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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. How do you calculate a diagonal inside a 3-dimensional rectangular box?
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'.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).

2. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
(n/2) * (t1+tn)
1/2bh
x°/360 times (?r²) - where x is the degrees in the angle
N x M

3. What is the probability?
Number of desired outcomes/number of total outcomes
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 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.
(a+b)(a²-ab+b²)

4. Volume of prism
Bh
Probability A + Probability B
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
A=bh

5. Define the 'Third side' rule for triangles

6. Volume of pyramid
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.
1/3Bh
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.
(y2-y1)/(x2-x1)

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

8. List two odd behaviors of exponents
(a-b)(a²+ab+b²)
Opens up
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.
2(pi)r(r+h)

9. Define the mode of a set of numbers.
1/3pir^2*h
Groups - teams - or committees.
x² + 2xy + y²
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.

10. Surface Area of Sphere
A+b
(n-2)180
4pir^2
Middle term

11. If something is possible but not certain - what is the numeric range of probability of it happening?
An ange whose vertex is the center of the circle
Between 0 and 1.
A+b
2 pi r

12. 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.
The set of points which are all the same distance (the radius) from a certain point (the center).
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x² + 2xy + y²

13. x^a * x^b = x^__
Probability A + Probability B
A+b
S^2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

14. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

15. Area of a sector
Lwh
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.
?r²
x°/360 times (?r²) - where x is the degrees in the angle

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

17. What is the circumference of a circle?
2(pi)r
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.
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.
(0 -0)

18. Area of a triangle
½(base x height) [or (base x height)÷2]
2x2x2x5x5
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

19. Define a factorial of a number - and how it is written.
x² -2xy + y²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A=?r2
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.

20. Perimeter of a square
4s (where s = length of a side)
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.
(x1+x2)/2 - (y1+y2)/2
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.

21. Surface Area of rectangular prism
y2-y1/x2-x1
2lw+2lh+2wh
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
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.

22. What is the area of a circle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Equal
(pi)r^2
(a+b)(a-b)

23. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
Pi*d
A segment connecting the center of a circle to any point on the circle
(x-y)²

24. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
The four big angles are equal and the four small angles are equal
2Length + 2width [or (length + width) x 2]
4s (where s = length of a side)

25. When you reverse FOIL - the term that needs to add out is the _____
(n-2)180
C =?d
(a-b)(a²+ab+b²)
Middle term

26. What is the length of an arc?
2(pi)r
4s
(n degrees/360) * 2(pi)r
Probability A * Probability B

27. What is the prime factorization of 200?
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.
(x-y)²
2x2x2x5x5
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

28. (a+b)(c+d)
2l+2w
2(pi)r(r+h)
Ac+ad+bc+bd
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.

29. a³+b³
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1
(a+b)(a²-ab+b²)
Order does matter for a permutation - but does not matter for a combination.

30. Lines reflected over the x or y axis have ____ slopes.
N x M
Negative
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.
?r²

31. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
Lw
1/2bh
4/3pir^3

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

33. Explain the special properties of zero.
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
x²-y²
A²-b²

34. Define the range of a set of numbers.
The four big angles are equal and the four small angles are equal
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.
Part of a circle connecting two points on the circle.
(pi)r^2(h)

35. To divide powers with the same base...
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.
1/2bh
(n-2)180
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

36. What is the factored version of x² + 2xy + y² ?
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.
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
(x+y)²
Probability A + Probability B

37. What is the area of a solid rectangle?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(n-2)180
2(lw+wh+lh)
x°/360 times (?r²) - where x is the degrees in the angle

38. In intersecting lines - opposite angles are _____.
y2-y1/x2-x1
Equal
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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. In a parabola - if the first term is positive - the parabola ________.
Opens up
Bh
A=bh
2l+2w

40. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
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.
Number of desired outcomes/number of total outcomes
1/2bh

41. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
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. 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

42. What is the point-slope form?
(y-y1)=m(x-x1)
Lwh
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2 pi r

43. What is the area of a triangle?
A+b
The total # of possible outcomes.
1/2bh
Part of a circle connecting two points on the circle.

44. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
The distance across the circle through the center of the circle.The diameter is twice the radius.
Pi*d
Probability A + Probability B
Between 0 and 1.

45. Area of a square
S^2
T1 * r^(n-1)/(r-1)
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.
S² - where s = length of a side

46. What is the unfactored version of x²-y² ?
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.
Sqr( x2 -x1) + (y2- y1)
Pir^2h
(x+y)(x-y)

47. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
?d OR 2?r
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
y2-y1/x2-x1

48. x^-a =
S² - where s = length of a side
1/2bh
(x+y)(x-y)
1/x^a

49. In a coordinate system - identify the quadrants and describe their location.
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.
(a-b)(a+b)
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

50. What is the average?
Sum of terms/number of terms
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A segment connecting the center of a circle to any point on the circle
C =?d