Test your basic knowledge |

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 a sector
x°/360 times (?r²) - where x is the degrees in the angle
2 pi r
2x2x2x5x5
Bh

2. What is the factored version of x² + 2xy + y² ?
(x+y)²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(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.

3. x^-a =
y-y1=m(x-x1)
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/x^a
2(lw+wh+lh)

4. What is the unfactored version of x²-y² ?
y = k/x
4pir^2
(x+y)(x-y)
1/2bh

5. Define a factorial of a number - and how it is written.
x² -2xy + y²
(a+b)²
Opens down
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.

6. Volume of Cone
1/3pir^2*h
(a+b)(a²-ab+b²)
1.7
1/1

7. What is the average speed?
T1 * r^(n-1)
Total distance/total time
(0 -0)
x°/360 times (?r²) - where x is the degrees in the angle

8. What is the volume of a cylinder?
Pi*r^2
Number of desired outcomes/number of total outcomes
(pi)r^2(h)
Opens down

9. Explain the special properties of zero.
(x-y)²
A segment connecting the center of a circle to any point on the circle
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.
Arrangements - orders - schedules - or lists.

10. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Pi*r^2
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.
Not necessarily. This is a trick question - because x could be either positive or 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.

11. What is the point-slope form?
Sqr( x2 -x1) + (y2- y1)
(y-y1)=m(x-x1)
T1 * r^(n-1)/(r-1)
1/3pir^2*h

12. If x² = 144 - does v144 = x?
(y2-y1)/(x2-x1)
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.
2(pi)r(r+h)
Not necessarily. This is a trick question - because x could be either positive or negative.

13. Perimeter of a square
4s (where s = length of a side)
A²-b²
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2lw+2lh+2wh

14. Diameter
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.

15. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
2 pi r
Groups - teams - or committees.
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.

16. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
1/1
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2pir^2 + 2pir*h

17. What is the area of a circle?
S*v2
(a+b)(a²-ab+b²)
(pi)r^2
Less

18. List two odd behaviors of exponents
2l+2w
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.
?r²
An ange whose vertex is the center of the circle

19. What is the factored version of x² -2xy + y² ?
(x-y)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.
Order does matter for a permutation - but does not matter for a combination.
y2-y1/x2-x1

20. Define the formula for calculating slope.
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
4/3pir^3
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.

21. In a parabola - if the first term is positive - the parabola ________.
S² - where s = length of a side
1/3Bh
Opens up
A²-b²

22. Area of Rectangle
Probability A + Probability B
(y-y1)=m(x-x1)
Lw
Percentage Change = Difference/Original * 100

23. a³-b³
An ange whose vertex is the center of the circle
(a-b)(a²+ab+b²)
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.
1.4

24. 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.
Opens down
S*v2
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

25. 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.
1. Given event A: A + notA = 1.
?d OR 2?r
(y-y1)=m(x-x1)

26. Volume of sphere
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.
2l+2w
The average - mean - median - or mode.
4/3pir^3

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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

28. Surface Area of Sphere
4pir^2
Equal
Middle term
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.

29. What do permutation problems often ask for?
Groups - teams - or committees.
Arrangements - orders - schedules - or lists.
A=bh
Number of desired outcomes/number of total outcomes

30. a²+2ab+b²
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
(a+b)²
2l+2w
(a-b)(a²+ab+b²)

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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

32. How do you find the slope?
2l+2w
y = k/x
y2-y1/x2-x1
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.

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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

34. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
(a+b)(a-b)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x² + 2xy + y²

35. When you reverse FOIL - the term that needs to add out is the _____
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.
Last term
Middle term
Pi*r^2

36. How do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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

37. (a+b)(a-b)=
A²-b²
x² + 2xy + y²
The set of points which are all the same distance (the radius) from a certain point (the center).
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

38. Radius (Radii)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A segment connecting the center of a circle to any point on the circle
1
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

39. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
N x M
?d OR 2?r
(a+b)(a-b)

40. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
2lw+2lh+2wh
x² -2xy + y²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Probability A + Probability B

41. What is the prime factorization of 200?
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
?d OR 2?r
1.7
2x2x2x5x5

42. Circumference of a circle
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Order does matter for a permutation - but does not matter for a combination.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
?d OR 2?r

43. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
(0 -0)
C =?d
N x M
1/2 h (b1 + b2)

44. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
(pi)r^2
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

45. What number goes on the bottom of a probability fraction?
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.
The total # of possible outcomes.
(x+y)(x-y)
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.

46. What is the area of a sector?
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.
(n degrees/360) * (pi)r^2
2(pi)r(r+h)
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

47. How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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.
Between 0 and 1.
2pir^2 + 2pir*h

48. What is the distance formula?
S² - where s = length of a side
Opens up
Sqr( x2 -x1) + (y2- y1)
4/3pir^3

49. The length of one side of any triangle is ____ than the sum of the other two sides.
(x+y)²
Less
Probability A + Probability B
1.7

50. Does order matter for a permutation? How about for a combination?
Bh
Order does matter for a permutation - but does not matter for a combination.
y-y1=m(x-x1)
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.