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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 'distributive law'?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a-b)²
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.

2. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
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
T1 * r^(n-1)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

3. What is directly proportional?
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.
N x M
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

4. How do you find the nth term of a geometric sequence?
A segment connecting the center of a circle to any point on the circle
Bh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
T1 * r^(n-1)

5. What is the unfactored version of (x-y)² ?
x² -2xy + y²
Arrangements - orders - schedules - or lists.
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).

6. Area of Square
(x+y)(x-y)
Opens up
S^2
1/2 h (b1 + b2)

7. Define the range of a set of numbers.
?r²
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.
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.
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.

8. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Order does matter for a permutation - but does not matter for a combination.
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.

9. Does order matter for a permutation? How about for a combination?
A segment connecting the center of a circle to any point on the circle
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.
Order does matter for a permutation - but does not matter for a combination.
y-y1=m(x-x1)

10. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
2x2x2x5x5
Pir^2h
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.

11. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
The distance from one point on the circle to another point on the circle.
2x2x2x5x5
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.

12. Lines reflected over the x or y axis have ____ slopes.
Less
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.
Negative

13. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Order does matter for a permutation - but does not matter for a combination.
1/3pir^2*h
1. Given event A: A + notA = 1.

14. (a+b)(a-b)=
2(pi)r(r+h)
A²-b²
½(b1 +b2) x h [or (b1 +b2) x h÷2]
1/x^a

15. Perimeter of rectangle
2l+2w
A segment connecting the center of a circle to any point on the circle
Bh
S*v2

16. In a parabola - if the first term is positive - the parabola ________.
x² -2xy + y²
Opens up
2(pi)r(r+h)
1/1

17. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
T1 + (n-1)d
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.
N x M
Less

18. How do you calculate a diagonal inside a 3-dimensional rectangular box?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
T1 * r^(n-1)/(r-1)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

19. What is the factored version of x² + 2xy + y² ?
(x+y)²
1/3pir^2*h
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(pi)r^2

20. What do permutation problems often ask for?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The average - mean - median - or mode.
Arrangements - orders - schedules - or lists.

21. Define the mode of a set of numbers.
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.
4pir^2
Lw
A+b

22. Circle
4/3pir^3
Sum of the lengths of the sides
The set of points which are all the same distance (the radius) from a certain point (the center).
Part of a circle connecting two points on the circle.

23. Define a factorial of a number - and how it is written.
Opens up
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.
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 segment connecting the center of a circle to any point on the circle

24. Circumference of a circle using radius
y = kx
2pi*r
C =?d
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

25. Area of Parallelogram
The total # of possible outcomes.
Bh
Equal
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'.

26. What is the area of a circle?
Not necessarily. This is a trick question - because x could be either positive or negative.
(pi)r^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.
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.

27. What is the side ratio for a Right Isosceles triangle?
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
1/3pir^2*h
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(pi)r^2(h)

28. The length of one side of any triangle is ____ than the sum of the other two 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
2(pi)r(r+h)
Less
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

29. What is the unfactored version of (x+y)² ?
x² + 2xy + y²
Between 0 and 1.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2(pi)r

30. List two odd behaviors of exponents
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.
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.
2lw+2lh+2wh
x²-y²

31. What'S the most important thing to remember about charts you'll see on the GRE?
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.
x²-y²
1/3pir^2*h
A+b

32. Perimeter (circumference) of a circle
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 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.
Between 0 and 1.
2 pi r

33. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
2 pi r
(0 -0)
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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

34. Define the formula for calculating slope.
A+b
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
b±[vb²-4ac]/2a
S² - where s = length of a side

35. What is the 'Third side' rule for triangles?
Middle term
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.
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.
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.

36. Quadratic Formula
b±[vb²-4ac]/2a
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.
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'.
Groups - teams - or committees.

37. How do you find the nth term of an arithmetic sequence?
The average - mean - median - or mode.
x²-y²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
T1 + (n-1)d

38. If x² = 144 - does v144 = x?
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
Not necessarily. This is a trick question - because x could be either positive or negative.
4/3pir^3
1.7

39. What is the circumference of a circle?
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.
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
Bh
2(pi)r

40. Surface Area of rectangular prism
1.7
2lw+2lh+2wh
y = kx
Opens up

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

42. What is the area of a sector?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(n degrees/360) * (pi)r^2
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2pir^2 + 2pir*h

43. What is the equation of a line?

44. In a coordinate system - identify the quadrants and describe their location.
2 pi r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
(x+y)²

45. How do you find the midpoint?
4s
4s (where s = length of a side)
The set of points which are all the same distance (the radius) from a certain point (the center).
(x1+x2)/2 - (y1+y2)/2

46. a²+2ab+b²
An ange whose vertex is the center of the circle
(a+b)²
Negative
Opens down

47. Area of a 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.
x°/360 times (?r²) - where x is the degrees in the angle
?r²
The four big angles are equal and the four small angles are equal

48. What is the average?
Equal
A segment connecting the center of a circle to any point on the circle
(pi)r^2
Sum of terms/number of terms

49. How do you find the slope?
Pi*d
y2-y1/x2-x1
Opens down
T1 * r^(n-1)/(r-1)

50. perimeter of square
4s
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.
(pi)r^2(h)
(x+y)²