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. How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x°/360 times (2 pi r) - where x is the degrees in the angle
?d OR 2?r
S² - where s = length of a side


2. What is the unfactored version of (x-y)² ?
2(pi)r(r+h)
x²-y²
The four big angles are equal and the four small angles are equal
x² -2xy + y²


3. Area of Circles
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A=?r2
y = kx
(n-2)180


4. What is the prime factorization of 200?
Last term
1/2bh
2x2x2x5x5
2pir^2 + 2pir*h


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

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6. What is the factored version of x² + 2xy + y² ?
y-y1=m(x-x1)
(x+y)²
y = k/x
2Length + 2width [or (length + width) x 2]


7. Area of Rectangle
x² -2xy + y²
Lw
(y2-y1)/(x2-x1)
x² + 2xy + y²


8. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
Sum of terms/number of terms
?d OR 2?r
(x1+x2)/2 - (y1+y2)/2


9. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
The average - mean - median - or mode.
x² -2xy + y²
4s


10. What is the area of a circle?
Lw
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.
(pi)r^2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


11. What is the area of a solid rectangle?
2lw+2lh+2wh
S² - where s = length of a side
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.
2(lw+wh+lh)


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

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13. Lines reflected over the x or y axis have ____ slopes.
Negative
T1 + (n-1)d
(x1+x2)/2 - (y1+y2)/2
x² + 2xy + y²


14. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
N x M
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
1.4


15. Perimeter of polygon
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
Not necessarily. This is a trick question - because x could be either positive or negative.
S² - where s = length of a side


16. Volume of Cylinder
Arrangements - orders - schedules - or lists.
1/2bh
Pir^2h
(0 -0)


17. Define the 'Third side' rule for triangles

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18. How do you find the nth term of a geometric sequence?
(0 -0)
(x1+x2)/2 - (y1+y2)/2
(n degrees/360) * (pi)r^2
T1 * r^(n-1)


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

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20. Surface Area of rectangular prism
2lw+2lh+2wh
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 set of points which are all the same distance (the radius) from a certain point (the center).
Ac+ad+bc+bd


21. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
4s (where s = length of a side)
(n-2)180
S*v2


22. What'S the most important thing to remember about charts you'll see on the GRE?
(n degrees/360) * (pi)r^2
2(pi)r
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.
(a+b)(a²-ab+b²)


23. How do you find the nth term of an arithmetic sequence?
Pi*d
Lwh
Percentage Change = Difference/Original * 100
T1 + (n-1)d


24. Area of a circle
4s
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.
?r²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


25. Area of a square
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.
A=bh
1/2bh
S² - where s = length of a side


26. Volume of sphere
T1 + (n-1)d
The set of points which are all the same distance (the radius) from a certain point (the center).
4/3pir^3
Opens down


27. a² - b² is equal to
(a+b)(a-b)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Not necessarily. This is a trick question - because x could be either positive or negative.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


28. What is the 'Third side' rule for triangles?
2Length + 2width [or (length + width) x 2]
4/3pir^3
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.
b±[vb²-4ac]/2a


29. a³-b³
(a-b)(a²+ab+b²)
The set of points which are all the same distance (the radius) from a certain point (the center).
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


30. Sector
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 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)r^2(h)
2 pi r


31. Point-Slope form
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 segment connecting the center of a circle to any point on the circle
y-y1=m(x-x1)
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


32. Quadratic Formula
b±[vb²-4ac]/2a
Less
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(a+b)²


33. 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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34. In a parabola - if the first term is negative - the parabola ________.
1/3Bh
S^2
1/x^a
Opens down


35. Surface Area of Cylinder
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.
2pir^2 + 2pir*h
(a+b)(a²-ab+b²)
2lw+2lh+2wh


36. What is the point-slope form?
1.7
(0 -0)
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
(y-y1)=m(x-x1)


37. a²-2ab+b²
(a-b)²
(a+b)(a-b)
S² - where s = length of a side
4s


38. What is the area of a sector?
1/1
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.
(n degrees/360) * (pi)r^2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


39. a³+b³
A²-b²
(a+b)(a²-ab+b²)
1.7
2(lw+wh+lh)


40. Circle
Groups - teams - or committees.
?r²
The set of points which are all the same distance (the radius) from a certain point (the center).
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'.


41. Diameter
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.
(a-b)(a+b)
The distance across the circle through the center of the circle.The diameter is twice the radius.
A=bh


42. What is directly proportional?
Bh
T1 * r^(n-1)
Pi*r^2
y = kx


43. Area of a trapezoid
(a+b)²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(n/2) * (t1+tn)
½(b1 +b2) x h [or (b1 +b2) x h÷2]


44. x^-a =
2 pi r
(a-b)²
1/x^a
Bh


45. Area of Parallelogram
Bh
y = k/x
y2-y1/x2-x1
x°/360 times (2 pi r) - where x is the degrees in the angle


46. What is a '30:60:90' triangle?
Bh
x°/360 times (2 pi r) - where x is the degrees in the angle
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
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


47. (a+b)(c+d)
Ac+ad+bc+bd
Sum of terms/number of terms
1
y = kx


48. What is the equation of a line?

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49. x^a * x^b = x^__
y = kx
A+b
x² -2xy + y²
Ac+ad+bc+bd


50. When a line crosses two parallel lines - ________.
1/3pir^2*h
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 four big angles are equal and the four small angles are equal
(a-b)(a+b)