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 must be true before a quadratic equation can be solved?

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2. List two odd behaviors of exponents
1/x^a
A segment connecting the center of a circle to any point on the circle
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'.
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.


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

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4. Area of a triangle
(a-b)(a+b)
Number of desired outcomes/number of total outcomes
½(base x height) [or (base x height)÷2]
2lw+2lh+2wh


5. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
1. Given event A: A + notA = 1.
T1 * r^(n-1)/(r-1)
?d OR 2?r


6. What is the area of a triangle?
S^2
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.
1/2bh
1.4


7. Sector
½(b1 +b2) x h [or (b1 +b2) x h÷2]
A=bh
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
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.


8. What is the unfactored version of x²-y² ?
Pi*d
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.
(x+y)(x-y)
½(b1 +b2) x h [or (b1 +b2) x h÷2]


9. Perimeter of a rectangle
Groups - teams - or committees.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
y = k/x
2Length + 2width [or (length + width) x 2]


10. Define the 'Third side' rule for triangles

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11. Surface Area of rectangular prism
Total distance/total time
4/3pir^3
(pi)r^2
2lw+2lh+2wh


12. Perimeter of a square
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
4s (where s = length of a side)
2x2x2x5x5


13. Lines reflected over the x or y axis have ____ slopes.
A²-b²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Negative
x°/360 times (?r²) - where x is the degrees in the angle


14. What is the probability?
(pi)r^2(h)
Number of desired outcomes/number of total outcomes
(a+b)(a-b)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


15. a³-b³
Part of a circle connecting two points on the circle.
N x M
(a-b)(a²+ab+b²)
(a+b)(a-b)


16. How do you calculate the percentage of change?
(x-y)²
Percentage Change = Difference/Original * 100
C =?d
S^2


17. Slope
Part of a circle connecting two points on the circle.
y = kx
(a+b)²
(y2-y1)/(x2-x1)


18. What is the equation of a line?

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19. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
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.
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
4s (where s = length of a side)


20. Define the range of a set of numbers.
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.
(x+y)²
Middle term
2(lw+wh+lh)


21. Area of Parallelogram
1/2bh
Bh
Middle term
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


22. What is the length of an arc?
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Sum of the lengths of the sides
(n degrees/360) * 2(pi)r


23. What is the sum of the inside angles of an n-sided polygon?
Bh
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.
4s
(n-2)180


24. a³+b³
x°/360 times (?r²) - where x is the degrees in the angle
2pir^2 + 2pir*h
2x2x2x5x5
(a+b)(a²-ab+b²)


25. Chord
2Length + 2width [or (length + width) x 2]
The distance from one point on the circle to another point on the circle.
2pir^2 + 2pir*h
(n degrees/360) * (pi)r^2


26. a²-2ab+b²
1/2bh
2l+2w
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.
(a-b)²


27. What is inversely proportional?
y = k/x
y-y1=m(x-x1)
S^2
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


28. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Arrangements - orders - schedules - or lists.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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=?r2


29. Volume of sphere
1.7
4/3pir^3
The distance from one point on the circle to another point on the circle.
(x+y)²


30. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
C =?d
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.
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.


31. Perimeter (circumference) of a circle
Between 0 and 1.
N x M
2 pi r
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'.


32. What is the 'Third side' rule for triangles?
(a+b)(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.
The average - mean - median - or mode.
1/2bh


33. Area of a square
1/1
S² - where s = length of a side
The total # of possible outcomes.
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


34. How do you multiply powers with the same base?
1
4s (where s = length of a side)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


35. What is the factored version of x² + 2xy + y² ?
(x+y)²
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.
4pir^2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


36. What is the volume of a solid rectangle?
Opens up
y = kx
Lwh
(a+b)(a²-ab+b²)


37. What is the surface area of a cylinder?
2pi*r
2(pi)r(r+h)
(a-b)(a+b)
x°/360 times (2 pi r) - where x is the degrees in the angle


38. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
The set of points which are all the same distance (the radius) from a certain point (the center).
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
Between 0 and 1.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


39. What is the average?
Sum of terms/number of terms
Number of desired outcomes/number of total outcomes
Pi*r^2
C =?d


40. What is the formula for the diagonal of any square?
(a-b)(a+b)
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.
(x1+x2)/2 - (y1+y2)/2
S*v2


41. How do you find the midpoint?
Negative
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.
Less
(x1+x2)/2 - (y1+y2)/2


42. a²+2ab+b²
(a+b)²
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(a-b)(a²+ab+b²)


43. Area of Circles
4s
A=?r2
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


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

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45. The probability of an event happening and the probability of an event NOT happening must add up to what number?
The set of points which are all the same distance (the radius) from a certain point (the center).
4s
1. Given event A: A + notA = 1.
Last term


46. Area of Trapezoid
The four big angles are equal and the four small angles are equal
x²-y²
x² -2xy + y²
1/2 h (b1 + b2)


47. Volume of Cone
1/3pir^2*h
Groups - teams - or committees.
Part of a circle connecting two points on the circle.
4pir^2


48. 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.
2(pi)r
S*v2
T1 * r^(n-1)/(r-1)


49. How do you find the nth term of an arithmetic sequence?
S² - where s = length of a side
1/1
T1 + (n-1)d
(pi)r^2


50. x^a * x^b = x^__
A+b
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.
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.
4pir^2