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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 unfactored version of x²-y² ?
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
(x+y)(x-y)
Opens down
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'.

2. Perimeter of polygon
Sum of the lengths of the sides
1/2bh
1.7
Probability A * Probability B

3. Area of a square
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2(pi)r(r+h)
S² - where s = length of a side
(y-y1)=m(x-x1)

4. When you reverse FOIL - the term that needs to add out is the _____
Middle term
(x+y)(x-y)
4s (where s = length of a side)
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.

5. To divide powers with the same base...
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Bh
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'.

6. Define the formula for calculating slope.
A+b
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Middle term
Less

7. What is the area of a triangle?
1/2bh
A segment connecting the center of a circle to any point on the circle
Probability A * Probability B
Sqr( x2 -x1) + (y2- y1)

8. What is a 'Right isosceles' triangle?
T1 * r^(n-1)/(r-1)
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.
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.
4s

9. How do you find the sum of an arithmetic sequence?
(a-b)(a²+ab+b²)
Sum of the lengths of the sides
(n/2) * (t1+tn)
The distance from one point on the circle to another point on the circle.

10. When a line crosses two parallel lines - ________.
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 four big angles are equal and the four small angles are equal
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.
x² -2xy + y²

11. What is inversely proportional?
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.
Negative
Number of desired outcomes/number of total outcomes
y = k/x

12. The length of one side of any triangle is ____ than the sum of the other two sides.
Sum of the lengths of the sides
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Less
y-y1=m(x-x1)

13. In intersecting lines - opposite angles are _____.
1. Given event A: A + notA = 1.
1/2bh
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.
Equal

14. a²-2ab+b²
(a-b)²
1.4
Percentage Change = Difference/Original * 100
A=bh

15. 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.
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.
Pi*r^2
1.4

16. What do combination problems usually ask for?
Less
Groups - teams - or committees.
The set of points which are all the same distance (the radius) from a certain point (the center).
(y-y1)=m(x-x1)

17. Area of Circle
Pi*r^2
2lw+2lh+2wh
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A+b

18. Volume of pyramid
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
1/3Bh
y = k/x
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

19. What is the length of an arc?
Negative
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.
(n degrees/360) * 2(pi)r
Groups - teams - or committees.

20. Surface Area of rectangular prism
x² + 2xy + y²
Arrangements - orders - schedules - or lists.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2lw+2lh+2wh

21. In a coordinate system - what is the origin?
y = k/x
(0 -0)
2(pi)r(r+h)
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.

22. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
?d OR 2?r
A segment connecting the center of a circle to any point on the circle
Total distance/total time

23. Area of Square
S^2
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Pi*r^2
2(pi)r(r+h)

24. What is the 'Third side' rule for triangles?
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.
Less
2pi*r
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.

25. What is the average?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Bh
Sum of terms/number of terms
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

26. Define the range of a set of numbers.
S*v2
Less
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.
?d OR 2?r

27. Circumference Formula
S² - where s = length of a side
4pir^2
C =?d
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.

28. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
1/3Bh
2lw+2lh+2wh
Order does matter for a permutation - but does not matter for a combination.
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.

29. Area of a circle
x² + 2xy + y²
Percentage Change = Difference/Original * 100
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
?r²

30. What is the area of a circle?
2(pi)r(r+h)
T1 * r^(n-1)
(y-y1)=m(x-x1)
(pi)r^2

31. When you reverse FOIL - the term that needs to multiply out is the _____
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.
Last term
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.
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.

32. How do you find the nth term of a geometric sequence?
Sum of the lengths of the sides
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.
T1 * r^(n-1)

33. Surface Area of Sphere
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
4pir^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
The distance across the circle through the center of the circle.The diameter is twice the radius.

34. Rough est. of v1 =
Pi*d
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
T1 + (n-1)d
1

35. a³-b³
(a-b)(a²+ab+b²)
2Length + 2width [or (length + width) x 2]
(n/2) * (t1+tn)
1

36. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
The set of points which are all the same distance (the radius) from a certain point (the center).
Part of a circle connecting two points on the circle.
A=bh
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.

37. What is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Not necessarily. This is a trick question - because x could be either positive or negative.
T1 * r^(n-1)
4pir^2

38. Slope
(y2-y1)/(x2-x1)
2pir^2 + 2pir*h
N x M
Arrangements - orders - schedules - or lists.

39. If something is possible but not certain - what is the numeric range of probability of it happening?
Number of desired outcomes/number of total outcomes
Total distance/total time
Between 0 and 1.
Probability A + Probability B

40. Define a factorial of a number - and how it is written.
A segment connecting the center of a circle to any point on the circle
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.
(pi)r^2(h)
Not necessarily. This is a trick question - because x could be either positive or negative.

41. Circumference of cirlce using diameter
y-y1=m(x-x1)
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.
Pi*d
Bh

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

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43. Point-Slope form
y-y1=m(x-x1)
Number of desired outcomes/number of total outcomes
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.
Not necessarily. This is a trick question - because x could be either positive or negative.

44. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
(n degrees/360) * 2(pi)r
Probability A + Probability B
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.
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'.

45. What is the average speed?
(x+y)²
y2-y1/x2-x1
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Total distance/total time

46. Rough est. of v3 =
(x+y)²
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'.
Between 0 and 1.

47. How do you calculate the percentage of change?
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.
Percentage Change = Difference/Original * 100
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.
1/2bh

48. Sector
(n degrees/360) * 2(pi)r
(x+y)(x-y)
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.
2x2x2x5x5

49. x^-a =
2(lw+wh+lh)
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+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.
1/x^a

50. What is the surface area of a cylinder?
2(pi)r(r+h)
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
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
A²-b²