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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. What is the factored version of x² -2xy + y² ?
Pi*r^2
(n degrees/360) * 2(pi)r
(x-y)²
y2-y1/x2-x1

2. 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 - and greater than the difference between the other two sides.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Negative
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

3. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The average - mean - median - or mode.
4/3pir^3
y-y1=m(x-x1)

4. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
S*v2
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A+b

5. What is the area of a sector?
A segment connecting the center of a circle to any point on the circle
(n degrees/360) * (pi)r^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.
y = kx

6. How do you find the slope?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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'.
y2-y1/x2-x1
The average - mean - median - or mode.

7. For a bell curve - what three terms might be used to describe the number in the middle?
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.
The average - mean - median - or mode.
y-y1=m(x-x1)
Arrangements - orders - schedules - or lists.

8. Central Angle
An ange whose vertex is the center of the circle
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
?d OR 2?r
2(lw+wh+lh)

9. Area of Parallelogram
1/1
Bh
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.
2lw+2lh+2wh

10. perimeter of square
2(pi)r(r+h)
Probability A * Probability B
Negative
4s

11. What do combination problems usually ask for?
Probability A + Probability B
T1 * r^(n-1)/(r-1)
Groups - teams - or committees.
Number of desired outcomes/number of total outcomes

12. Perimeter of a rectangle
(x+y)²
2Length + 2width [or (length + width) x 2]
A=bh
Opens up

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

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14. What is the probability?
1/x^a
Number of desired outcomes/number of total outcomes
A=bh
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.

15. What is the 'distributive law'?
A=bh
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2pir^2 + 2pir*h

16. What do permutation problems often ask for?
Percentage Change = Difference/Original * 100
4pir^2
Arrangements - orders - schedules - or lists.
A=bh

17. The probability of an event happening and the probability of an event NOT happening must add up to what number?
S² - where s = length of a side
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.
(n degrees/360) * 2(pi)r
1. Given event A: A + notA = 1.

18. In a parabola - if the first term is positive - the parabola ________.
Opens up
Sqr( x2 -x1) + (y2- y1)
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
2x2x2x5x5

19. a²-2ab+b²
(a-b)²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2pir^2 + 2pir*h
(a-b)(a+b)

20. a³-b³
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-b)(a²+ab+b²)
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.
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.

21. What is the formula for the diagonal of any square?
(y2-y1)/(x2-x1)
C =?d
S*v2
Opens up

22. a²+2ab+b²
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(a+b)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

23. In a coordinate system - identify the quadrants and describe their location.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Sum of the lengths of the sides
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(a-b)(a+b)

24. List two odd behaviors of exponents
The set of points which are all the same distance (the radius) from a certain point (the center).
1/1
y2-y1/x2-x1
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.

25. Perimeter of a square
The four big angles are equal and the four small angles are equal
4s (where s = length of a side)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.

26. What'S the most important thing to remember about charts you'll see on the GRE?
(a+b)(a²-ab+b²)
2lw+2lh+2wh
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.
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.

27. What is the side ratio for a 30:60:90 triangle?
Number of desired outcomes/number of total outcomes
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Opens up
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.

28. What is the circumference of a circle?
2(pi)r
A=bh
The total # of possible outcomes.
2lw+2lh+2wh

29. Area of Triangle
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 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.
T1 * r^(n-1)
1/2bh

30. Volume of prism
Opens down
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.
Total distance/total time
Bh

31. Rough est. of v3 =
The distance across the circle through the center of the circle.The diameter is twice the radius.
(y2-y1)/(x2-x1)
1.7
Opens down

32. Sector
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.
Pi*d
Lwh
1.4

33. Volume of sphere
(a+b)(a²-ab+b²)
1. Given event A: A + notA = 1.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4/3pir^3

34. Circumference Formula
1.4
C =?d
(n degrees/360) * (pi)r^2
2lw+2lh+2wh

35. Area of Circles
A=?r2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1/3Bh
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.

36. What is inversely proportional?
N x M
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A=bh
y = k/x

37. When a line crosses two parallel lines - ________.
Not necessarily. This is a trick question - because x could be either positive or negative.
2(pi)r(r+h)
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 four big angles are equal and the four small angles are equal

38. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Ac+ad+bc+bd
2lw+2lh+2wh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.

39. What is a '30:60:90' triangle?
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.
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
(pi)r^2
S^2

40. What is the area of a cylinder?
1/2bh
2(pi)r(r+h)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
½(base x height) [or (base x height)÷2]

41. Define 'proportionate' values
(x-y)²
1/3pir^2*h
(x+y)(x-y)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

42. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
Less
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(n degrees/360) * (pi)r^2

43. What is the volume of a solid rectangle?
1/x^a
A=?r2
T1 * r^(n-1)
Lwh

44. What is the distance formula?
(y2-y1)/(x2-x1)
Sqr( x2 -x1) + (y2- y1)
Number of desired outcomes/number of total outcomes
(n/2) * (t1+tn)

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

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46. a² - b² is equal to
(a+b)(a-b)
Pi*d
(0 -0)
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.

47. What is a 'Right isosceles' triangle?
S^2
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1.4

48. How do you find the sum of a geometric sequence?
Ac+ad+bc+bd
Probability A + Probability B
T1 * r^(n-1)/(r-1)
Pi*d

49. Explain the special properties of zero.
x°/360 times (?r²) - where x is the degrees in the angle
T1 + (n-1)d
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.
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.

50. What is the average speed?
4s (where s = length of a side)
Total distance/total time
4s
1.4