

44. What do combination problems usually ask for?
A²-b²
Sqr( x2 -x1) + (y2- y1)
A+b
Groups - teams - or committees.

45. What is the surface area of a cylinder?
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.
Bh
4s (where s = length of a side)
2(pi)r(r+h)

46. What is the formula for the diagonal of any square?
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.
S*v2
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

47. a²-2ab+b²
(a-b)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.
A=bh
b±[vb²-4ac]/2a

48. What is the volume of a solid rectangle?
1. Given event A: A + notA = 1.
2Length + 2width [or (length + width) x 2]
Lwh
y = k/x

49. Sector
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.
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.
Equal
Bh

50. 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.
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.
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.
y-y1=m(x-x1)

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GRE Math 2

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