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. a³+b³
(a+b)(a²-ab+b²)
A+b
1/2bh
An ange whose vertex is the center of the circle

2. How do you find the sum of a geometric sequence?
(y2-y1)/(x2-x1)
T1 * r^(n-1)/(r-1)
Total distance/total time
(x+y)²

3. What is the factored version of (x+y)(x-y) ?
(x+y)(x-y)
2pir^2 + 2pir*h
(n degrees/360) * 2(pi)r
x²-y²

4. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
x² + 2xy + y²
The distance from one point on the circle to another point on the circle.
(a+b)²

5. What is the side ratio for a 30:60:90 triangle?
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Total distance/total time
Part of a circle connecting two points on the circle.

6. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Lw
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.
2(pi)r(r+h)
1. Given event A: A + notA = 1.

7. Perimeter of rectangle
2l+2w
Probability A + Probability B
T1 * r^(n-1)
2 pi r

8. Volume of pyramid
1/3Bh
(a-b)(a+b)
(x-y)²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

9. Area of a circle
1
Negative
?r²
?d OR 2?r

10. Area of Square
A+b
Pi*r^2
S^2
y-y1=m(x-x1)

11. What is the side ratio for a Right Isosceles triangle?
Pi*r^2
2pi*r
(a+b)²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

12. (a+b)(c+d)
(x-y)²
(x1+x2)/2 - (y1+y2)/2
Ac+ad+bc+bd
The distance from one point on the circle to another point on the circle.

13. Central Angle
An ange whose vertex is the center of the circle
(y-y1)=m(x-x1)
1.7
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

14. What is the probability?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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
Number of desired outcomes/number of total outcomes
Bh

15. Perimeter (circumference) of a circle
1/1
x²-y²
2 pi r
2(lw+wh+lh)

16. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
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.
b±[vb²-4ac]/2a
Not necessarily. This is a trick question - because x could be either positive or negative.

17. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
2(lw+wh+lh)
x²-y²
(a+b)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.

18. What is a '30:60:90' triangle?
½(base x height) [or (base x height)÷2]
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
Lw
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
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.
A=bh
Opens up
4s (where s = length of a side)

20. (a+b)(a-b)=
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
A²-b²
4pir^2
y2-y1/x2-x1

21. 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.
Ac+ad+bc+bd
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.
S^2

22. What is the factored version of x² -2xy + y² ?
1/3pir^2*h
1.7
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

23. Chord
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 from one point on the circle to another point on the circle.
Percentage Change = Difference/Original * 100
2 pi r

24. Area of Triangle
Opens up
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/2bh
x°/360 times (?r²) - where x is the degrees in the angle

25. Volume of Cone
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/3pir^2*h
The set of points which are all the same distance (the radius) from a certain point (the center).
A+b

26. What is the circumference of a circle?
1/2bh
Probability A + Probability B
Pi*r^2
2(pi)r

27. What are the side ratios for a 30:60:90 triangle?
x°/360 times (2 pi r) - where x is the degrees in the angle
Negative
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The distance from one point on the circle to another point on the circle.

28. Rough est. of v3 =
2pi*r
y2-y1/x2-x1
The total # of possible outcomes.
1.7

29. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
½(base x height) [or (base x height)÷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.
S*v2

30. a³-b³
1/3Bh
2(lw+wh+lh)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(a-b)(a²+ab+b²)

31. Area of rectangle - square - parallelogram
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=bh
(a-b)²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

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

33. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
x°/360 times (?r²) - where x is the degrees in the angle
A=bh
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

34. What is the formula for the diagonal of any square?
x² -2xy + y²
S*v2
Opens down
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.

35. Rough est. of v2 =
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
1.4
Less

36. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
Order does matter for a permutation - but does not matter for a combination.
½(base x height) [or (base x height)÷2]
(x1+x2)/2 - (y1+y2)/2

37. What is the unfactored version of x²-y² ?
2(lw+wh+lh)
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.
(x+y)(x-y)
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.

38. Surface Area of Cylinder
Lwh
2pir^2 + 2pir*h
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.
(0 -0)

39. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

40. What is the length of an arc?
(n degrees/360) * 2(pi)r
Lw
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
Between 0 and 1.

41. Area of Rectangle
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
b±[vb²-4ac]/2a
(a-b)(a+b)
Lw

42. What is the volume of a cylinder?
(pi)r^2(h)
(a+b)(a-b)
A segment connecting the center of a circle to any point on the circle
Total distance/total time

43. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
(0 -0)
4s (where s = length of a side)
1/3Bh

44. Perimeter of polygon
Sum of the lengths of the sides
2x2x2x5x5
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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.

45. Lines reflected over the x or y axis have ____ slopes.
Negative
Pi*r^2
(x+y)²
Less

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

47. To divide powers with the same base...
Pir^2h
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.
(x1+x2)/2 - (y1+y2)/2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

48. How do you calculate a diagonal inside a 3-dimensional rectangular box?
The set of points which are all the same distance (the radius) from a certain point (the center).
Ac+ad+bc+bd
1/3Bh
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

49. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
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.
Pi*d
(n-2)180

50. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
A²-b²
T1 * r^(n-1)
A=bh
N x M