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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. Circumference of a circle
y2-y1/x2-x1
?d OR 2?r
T1 * r^(n-1)/(r-1)
Middle term

2. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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'.
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.
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

3. What is the area of a circle?
Negative
(pi)r^2
x°/360 times (?r²) - where x is the degrees in the angle
(x+y)(x-y)

4. x^-a =
1/x^a
(a+b)(a²-ab+b²)
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.
Sum of the lengths of the sides

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

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6. Lines reflected over the x or y axis have ____ slopes.
2lw+2lh+2wh
Negative
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2l+2w

7. Define 'proportionate' values
1/x^a
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2(pi)r(r+h)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

8. Define the 'Third side' rule for triangles

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9. Quadratic Formula
A=bh
The average - mean - median - or mode.
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.
b±[vb²-4ac]/2a

10. Rough est. of v3 =
(x+y)(x-y)
Pi*r^2
1.7
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.

11. (a+b)(a-b)=
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.
A²-b²
x² -2xy + y²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

12. Define a factorial of a number - and how it is written.
Pir^2h
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
Order does matter for a permutation - but does not matter for a combination.

13. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
1/x^a
1/2bh
(a-b)²

14. What is a 'Right isosceles' triangle?
2Length + 2width [or (length + width) x 2]
1/3pir^2*h
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 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.

15. a²+2ab+b²
2pir^2 + 2pir*h
2(pi)r
Not necessarily. This is a trick question - because x could be either positive or negative.
(a+b)²

16. What is the 'Third side' rule for triangles?
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Percentage Change = Difference/Original * 100
2pi*r

17. Define the mode of a set of numbers.
Between 0 and 1.
The set of points which are all the same distance (the radius) from a certain point (the center).
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.

18. Area of Trapezoid
2(pi)r(r+h)
(a-b)(a²+ab+b²)
Groups - teams - or committees.
1/2 h (b1 + b2)

19. The probability of an event happening and the probability of an event NOT happening must add up to what number?
(a-b)(a²+ab+b²)
1. Given event A: A + notA = 1.
The set of points which are all the same distance (the radius) from a certain point (the center).
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.

20. 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.
Probability A + Probability B
?d OR 2?r
2pir^2 + 2pir*h

21. What is the unfactored version of (x-y)² ?
1/2bh
A=?r2
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.
x² -2xy + y²

22. Point-Slope form
y-y1=m(x-x1)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4s (where s = length of a side)

23. When you reverse FOIL - the term that needs to add out is the _____
An ange whose vertex is the center of the circle
Middle term
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
½(b1 +b2) x h [or (b1 +b2) x h÷2]

24. Area of Circle
x°/360 times (?r²) - where x is the degrees in the angle
Pi*r^2
Pi*d
(a-b)(a+b)

25. In a coordinate system - identify the quadrants and describe their location.
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.
Lwh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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

26. Circumference of a circle using radius
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'.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
2pi*r

27. Area of Circles
A=?r2
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Part of a circle connecting two points on the circle.
An ange whose vertex is the center of the circle

28. If something is certain to happen - how is the probability of this event expressed mathematically?
Probability A + Probability B
x² + 2xy + y²
1/1
1. Given event A: A + notA = 1.

29. In a coordinate system - what is the origin?
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.
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(0 -0)

30. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
1/2bh
Equal
?d OR 2?r
Probability A + Probability B

31. For a bell curve - what three terms might be used to describe the number in the middle?
(a+b)(a²-ab+b²)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The average - mean - median - or 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.

32. Area of Rectangle
Groups - teams - or committees.
Lw
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(x-y)²

33. What is the equation of a line?

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34. When a line crosses two parallel lines - ________.
Not necessarily. This is a trick question - because x could be either positive or negative.
Probability A * Probability B
The four big angles are equal and the four small angles are equal
Arrangements - orders - schedules - or lists.

35. Circumference of cirlce using diameter
Pi*d
Last term
Number of desired outcomes/number of total outcomes
4s (where s = length of a side)

36. a³-b³
T1 * r^(n-1)/(r-1)
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.
(a-b)(a²+ab+b²)
(a+b)(a²-ab+b²)

37. What is the unfactored version of (x+y)² ?
x² + 2xy + y²
Lw
b±[vb²-4ac]/2a
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.

38. 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.
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.
1/2bh

39. 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.
(0 -0)
2 pi r
Sqr( x2 -x1) + (y2- y1)

40. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
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+b)(a-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

41. What is the side ratio for a 30:60:90 triangle?
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
1/2 h (b1 + b2)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

42. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

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43. How do you find the sum of a geometric sequence?
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
1/3pir^2*h
T1 * r^(n-1)/(r-1)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

44. Define the formula for calculating slope.
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.
(a+b)(a-b)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(n-2)180

45. In a parabola - if the first term is negative - the parabola ________.
(a-b)²
Order does matter for a permutation - but does not matter for a combination.
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.
Opens down

46. Area of Triangle
(a+b)²
Order does matter for a permutation - but does not matter for a combination.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1/2bh

47. (a+b)(c+d)
Ac+ad+bc+bd
Total distance/total time
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1

48. Volume of sphere
4/3pir^3
1/2bh
?d OR 2?r
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.

49. What do permutation problems often ask for?
Between 0 and 1.
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.
Arrangements - orders - schedules - or lists.
2x2x2x5x5

50. How do you calculate the percentage of change?
(pi)r^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.
Percentage Change = Difference/Original * 100
(n degrees/360) * 2(pi)r