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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 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.
Percentage Change = Difference/Original * 100
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
A segment connecting the center of a circle to any point on the circle

2. What is the area of a circle?
1
(pi)r^2
Equal
2(lw+wh+lh)

3. a³+b³
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
Number of desired outcomes/number of total outcomes
(a+b)(a²-ab+b²)
b±[vb²-4ac]/2a

4. a²-b²
The average - mean - median - or mode.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
S² - where s = length of a side
(a-b)(a+b)

5. What is the average speed?
Total distance/total time
2(pi)r(r+h)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.

6. What is the unfactored version of x²-y² ?
(x+y)(x-y)
1/3Bh
4s
Arrangements - orders - schedules - or lists.

7. a³-b³
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
(n-2)180
(a-b)(a²+ab+b²)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

8. How do you find the nth term of an arithmetic sequence?
1/2bh
T1 + (n-1)d
½(b1 +b2) x h [or (b1 +b2) x h÷2]
1

9. How do you calculate the surface area of a rectangular box?
A=bh
2(pi)r(r+h)
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(lw+wh+lh)

10. What is an 'equilateral' triangle?
(a+b)(a²-ab+b²)
Arrangements - orders - schedules - or lists.
(y-y1)=m(x-x1)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

11. Slope
Sqr( x2 -x1) + (y2- y1)
(y2-y1)/(x2-x1)
x² -2xy + y²
2l+2w

12. a²-2ab+b²
4s (where s = length of a side)
2(pi)r
(a-b)²
(a+b)(a²-ab+b²)

13. When a line crosses two parallel lines - ________.
(y-y1)=m(x-x1)
N x M
Probability A * Probability B
The four big angles are equal and the four small angles are equal

14. Area of a trapezoid
A=bh
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(x-y)²
Lw

15. What is the area of a triangle?
2lw+2lh+2wh
1/2bh
2Length + 2width [or (length + width) x 2]
The total # of possible outcomes.

16. What is inversely proportional?
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.
(a-b)(a²+ab+b²)
y = k/x
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.

17. What is the unfactored version of (x+y)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.
x²-y²
y-y1=m(x-x1)
x² + 2xy + y²

18. Surface Area of rectangular prism
2 pi r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
2lw+2lh+2wh

19. In a coordinate system - identify the quadrants and describe their location.
Between 0 and 1.
1/3Bh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2Length + 2width [or (length + width) x 2]

20. Area of rectangle - square - parallelogram
S^2
A²-b²
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
A=bh

21. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
S^2
(n-2)180
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.
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.

22. When you reverse FOIL - the term that needs to add out is the _____
The four big angles are equal and the four small angles are equal
The distance from one point on the circle to another point on the circle.
Middle term
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

23. What is the sum of the inside angles of an n-sided polygon?
2pir^2 + 2pir*h
(n-2)180
Sum of the lengths of the sides
The average - mean - median - or mode.

24. Area of Triangle
1/3pir^2*h
(y2-y1)/(x2-x1)
1/2bh
?r²

25. Perimeter of polygon
Sum of the lengths of the sides
4pir^2
T1 * r^(n-1)
1.4

26. Define the mode of a set of numbers.
(x+y)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 set of points which are all the same distance (the radius) from a certain point (the center).
?d OR 2?r

27. Perimeter of rectangle
4s
2l+2w
C =?d
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.

28. How do you find the sum of a geometric sequence?
(x+y)(x-y)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2(pi)r
T1 * r^(n-1)/(r-1)

29. The probability of an event happening and the probability of an event NOT happening must add up to what number?
S*v2
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.
1. Given event A: A + notA = 1.
4pir^2

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

31. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
N x M
x² + 2xy + y²

32. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
The total # of possible outcomes.
T1 * r^(n-1)
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.

33. How do you calculate the probability of two events in a row? (Probability of A and B)
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.
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
The distance from one point on the circle to another point on the circle.
Probability A * Probability B

34. In a parabola - if the first term is positive - the parabola ________.
S*v2
1
S² - where s = length of a side
Opens up

35. Define the 'Third side' rule for triangles

36. Chord
The distance from one point on the circle to another point on the circle.
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-y²
The distance across the circle through the center of the circle.The diameter is twice the radius.

37. a² - b² is equal to
(a+b)(a-b)
Sum of terms/number of terms
A+b
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

38. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
x°/360 times (2 pi r) - where x is the degrees in the angle
(y-y1)=m(x-x1)
N x M
½(b1 +b2) x h [or (b1 +b2) x h÷2]

39. What is the factored version of (x+y)(x-y) ?
S^2
x²-y²
T1 + (n-1)d
1/x^a

40. Point-Slope form
2(pi)r(r+h)
Arrangements - orders - schedules - or lists.
x°/360 times (2 pi r) - where x is the degrees in the angle
y-y1=m(x-x1)

41. The length of one side of any triangle is ____ than the sum of the other two sides.
(n-2)180
?r²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Less

42. What is the circumference of a circle?
2(pi)r(r+h)
(x1+x2)/2 - (y1+y2)/2
2(pi)r
A segment connecting the center of a circle to any point on the circle

43. Area of Rectangle
Not necessarily. This is a trick question - because x could be either positive or negative.
Lw
(pi)r^2(h)
The set of points which are all the same distance (the radius) from a certain point (the center).

44. Area of Circles
C =?d
A=?r2
The distance across the circle through the center of the circle.The diameter is twice the radius.
2(pi)r(r+h)

45. What is the average?
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.
Sum of terms/number of terms
x² -2xy + y²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

46. Area of a circle
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.
?r²
x² -2xy + y²
Equal

47. Define 'proportionate' values
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)
Arrangements - orders - schedules - or lists.
Sum of terms/number of terms

48. 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.
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.
2 pi r

49. What is the distance formula?
(pi)r^2
Less
Sqr( x2 -x1) + (y2- y1)
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.

50. x^a * x^b = x^__
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
A+b
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.