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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. What is the distance formula?
2Length + 2width [or (length + width) x 2]
Opens down
Sqr( x2 -x1) + (y2- y1)
Sum of terms/number of terms

2. Area of Circles
Lwh
A=?r2
Total distance/total time
(0 -0)

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

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4. What is the average?
The average - mean - median - or mode.
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.
Sum of terms/number of terms
The set of points which are all the same distance (the radius) from a certain point (the center).

5. Define the range of a set of numbers.
y = k/x
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.
2Length + 2width [or (length + width) x 2]
Order does matter for a permutation - but does not matter for a combination.

6. 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.
Equal
Less
Pir^2h

7. Volume of Cylinder
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
y-y1=m(x-x1)
Arrangements - orders - schedules - or lists.
Pir^2h

8. 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. Given event A: A + notA = 1.
(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.

9. Perimeter of rectangle
2l+2w
Number of desired outcomes/number of total outcomes
½(b1 +b2) x h [or (b1 +b2) x h÷2]
1.7

10. Area of a sector
The four big angles are equal and the four small angles are equal
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
x°/360 times (?r²) - where x is the degrees in the angle

11. Define the mode of a set of numbers.
Opens up
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.
½(base x height) [or (base x height)÷2]
C =?d

12. Radius (Radii)
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.
An ange whose vertex is the center of the circle
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 segment connecting the center of a circle to any point on the circle

13. Lines reflected over the x or y axis have ____ slopes.
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
Negative
(n degrees/360) * (pi)r^2
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.

14. What is the circumference of a circle?
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.
(a-b)(a²+ab+b²)
2(pi)r
2lw+2lh+2wh

15. Area of Parallelogram
2(lw+wh+lh)
Percentage Change = Difference/Original * 100
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

16. What is a 'Right isosceles' triangle?
(x+y)(x-y)
(a-b)(a²+ab+b²)
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.
Number of desired outcomes/number of total outcomes

17. a² - b² is equal to
(a+b)(a-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.
A²-b²
Between 0 and 1.

18. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
(pi)r^2(h)
2pi*r
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.
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.

19. What is the volume of a cylinder?
(pi)r^2(h)
(n degrees/360) * 2(pi)r
x² + 2xy + y²
Pir^2h

20. Surface Area of rectangular prism
2lw+2lh+2wh
C =?d
2(pi)r
A²-b²

21. What is the 'distributive law'?
b±[vb²-4ac]/2a
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.
(a-b)(a²+ab+b²)
(a-b)(a+b)

22. Define a factorial of a number - and how it is written.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
S² - where s = length of a side
(pi)r^2(h)
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.

23. How do you find the midpoint?
Not necessarily. This is a trick question - because x could be either positive or negative.
Sum of terms/number of terms
Groups - teams - or committees.
(x1+x2)/2 - (y1+y2)/2

24. What is the length of an arc?
T1 + (n-1)d
The distance across the circle through the center of the circle.The diameter is twice the radius.
Pi*r^2
(n degrees/360) * 2(pi)r

25. What is the unfactored version of x²-y² ?
Lw
?d OR 2?r
(x+y)(x-y)
2(lw+wh+lh)

26. Define the 'Third side' rule for triangles

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27. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
N x M
A=?r2
?d OR 2?r
1/2 h (b1 + b2)

28. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
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'.
Sum of terms/number of terms
Sum of the lengths of the sides

29. Arc
1/2bh
(n degrees/360) * 2(pi)r
Part of a circle connecting two points on the circle.
Arrangements - orders - schedules - or lists.

30. The probability of an event happening and the probability of an event NOT happening must add up to what number?
b±[vb²-4ac]/2a
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.
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.
1. Given event A: A + notA = 1.

31. The length of one side of any triangle is ____ than the sum of the other two sides.
Lwh
Less
b±[vb²-4ac]/2a
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

32. To divide powers with the same base...
A=bh
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.
Groups - teams - or committees.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

33. Define 'proportionate' values
½(b1 +b2) x h [or (b1 +b2) x h÷2]
1/2 h (b1 + b2)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

34. Circle
The set of points which are all the same distance (the radius) from a certain point (the center).
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 part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.
1/2bh

35. Perimeter of a square
2(pi)r
Pir^2h
4s (where s = length of a side)
Pi*r^2

36. What is the unfactored version of (x+y)² ?
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.
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)²
x² + 2xy + y²

37. Surface Area of Sphere
Ac+ad+bc+bd
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Middle term
4pir^2

38. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Lw
Probability A + Probability B
y = kx

39. a²-2ab+b²
A segment connecting the center of a circle to any point on the circle
1
(a-b)²
½(b1 +b2) x h [or (b1 +b2) x h÷2]

40. a²-b²
Between 0 and 1.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a-b)(a+b)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

41. What is inversely proportional?
y = k/x
4s
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Lwh

42. Perimeter (circumference) of a circle
2 pi r
2x2x2x5x5
Pir^2h
x°/360 times (2 pi r) - where x is the degrees in the angle

43. What is the volume of a solid rectangle?
Middle term
(a-b)(a+b)
(x1+x2)/2 - (y1+y2)/2
Lwh

44. What is the factored version of x² + 2xy + y² ?
½(base x height) [or (base x height)÷2]
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a+b)(a²-ab+b²)
(x+y)²

45. How do you multiply powers with the same base?
Pi*r^2
1/2 h (b1 + b2)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(x1+x2)/2 - (y1+y2)/2

46. 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.
The distance across the circle through the center of the circle.The diameter is twice the radius.
(x+y)(x-y)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

47. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Negative
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
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.
1

48. What do combination problems usually ask for?
(y2-y1)/(x2-x1)
Groups - teams - or committees.
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.
Order does matter for a permutation - but does not matter for a combination.

49. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
2(pi)r(r+h)
1/x^a
(n-2)180

50. perimeter of square
S*v2
Probability A * Probability B
4s
1.4