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. Perimeter of a rectangle
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
2 pi r
2Length + 2width [or (length + width) x 2]
T1 + (n-1)d


2. Point-Slope form
y-y1=m(x-x1)
1/3Bh
Pi*r^2
Sqr( x2 -x1) + (y2- y1)


3. Slope
(a-b)(a²+ab+b²)
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
(y2-y1)/(x2-x1)
(0 -0)


4. What is the point-slope form?
(y-y1)=m(x-x1)
Opens up
y-y1=m(x-x1)
1.7


5. What is the unfactored version of (x+y)² ?
The set of points which are all the same distance (the radius) from a certain point (the center).
½(base x height) [or (base x height)÷2]
1.4
x² + 2xy + y²


6. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Arrangements - orders - schedules - or lists.
2(pi)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
Part of a circle connecting two points on the circle.


7. What is the surface area of a cylinder?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2(pi)r(r+h)
Probability A + Probability B
The total # of possible outcomes.


8. In a coordinate system - what is the origin?
(0 -0)
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.
x² + 2xy + y²
S^2


9. a³-b³
Order does matter for a permutation - but does not matter for a combination.
A=?r2
2(pi)r(r+h)
(a-b)(a²+ab+b²)


10. Define the 'Third side' rule for triangles

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11. Surface Area of Cylinder
2pir^2 + 2pir*h
(a-b)(a²+ab+b²)
A=?r2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


12. What is the probability?
(a+b)(a-b)
Number of desired outcomes/number of total outcomes
(a-b)(a²+ab+b²)
S² - where s = length of a side


13. Area of Parallelogram
(x1+x2)/2 - (y1+y2)/2
A=bh
Bh
1/2bh


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

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15. What is the sum of the inside angles of an n-sided polygon?
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.
(n-2)180
Sqr( x2 -x1) + (y2- y1)
y = kx


16. Define the range of a set of numbers.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The four big angles are equal and the four small angles are equal
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.
(0 -0)


17. What is the area of a circle?
Sum of terms/number of terms
(pi)r^2
Negative
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.


18. Volume of Cylinder
Pir^2h
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.
(x+y)(x-y)
2 pi r


19. Volume of sphere
Pi*d
x°/360 times (2 pi r) - where x is the degrees in the angle
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4/3pir^3


20. Circumference of a circle
x² -2xy + y²
?d OR 2?r
y = k/x
(x1+x2)/2 - (y1+y2)/2


21. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
1/2bh
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.
Between 0 and 1.
(pi)r^2


22. To divide powers with the same base...
Sum of terms/number of terms
(n degrees/360) * 2(pi)r
(a+b)(a²-ab+b²)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


23. Perimeter (circumference) of a circle
A+b
2 pi r
x² -2xy + y²
(a-b)(a+b)


24. Chord
The average - mean - median - or mode.
(x+y)(x-y)
Sum of the lengths of the sides
The distance from one point on the circle to another point on the circle.


25. Area of a square
S² - where s = length of a side
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.
1.4


26. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
(x-y)²
4pir^2
Pir^2h


27. What is the length of an arc?
4pir^2
Pi*r^2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(n degrees/360) * 2(pi)r


28. How do you calculate the surface area of a rectangular box?
(0 -0)
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.
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.
Sqr( x2 -x1) + (y2- y1)


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


30. Area of a trapezoid
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.
2(pi)r
½(b1 +b2) x h [or (b1 +b2) x h÷2]
4pir^2


31. What is inversely proportional?
4s
y = k/x
A=bh
(pi)r^2(h)


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

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33. How do you multiply and divide square roots?
2pir^2 + 2pir*h
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Less


34. Area of Square
T1 * r^(n-1)
(n degrees/360) * (pi)r^2
S^2
(x+y)²


35. a² - b² is equal to
A+b
(a+b)(a-b)
Opens up
Probability A * Probability B


36. Define 'proportionate' values
1.4
1/1
1/3Bh
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


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

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38. What is the distance formula?
(n/2) * (t1+tn)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Opens down
Sqr( x2 -x1) + (y2- y1)


39. Central Angle
Probability A + Probability B
An ange whose vertex is the center of the circle
Sqr( x2 -x1) + (y2- y1)
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.


40. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
A=bh
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.
1.7


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

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42. a³+b³
(x-y)²
Number of desired outcomes/number of total outcomes
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(a+b)(a²-ab+b²)


43. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
The distance across the circle through the center of the circle.The diameter is twice the radius.
(n-2)180
A²-b²


44. What is the area of a cylinder?
2(pi)r(r+h)
1/1
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.
y2-y1/x2-x1


45. Circumference of a circle using radius
Last term
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.
Ac+ad+bc+bd
2pi*r


46. Surface Area of Sphere
1
Bh
Pir^2h
4pir^2


47. 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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48. a²-b²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Between 0 and 1.
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)


49. What is the area of a sector?
(n degrees/360) * (pi)r^2
Negative
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.
Ac+ad+bc+bd


50. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
A²-b²
T1 + (n-1)d
Groups - teams - or committees.
N x M