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. What is the volume of a solid rectangle?
The distance from one point on the circle to another point on the circle.
Lwh
1/2 h (b1 + b2)
x²-y²

2. What do permutation problems often ask for?
(x1+x2)/2 - (y1+y2)/2
Arrangements - orders - schedules - or lists.
Groups - teams - or committees.
1/3Bh

3. Arc
(n/2) * (t1+tn)
2 pi r
Part of a circle connecting two points on the circle.
A segment connecting the center of a circle to any point on the circle

4. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
y-y1=m(x-x1)
y = kx
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

5. What is the area of a triangle?
1/2bh
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
Opens down
Groups - teams - or committees.

6. Area of a sector
2(pi)r(r+h)
x°/360 times (?r²) - where x is the degrees in the angle
Sum of terms/number of terms
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

7. Area of a circle
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
?r²
Between 0 and 1.
N x M

8. What is the factored version of x² + 2xy + y² ?
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.
Order does matter for a permutation - but does not matter for a combination.
4s
(x+y)²

9. Area of Circles
A+b
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.
A=?r2

10. What is the 'Third side' rule for triangles?
Less
?d OR 2?r
(x1+x2)/2 - (y1+y2)/2
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.

11. Lines reflected over the x or y axis have ____ slopes.
Negative
2l+2w
Ac+ad+bc+bd
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.

12. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Lw
Probability A + Probability B
2Length + 2width [or (length + width) x 2]
Middle term

13. What are the side ratios for a 30:60:90 triangle?
Middle term
x°/360 times (?r²) - where x is the degrees in the angle
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Sum of terms/number of terms

14. In a coordinate system - identify the quadrants and describe their location.
1/3pir^2*h
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(n degrees/360) * 2(pi)r
Sqr( x2 -x1) + (y2- y1)

15. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Not necessarily. This is a trick question - because x could be either positive or negative.
Negative
Arrangements - orders - schedules - or lists.

16. a²+2ab+b²
4s
(a+b)²
?r²
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.

17. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Pir^2h
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2(pi)r(r+h)

18. Define the range of a set of numbers.
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.
Bh
Opens down
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

19. Perimeter of a square
Pir^2h
4s (where s = length of a side)
1.7
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

20. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Groups - teams - or committees.
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.
Pir^2h

21. Volume of pyramid
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.
1/3Bh
x°/360 times (?r²) - where x is the degrees in the angle
(pi)r^2

22. What is the unfactored version of (x-y)² ?
x² -2xy + y²
Opens down
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'.
(n degrees/360) * 2(pi)r

23. What is the unfactored version of x²-y² ?
The distance from one point on the circle to another point on the circle.
(x+y)(x-y)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.

24. The length of one side of any triangle is ____ than the sum of the other two sides.
Arrangements - orders - schedules - or lists.
(0 -0)
Less
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.

25. a² - b² is equal to
?r²
Middle term
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a+b)(a-b)

26. How do you calculate the probability of two events in a row? (Probability of A and B)
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.
Probability A * Probability B
Probability A + Probability B
Pi*d

27. What is the area of a solid rectangle?
2(lw+wh+lh)
(y2-y1)/(x2-x1)
1/x^a
x² + 2xy + y²

28. In a parabola - if the first term is positive - the parabola ________.
x² + 2xy + y²
Opens up
C =?d
1

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

30. perimeter of square
4pir^2
The set of points which are all the same distance (the radius) from a certain point (the center).
4s
x°/360 times (2 pi r) - where x is the degrees in the angle

31. Quadratic Formula
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x² + 2xy + y²
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.
b±[vb²-4ac]/2a

32. Rough est. of v1 =
1
x² -2xy + y²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2 pi r

33. Radius (Radii)
(a+b)(a-b)
A segment connecting the center of a circle to any point on the circle
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.

34. What is the probability?
Number of desired outcomes/number of total outcomes
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.
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.
4pir^2

35. (a+b)(c+d)
Opens up
Ac+ad+bc+bd
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 distance across the circle through the center of the circle.The diameter is twice the radius.

36. Area of rectangle - square - parallelogram
Ac+ad+bc+bd
The four big angles are equal and the four small angles are equal
A=bh
Equal

37. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
4/3pir^3
A segment connecting the center of a circle to any point on the circle
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.

38. 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
1/3pir^2*h
2(pi)r
x² -2xy + y²

39. How do you solve a permutation?
2Length + 2width [or (length + width) x 2]
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
?r²

40. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Pir^2h
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.

41. What is the 'distributive law'?
1/3Bh
2 pi r
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.
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.

42. Diameter
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a+b)(a-b)
The distance across the circle through the center of the circle.The diameter is twice the radius.
1/2bh

43. What is inversely proportional?
Lwh
An ange whose vertex is the center of the circle
y = k/x
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

44. How do you find the nth term of a geometric sequence?
Pi*d
T1 * r^(n-1)
Sum of terms/number of terms
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.

45. How do you find the sum of a geometric sequence?
(0 -0)
b±[vb²-4ac]/2a
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
T1 * r^(n-1)/(r-1)

46. Area of Square
Sum of terms/number of terms
S^2
Part of a circle connecting two points on the circle.
(x-y)²

47. Rough est. of v3 =
T1 * r^(n-1)/(r-1)
Order does matter for a permutation - but does not matter for a combination.
Total distance/total time
1.7

48. What is directly proportional?
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
y = kx
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

49. In a coordinate system - what is the origin?
The distance across the circle through the center of the circle.The diameter is twice the radius.
(0 -0)
y = k/x
(a-b)(a²+ab+b²)

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