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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. Perimeter of a square
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.
4s (where s = length of a side)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(x1+x2)/2 - (y1+y2)/2

2. If x² = 144 - does v144 = x?
The four big angles are equal and the four small angles are equal
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
(x-y)²

3. Define the mode of a set of numbers.
Sqr( x2 -x1) + (y2- y1)
?d OR 2?r
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.
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.

4. What is the average?
Sum of terms/number of terms
(a+b)(a²-ab+b²)
2lw+2lh+2wh
Arrangements - orders - schedules - or lists.

5. How do you calculate the surface area of a rectangular box?
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.
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.
(x1+x2)/2 - (y1+y2)/2
The four big angles are equal and the four small angles are equal

6. What is the factored version of x² -2xy + y² ?
Groups - teams - or committees.
(x1+x2)/2 - (y1+y2)/2
T1 * r^(n-1)
(x-y)²

7. What is the length of an arc?
(n degrees/360) * 2(pi)r
(x+y)²
Less
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

8. (a+b)(a-b)=
(x-y)²
y = k/x
Opens up
A²-b²

9. Lines reflected over the x or y axis have ____ slopes.
4pir^2
(x+y)²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Negative

10. Perimeter of polygon
Sum of the lengths of the sides
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
(x+y)(x-y)
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 equation of a line?

12. What do combination problems usually ask for?
(x+y)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.
Groups - teams - or committees.
(pi)r^2(h)

13. How do you calculate the percentage of change?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
Percentage Change = Difference/Original * 100
(a+b)²

14. What is the volume of a solid rectangle?
1. Given event A: A + notA = 1.
Lwh
Not necessarily. This is a trick question - because x could be either positive or negative.
(a+b)²

15. a³+b³
y2-y1/x2-x1
Bh
T1 * r^(n-1)
(a+b)(a²-ab+b²)

16. Rough est. of v3 =
1.7
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Pi*r^2
Sum of the lengths of the sides

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

18. What is the side ratio for a 30:60:90 triangle?
A=bh
2 pi r
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4s (where s = length of a side)

19. What is the unfactored version of (x-y)² ?
2x2x2x5x5
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.
x² -2xy + y²
y = k/x

20. What is the 'distributive law'?
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)²
An ange whose vertex is the center of the circle
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.

21. Perimeter of a rectangle
Opens down
1/2bh
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.
2Length + 2width [or (length + width) x 2]

22. The length of one side of any triangle is ____ than the sum of the other two sides.
T1 * r^(n-1)/(r-1)
Opens up
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.
Less

23. How do you multiply powers with the same base?
(a+b)(a²-ab+b²)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2(pi)r(r+h)
1/3Bh

24. Explain the special properties of zero.
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 distance across the circle through the center of the circle.The diameter is twice the radius.
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.
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.

25. How do you find the slope?
4/3pir^3
Bh
1.4
y2-y1/x2-x1

26. Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a+b)(a-b)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

27. Slope
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)
The total # of possible outcomes.
2lw+2lh+2wh

28. Circumference of a circle
A segment connecting the center of a circle to any point on the circle
?d OR 2?r
y2-y1/x2-x1
Last term

29. Quadratic Formula
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
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.
b±[vb²-4ac]/2a
x²-y²

30. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
1/1
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.
(pi)r^2(h)

31. Circumference of a circle using radius
1/2bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2pi*r
Less

32. Area of a circle
?r²
1
(n degrees/360) * (pi)r^2
2l+2w

33. What is a '30:60:90' triangle?
(a-b)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
2(pi)r(r+h)
The total # of possible outcomes.

34. How do you multiply and divide square roots?
½(b1 +b2) x h [or (b1 +b2) x h÷2]
T1 + (n-1)d
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(x+y)²

35. What is the factored version of x² + 2xy + y² ?
2(pi)r(r+h)
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.
(x-y)²
(x+y)²

36. How do you calculate a diagonal inside a 3-dimensional rectangular box?
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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.

37. In a coordinate system - identify the quadrants and describe their location.
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
(x+y)²
The distance across the circle through the center of the circle.The diameter is twice the radius.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

38. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
2pir^2 + 2pir*h
1. Given event A: A + notA = 1.
½(b1 +b2) x h [or (b1 +b2) x h÷2]

39. If something is possible but not certain - what is the numeric range of probability of it happening?
Lwh
x°/360 times (2 pi r) - 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.
Between 0 and 1.

40. What'S the most important thing to remember about charts you'll see on the GRE?
(a+b)(a²-ab+b²)
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.
T1 * r^(n-1)/(r-1)
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

41. a²-2ab+b²
(a-b)²
T1 + (n-1)d
Last term
2l+2w

42. Define the range of a set of numbers.
2(pi)r
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.
Percentage Change = Difference/Original * 100
1/1

43. Does order matter for a permutation? How about for a combination?
Part of a circle connecting two points on the circle.
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.
A segment connecting the center of a circle to any point on the circle

44. What is the unfactored version of x²-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.
S*v2
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
(x+y)(x-y)

45. Arc
2Length + 2width [or (length + width) x 2]
(pi)r^2
Bh
Part of a circle connecting two points on the circle.

46. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
(x+y)(x-y)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(n degrees/360) * (pi)r^2

47. Rough est. of v2 =
Order does matter for a permutation - but does not matter for a combination.
(pi)r^2
Pi*r^2
1.4

48. What is the factored version of (x+y)(x-y) ?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Number of desired outcomes/number of total outcomes
Pi*r^2
x²-y²

49. List two odd behaviors of exponents
(y2-y1)/(x2-x1)
Opens down
A segment connecting the center of a circle to any point on the circle
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.

50. a³-b³
4pir^2
(a-b)(a²+ab+b²)
Probability A + Probability B
S*v2