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. What is the prime factorization of 200?
x² + 2xy + y²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
4s (where s = length of a side)
2x2x2x5x5


2. What is the 'Third side' rule for triangles?
A+b
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.
x°/360 times (?r²) - where x is the degrees in the angle
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.


3. In a parabola - if the first term is negative - the parabola ________.
The four big angles are equal and the four small angles are equal
Opens down
1.7
(a+b)(a-b)


4. What number goes on the bottom of a probability fraction?
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 total # of possible outcomes.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/1


5. Central Angle
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
4pir^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.


6. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
(y2-y1)/(x2-x1)
2Length + 2width [or (length + width) x 2]
x°/360 times (2 pi r) - where x is the degrees in the angle


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

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8. Volume of Cone
2(pi)r(r+h)
1/3pir^2*h
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.
1/2bh


9. Perimeter (circumference) of a circle
2 pi r
S^2
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.
(x1+x2)/2 - (y1+y2)/2


10. How do you find the nth term of a geometric sequence?
x² -2xy + y²
2Length + 2width [or (length + width) x 2]
T1 * r^(n-1)
Lwh


11. Slope
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 from one point on the circle to another point on the circle.
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.
(y2-y1)/(x2-x1)


12. Area of Circle
Ac+ad+bc+bd
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.
Pi*r^2
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.


13. Lines reflected over the x or y axis have ____ slopes.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
?d OR 2?r
Negative
(n/2) * (t1+tn)


14. What do combination problems usually ask for?
(a-b)²
Groups - teams - or committees.
(n-2)180
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'.


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

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16. perimeter of square
4s
The average - mean - median - or mode.
(x-y)²
(a-b)(a²+ab+b²)


17. x^a * x^b = x^__
y2-y1/x2-x1
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
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.


18. Area of a sector
A+b
x°/360 times (?r²) - where x is the degrees in the angle
(y-y1)=m(x-x1)
S*v2


19. What is the distance formula?
T1 + (n-1)d
1/x^a
Sqr( x2 -x1) + (y2- y1)
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.


20. Diameter
Probability A * Probability B
C =?d
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
The distance across the circle through the center of the circle.The diameter is twice the radius.


21. What is the area of a solid rectangle?
Groups - teams - or committees.
?r²
Last term
2(lw+wh+lh)


22. Area of Rectangle
Lw
x² + 2xy + y²
Percentage Change = Difference/Original * 100
y = kx


23. Volume of pyramid
Pir^2h
1/3Bh
(a+b)(a-b)
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.


24. Circumference of a circle
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.
?d OR 2?r
4s
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


25. What must be true before a quadratic equation can be solved?

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26. Circumference of cirlce using diameter
Pi*d
1/1
x²-y²
1/3pir^2*h


27. What is a '30:60:90' 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
N x M
(a-b)(a+b)
Less


28. If x² = 144 - does v144 = x?
Probability A * Probability B
Not necessarily. This is a trick question - because x could be either positive or negative.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1/3pir^2*h


29. Perimeter of polygon
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Sum of the lengths of the sides
1.7
?d OR 2?r


30. Rough est. of v3 =
Pir^2h
4s (where s = length of a side)
1.7
(0 -0)


31. List two odd behaviors of exponents
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.


32. What is the probability?
2pi*r
1/2bh
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.
Number of desired outcomes/number of total outcomes


33. What is the surface area of a cylinder?
2(pi)r(r+h)
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
A=?r2


34. Area of rectangle - square - parallelogram
2l+2w
A=bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Groups - teams - or committees.


35. What is the formula for the diagonal of any square?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Bh
S*v2
(x+y)²


36. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Negative


37. (a+b)(a-b)=
A²-b²
2x2x2x5x5
(a+b)²
1/2bh


38. What is an 'equilateral' triangle?
A segment connecting the center of a circle to any point on the circle
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
S*v2
1.7


39. 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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40. In a parabola - if the first term is positive - the parabola ________.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Opens up
(a-b)(a+b)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


41. a²+2ab+b²
x°/360 times (2 pi r) - where x is the degrees in the angle
2lw+2lh+2wh
(a+b)²
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.


42. Define a factorial of a number - and how it is written.
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.
(y-y1)=m(x-x1)
Pir^2h
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.


43. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
1/x^a
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.
Pi*r^2
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.


44. When you reverse FOIL - the term that needs to multiply out is the _____
4/3pir^3
Last term
y = k/x
The four big angles are equal and the four small angles are equal


45. When a line crosses two parallel lines - ________.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The four big angles are equal and the four small angles are equal
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.
Ac+ad+bc+bd


46. Define the formula for calculating slope.
The average - mean - median - or mode.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Pir^2h
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.


47. a²-2ab+b²
(a-b)²
Arrangements - orders - schedules - or lists.
?r²
2(pi)r(r+h)


48. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
(x1+x2)/2 - (y1+y2)/2
T1 + (n-1)d
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.


49. What is the equation of a line?

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50. What is the factored version of x² -2xy + y² ?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
4/3pir^3
(x-y)²
Between 0 and 1.