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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. Surface Area of rectangular prism
2lw+2lh+2wh
Between 0 and 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.
Opens up

2. Volume of sphere
4/3pir^3
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1.7
(a+b)(a²-ab+b²)

3. What is the formula for the diagonal of any square?
Ac+ad+bc+bd
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
S*v2
A=?r2

4. Volume of Cone
y = k/x
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
1/3pir^2*h

5. What is the 'Third side' rule for triangles?
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.
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.
(0 -0)
1/2bh

6. Define the formula for calculating slope.
1.4
1/2 h (b1 + b2)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.

7. What is the probability?
2lw+2lh+2wh
Number of desired outcomes/number of total outcomes
The set of points which are all the same distance (the radius) from a certain point (the center).
2x2x2x5x5

8. Volume of pyramid
(n/2) * (t1+tn)
x² + 2xy + y²
1/3Bh
(a+b)²

9. In a parabola - if the first term is positive - the parabola ________.
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'.
Opens up
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

10. Define the 'Third side' rule for triangles

11. Area of a trapezoid
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

12. Define the mode of a set of numbers.
(pi)r^2
x²-y²
2lw+2lh+2wh
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.

13. Area of a circle
?r²
2l+2w
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.
½(base x height) [or (base x height)÷2]

14. List two odd behaviors of exponents
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.
(n degrees/360) * 2(pi)r
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
Groups - teams - or committees.

15. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
1.7
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.
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 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.

16. How do you find the nth term of a geometric sequence?
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
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.
An ange whose vertex is the center of the circle
T1 * r^(n-1)

17. In a coordinate system - what is the origin?
T1 * r^(n-1)/(r-1)
(0 -0)
2Length + 2width [or (length + width) x 2]
(a+b)(a-b)

18. What is the area of a 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.
Part of a circle connecting two points on the circle.
1.4
(n degrees/360) * (pi)r^2

19. How do you calculate the probability of two events in a row? (Probability of A and B)
The total # of possible outcomes.
Probability A * Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Negative

20. Circumference of a circle using radius
The four big angles are equal and the four small angles are equal
1/1
(n-2)180
2pi*r

21. Explain the special properties of zero.
½(base x height) [or (base x height)÷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.
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.
(x-y)²

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

23. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

24. a²+2ab+b²
?d OR 2?r
(n/2) * (t1+tn)
T1 * r^(n-1)/(r-1)
(a+b)²

25. If x² = 144 - does v144 = x?
Pir^2h
A segment connecting the center of a circle to any point on the circle
Not necessarily. This is a trick question - because x could be either positive or negative.
The average - mean - median - or mode.

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

27. Rough est. of v3 =
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.
1.7
x² + 2xy + y²
Arrangements - orders - schedules - or lists.

28. What is the side ratio 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.
2x2x2x5x5
Percentage Change = Difference/Original * 100
?d OR 2?r

29. What is directly proportional?
2pir^2 + 2pir*h
y = kx
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.
A segment connecting the center of a circle to any point on the circle

30. What is the area of a circle?
1. Given event A: A + notA = 1.
(n degrees/360) * (pi)r^2
Groups - teams - or committees.
(pi)r^2

31. How do you calculate the percentage of change?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Sum of the lengths of the sides
Percentage Change = Difference/Original * 100

32. a³+b³
2pir^2 + 2pir*h
Lwh
(a+b)(a²-ab+b²)
Opens up

33. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
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.
Lwh
(pi)r^2(h)

34. What is a '30:60:90' triangle?
1/1
(x+y)(x-y)
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
(a-b)(a²+ab+b²)

35. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Probability A * Probability B
T1 * r^(n-1)/(r-1)
Less

36. What is a 'Right isosceles' triangle?
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
2(pi)r
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

37. Rough est. of v2 =
(a-b)(a²+ab+b²)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1.4
The set of points which are all the same distance (the radius) from a certain point (the center).

38. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
(n/2) * (t1+tn)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

39. Area of Triangle
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.
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
Equal

40. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
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.
1/1
2(lw+wh+lh)

41. Area of rectangle - square - parallelogram
Number of desired outcomes/number of total outcomes
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.
2(lw+wh+lh)
A=bh

42. Area of Trapezoid
1/2 h (b1 + b2)
Between 0 and 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.
1.7

43. (a+b)(c+d)
Ac+ad+bc+bd
y2-y1/x2-x1
?d OR 2?r
(x-y)²

44. What is the 'distributive law'?
A=bh
1/x^a
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).

45. What is the side ratio for a Right Isosceles triangle?
Probability A + Probability B
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(pi)r^2(h)
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.

46. What is the factored version of x² + 2xy + y² ?
(x+y)²
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
4s (where s = length of a side)

47. How do you find the slope?
4pir^2
y2-y1/x2-x1
2x2x2x5x5
(y-y1)=m(x-x1)

48. Area of Square
1/2 h (b1 + b2)
1.4
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
S^2

49. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

50. How do you calculate the surface area of a rectangular box?
(pi)r^2
The average - mean - median - or mode.
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.
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.