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. In a parabola - if the first term is negative - the parabola ________.
?d OR 2?r
x°/360 times (?r²) - where x is the degrees in the angle
Opens down
2(pi)r


2. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
1/x^a
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(n/2) * (t1+tn)
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.


3. Volume of prism
Bh
Percentage Change = Difference/Original * 100
2pir^2 + 2pir*h
1/x^a


4. Area of Trapezoid
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
1/2 h (b1 + b2)
2pir^2 + 2pir*h
C =?d


5. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
Groups - teams - or committees.
1
4pir^2


6. Area of Triangle
2(pi)r
Pi*r^2
(0 -0)
1/2bh


7. Perimeter of rectangle
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.
Part of a circle connecting two points on the circle.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2l+2w


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

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9. What is the area of a circle?
Number of desired outcomes/number of total outcomes
(pi)r^2
1
2lw+2lh+2wh


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

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11. When a line crosses two parallel lines - ________.
S*v2
The four big angles are equal and the four small angles are equal
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.


12. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
A+b
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
An ange whose vertex is the center of the circle
T1 * r^(n-1)


13. What is the side ratio for a Right Isosceles triangle?
The average - mean - median - or mode.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Less


14. What is the unfactored version of (x+y)² ?
x² + 2xy + y²
1/3Bh
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.
(a-b)(a²+ab+b²)


15. What is the area of a cylinder?
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.
2(pi)r(r+h)
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


16. What is inversely proportional?
y = k/x
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.
Less
(n degrees/360) * 2(pi)r


17. Define the 'Third side' rule for triangles

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18. perimeter of square
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.
4s
(y-y1)=m(x-x1)
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.


19. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Between 0 and 1.
Number of desired outcomes/number of total outcomes


20. How do you find the sum of a geometric sequence?
y2-y1/x2-x1
Order does matter for a permutation - but does not matter for a combination.
(a-b)(a+b)
T1 * r^(n-1)/(r-1)


21. Quadratic Formula
1. Given event A: A + notA = 1.
b±[vb²-4ac]/2a
?d OR 2?r
(x+y)(x-y)


22. Circumference of a circle
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
?d OR 2?r
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
Percentage Change = Difference/Original * 100


23. What is the factored version of x² + 2xy + y² ?
(x+y)²
Less
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1/x^a


24. What is the average speed?
1.7
x² + 2xy + y²
y2-y1/x2-x1
Total distance/total time


25. 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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26. What is a '30:60:90' triangle?
?d OR 2?r
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
2lw+2lh+2wh
Order does matter for a permutation - but does not matter for a combination.


27. What is the circumference of a circle?
y2-y1/x2-x1
S² - where s = length of a side
2(pi)r
(a+b)(a²-ab+b²)


28. What number goes on the bottom of a probability fraction?
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.
A+b
(n/2) * (t1+tn)
The total # of possible outcomes.


29. What is the formula for the diagonal of any square?
The distance from one point on the circle to another point on the circle.
S*v2
(a+b)(a²-ab+b²)
Not necessarily. This is a trick question - because x could be either positive or negative.


30. a³+b³
The set of points which are all the same distance (the radius) from a certain point (the center).
1/2bh
(a+b)(a²-ab+b²)
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.


31. Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a-b)(a+b)
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
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


32. Area of a square
S² - where s = length of a side
Last term
2(pi)r(r+h)
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.


33. Area of Circle
Pi*r^2
(a+b)(a-b)
T1 + (n-1)d
Last term


34. How do you find the midpoint?
Part of a circle connecting two points on the circle.
A=?r2
(x1+x2)/2 - (y1+y2)/2
y = k/x


35. Area of rectangle - square - parallelogram
The average - mean - median - or mode.
(n degrees/360) * (pi)r^2
A=bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


36. Surface Area of rectangular prism
(a+b)²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
S*v2
2lw+2lh+2wh


37. Area of a circle
1.7
?r²
x² + 2xy + y²
y = k/x


38. a² - b² is equal to
(a+b)(a-b)
C =?d
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.
(a+b)(a²-ab+b²)


39. What is the distance formula?
x²-y²
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Sqr( x2 -x1) + (y2- y1)


40. What is the unfactored version of x²-y² ?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(x+y)(x-y)
1/x^a
The four big angles are equal and the four small angles are equal


41. Area of Parallelogram
(n/2) * (t1+tn)
1/3Bh
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.
Bh


42. Area of a triangle
An ange whose vertex is the center of the circle
1/1
A=bh
½(base x height) [or (base x height)÷2]


43. In a coordinate system - identify the quadrants and describe their location.
Lw
2 pi r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
S*v2


44. What is the area of a solid rectangle?
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.
Groups - teams - or committees.
2(lw+wh+lh)
(n/2) * (t1+tn)


45. What is the factored version of x² -2xy + y² ?
(x-y)²
(a+b)(a²-ab+b²)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
y = k/x


46. x^-a =
(n degrees/360) * 2(pi)r
y = k/x
(a+b)(a-b)
1/x^a


47. 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.
The set of points which are all the same distance (the radius) from a certain point (the center).
Opens up
(y2-y1)/(x2-x1)


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

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49. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
Pir^2h
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.


50. Surface Area of Sphere
1/1
1. Given event A: A + notA = 1.
S*v2
4pir^2