GRE Math 2

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. Area of Trapezoid
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/2 h (b1 + b2)
(a-b)(a²+ab+b²)
2(lw+wh+lh)


2. In a parabola - if the first term is negative - the parabola ________.
Probability A + Probability B
Opens down
2Length + 2width [or (length + width) x 2]
x² + 2xy + y²


3. Define the 'Third side' rule for triangles

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4. Perimeter of a square
4s (where s = length of a side)
A=bh
A=?r2
2 pi r


5. 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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6. What is the area of a solid rectangle?
2x2x2x5x5
2(lw+wh+lh)
Probability A + Probability B
(a-b)(a²+ab+b²)


7. How do you calculate the probability of two events in a row? (Probability of A and B)
C =?d
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
A²-b²
Probability A * Probability B


8. Circumference of a circle using radius
x²-y²
2pi*r
1.7
1/3Bh


9. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
The four big angles are equal and the four small angles are equal
The distance from one point on the circle to another point on the circle.
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.
2(pi)r


10. Rough est. of v2 =
4/3pir^3
2Length + 2width [or (length + width) x 2]
(x-y)²
1.4


11. What is the side ratio for a 30:60:90 triangle?
(a+b)(a-b)
Probability A + Probability B
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/x^a


12. What is the unfactored version of x²-y² ?
(x+y)(x-y)
The distance from one point on the circle to another point on the circle.
2pir^2 + 2pir*h
y-y1=m(x-x1)


13. What is the average speed?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/3pir^2*h
Total distance/total time
(n-2)180


14. Rough est. of v1 =
1
y2-y1/x2-x1
Last term
2(pi)r


15. In intersecting lines - opposite angles are _____.
1/3pir^2*h
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Equal
Sum of terms/number of terms


16. Rough est. of v3 =
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2(pi)r(r+h)
2(pi)r(r+h)
1.7


17. a³+b³
x°/360 times (2 pi r) - where x is the degrees in the angle
(a+b)(a²-ab+b²)
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.
x² + 2xy + y²


18. Area of Circle
Pi*r^2
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
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


19. In a parabola - if the first term is positive - the parabola ________.
2l+2w
Lw
Opens up
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


20. Area of Circles
(a+b)(a²-ab+b²)
A=?r2
1/2 h (b1 + b2)
1/2bh


21. What is inversely proportional?
2x2x2x5x5
2(pi)r(r+h)
Total distance/total time
y = k/x


22. What is the volume of a cylinder?
A²-b²
(pi)r^2(h)
Lw
(0 -0)


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

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24. When you reverse FOIL - the term that needs to multiply out is the _____
(a+b)²
Not necessarily. This is a trick question - because x could be either positive or negative.
Last term
S² - where s = length of a side


25. What number goes on the bottom of a probability fraction?
?d OR 2?r
Sum of the lengths of the sides
T1 * r^(n-1)
The total # of possible outcomes.


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

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27. The length of one side of any triangle is ____ than the sum of the other two sides.
The distance from one point on the circle to another point on the circle.
Less
Opens down
(n degrees/360) * (pi)r^2


28. Define a factorial of a number - and how it is written.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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.
The distance from one point on the circle to another point on the circle.


29. Volume of prism
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(a-b)²
Bh
?r²


30. What is directly proportional?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
y = kx
2 pi r
Sqr( x2 -x1) + (y2- y1)


31. How do you calculate a diagonal inside a 3-dimensional rectangular box?
y2-y1/x2-x1
(a+b)²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2(pi)r(r+h)


32. How do you find the nth term of a geometric sequence?
Opens down
The total # of possible outcomes.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
T1 * r^(n-1)


33. (a+b)(c+d)
Less
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.
Negative
Ac+ad+bc+bd


34. 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
(a-b)(a+b)
Order does matter for a permutation - but does not matter for a combination.


35. How do you multiply powers with the same base?
Pi*r^2
Sqr( x2 -x1) + (y2- y1)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(n degrees/360) * (pi)r^2


36. a³-b³
(pi)r^2
(a+b)(a-b)
(a-b)(a²+ab+b²)
Percentage Change = Difference/Original * 100


37. Volume of Cylinder
A segment connecting the center of a circle to any point on the circle
Pir^2h
2lw+2lh+2wh
2(pi)r


38. Diameter
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.
4pir^2
y = k/x


39. What is the volume of a solid rectangle?
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.
Part of a circle connecting two points on the circle.
Not necessarily. This is a trick question - because x could be either positive or negative.
Lwh


40. What is the probability?
(y2-y1)/(x2-x1)
Pir^2h
Groups - teams - or committees.
Number of desired outcomes/number of total outcomes


41. Point-Slope form
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The set of points which are all the same distance (the radius) from a certain point (the center).
y-y1=m(x-x1)
A²-b²


42. Circumference of cirlce using diameter
4s
C =?d
Bh
Pi*d


43. length of a sector
2pir^2 + 2pir*h
x°/360 times (2 pi r) - where x is the degrees in the angle
S^2
x² -2xy + y²


44. a²-2ab+b²
(x1+x2)/2 - (y1+y2)/2
(a-b)²
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.
1/2bh


45. Surface Area of rectangular prism
1/3pir^2*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.
2lw+2lh+2wh
1/2 h (b1 + b2)


46. How do you multiply and divide square roots?
Probability A + Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/2 h (b1 + b2)


47. Surface Area of Cylinder
2pir^2 + 2pir*h
(a+b)²
The set of points which are all the same distance (the radius) from a certain point (the center).
x² -2xy + y²


48. Lines reflected over the x or y axis have ____ slopes.
T1 + (n-1)d
The distance from one point on the circle to another point on the circle.
?d OR 2?r
Negative


49. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Middle term
?r²
A+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.


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

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