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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. Area of Square
S^2
Pir^2h
The distance from one point on the circle to another point on the circle.
Ac+ad+bc+bd

2. How do you find the sum of a geometric sequence?
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
T1 * r^(n-1)/(r-1)
Total distance/total time

3. Define the formula for calculating slope.
Equal
Middle term
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Bh

4. What is the formula for the diagonal of any square?
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.
1/2 h (b1 + b2)
S*v2
(a+b)(a-b)

5. Area of Triangle
(a+b)(a²-ab+b²)
Lw
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.
1/2bh

6. Define a factorial of a number - and how it is written.
x² + 2xy + y²
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.
4pir^2
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.

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

8. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
N x M
S*v2
x²-y²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

9. How do you multiply and divide square roots?
(x1+x2)/2 - (y1+y2)/2
Probability A * Probability B
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

10. The length of one side of any triangle is ____ than the sum of the other two sides.
(pi)r^2(h)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Less

11. What is the unfactored version of x²-y² ?
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.
(y2-y1)/(x2-x1)
(x+y)(x-y)
S*v2

12. a²-2ab+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
b±[vb²-4ac]/2a
(a-b)²

13. Perimeter of rectangle
(n degrees/360) * 2(pi)r
(x+y)²
2l+2w
Middle term

14. What is the average speed?
1/3Bh
Lw
2x2x2x5x5
Total distance/total time

15. How do you find the sum of an arithmetic sequence?
2pi*r
(n-2)180
A=bh
(n/2) * (t1+tn)

16. Circumference Formula
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.
A=?r2
C =?d
(x-y)²

17. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
An ange whose vertex is the center of the circle
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
T1 * r^(n-1)/(r-1)

18. What is directly proportional?
A segment connecting the center of a circle to any point on the circle
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.
y = kx
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.

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

20. In a parabola - if the first term is negative - the parabola ________.
Between 0 and 1.
The average - mean - median - or mode.
Last term
Opens down

21. Area of a triangle
½(base x height) [or (base x height)÷2]
4pir^2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Negative

22. Perimeter of a rectangle
Number of desired outcomes/number of total outcomes
2Length + 2width [or (length + width) x 2]
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.
2(pi)r(r+h)

23. a²-b²
The distance from one point on the circle to another point on the circle.
1/3Bh
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)(a+b)

24. Area of a square
S² - where s = length of a side
(a+b)(a²-ab+b²)
Less
(a-b)(a²+ab+b²)

25. 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.
(x+y)²
2l+2w
Bh

26. length of a sector
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.
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
Less

27. Define the 'Third side' rule for triangles

28. How do you find the slope?
(a-b)²
N x M
y2-y1/x2-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.

29. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
S^2
Probability A + Probability B
Not necessarily. This is a trick question - because x could be either positive or negative.

30. What is the area of a sector?
S^2
(n degrees/360) * (pi)r^2
N x M
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.

31. Perimeter of polygon
T1 * r^(n-1)/(r-1)
Sum of the lengths of the sides
Between 0 and 1.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

32. Define the range of a set of numbers.
2x2x2x5x5
Sum of the lengths of the sides
(a-b)²
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.

33. Rough est. of v2 =
1.4
S^2
(n-2)180
4s (where s = length of a side)

34. What is the volume of a cylinder?
(pi)r^2(h)
Sum of the lengths of the sides
The average - mean - median - or mode.
(x-y)²

35. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
2(lw+wh+lh)

36. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
x°/360 times (?r²) - where x is the degrees in the angle
Part of a circle connecting two points on the circle.
Probability A * Probability B

37. What is the factored version of x² + 2xy + y² ?
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.
Total distance/total time
(x+y)²
Ac+ad+bc+bd

38. What is the average?
y = kx
(a-b)(a+b)
Sum of terms/number of terms
1/2bh

39. What is the side ratio for a 30:60:90 triangle?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(x+y)²

40. Does order matter for a permutation? How about for a combination?
Sum of terms/number of terms
(n degrees/360) * 2(pi)r
Order does matter for a permutation - but does not matter for a combination.
?d OR 2?r

41. How do you solve a permutation?
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.
4pir^2
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+b)²

42. 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
2pi*r
Between 0 and 1.
Lwh

43. How do you calculate a diagonal inside a 3-dimensional rectangular box?
1/2 h (b1 + b2)
2x2x2x5x5
2pir^2 + 2pir*h
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

44. Area of Trapezoid
Lw
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1/2 h (b1 + b2)

45. Chord
Part of a circle connecting two points on the circle.
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.
The distance from one point on the circle to another point on the circle.
x² -2xy + y²

46. What is the equation of a line?

47. Central Angle
x°/360 times (?r²) - where x is the degrees in the angle
Ac+ad+bc+bd
An ange whose vertex is the center of the circle
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.

48. Volume of prism
2 pi r
Bh
(0 -0)
2lw+2lh+2wh

49. Area of Rectangle
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.
(pi)r^2(h)
Lw
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.

50. Circle
2 pi r
The set of points which are all the same distance (the radius) from a certain point (the center).
?d OR 2?r
4/3pir^3