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. Circle
The average - mean - median - or mode.
Pi*d
A=?r2
The set of points which are all the same distance (the radius) from a certain point (the center).


2. Circumference Formula
1. Given event A: A + notA = 1.
C =?d
The average - mean - median - or mode.
The four big angles are equal and the four small angles are equal


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

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4. What is the average speed?
(a-b)(a²+ab+b²)
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'.
Bh
Total distance/total time


5. Explain the special properties of zero.
?d OR 2?r
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.
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.
Less


6. Chord
The distance from one point on the circle to another point on the circle.
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)(a²+ab+b²)
1.4


7. How do you calculate the surface area of a rectangular box?
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
Last term
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.


8. Perimeter (circumference) of a circle
Part of a circle connecting two points on the circle.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2 pi r
y = kx


9. Area of Square
S*v2
An ange whose vertex is the center of the circle
Percentage Change = Difference/Original * 100
S^2


10. 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.
(a-b)(a²+ab+b²)
T1 * r^(n-1)/(r-1)
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.


11. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
The average - mean - median - or mode.
C =?d
Between 0 and 1.
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.


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

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13. length of a sector
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
?r²
x°/360 times (2 pi r) - where x is the degrees in the angle
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


14. What is the average?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Probability A * Probability B
Sum of terms/number of terms
x°/360 times (2 pi r) - where x is the degrees in the angle


15. What number goes on the bottom of a probability fraction?
Probability A * Probability B
(a-b)²
The total # of possible outcomes.
C =?d


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

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17. a³+b³
(a+b)(a²-ab+b²)
2pi*r
An ange whose vertex is the center of the circle
The set of points which are all the same distance (the radius) from a certain point (the center).


18. Area of Triangle
1/2bh
(a-b)(a+b)
(a+b)²
Groups - teams - or committees.


19. Diameter
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The distance across the circle through the center of the circle.The diameter is twice the radius.
y = kx
(pi)r^2


20. What is inversely proportional?
1/2bh
y = k/x
1/1
x°/360 times (?r²) - where x is the degrees in the angle


21. What is the area of a triangle?
(a+b)(a²-ab+b²)
1/2bh
Equal
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.


22. When a line crosses two parallel lines - ________.
Arrangements - orders - schedules - or lists.
2lw+2lh+2wh
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 - and greater than the difference between the other two sides.


23. Rough est. of v3 =
1/2bh
1.7
Last term
Groups - teams - or committees.


24. a² - b² is equal to
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
y = k/x
(a+b)(a-b)
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.


25. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Total distance/total time
1. Given event A: A + notA = 1.
(a-b)(a²+ab+b²)
(a-b)(a+b)


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

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27. Volume of Cylinder
x²-y²
x°/360 times (2 pi r) - where x is the degrees in the angle
Pir^2h
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


28. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
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.
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.
1.7


29. How do you solve a permutation?
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
1.7
2 pi r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


30. Area of a square
Number of desired outcomes/number of total outcomes
4pir^2
1/2bh
S² - where s = length of a side


31. Circumference of a circle using radius
1.4
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2pi*r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


32. What is directly proportional?
y = kx
1/1
1.4
2(pi)r(r+h)


33. What is the factored version of x² -2xy + y² ?
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.
(x-y)²
The distance across the circle through the center of the circle.The diameter is twice the radius.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


34. What is the prime factorization of 200?
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)(a²-ab+b²)
2x2x2x5x5
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.


35. What is the volume of a cylinder?
(pi)r^2(h)
2pi*r
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.
2lw+2lh+2wh


36. Surface Area of Sphere
4pir^2
Sqr( x2 -x1) + (y2- y1)
The distance from one point on the circle to another point on the circle.
The four big angles are equal and the four small angles are equal


37. If x² = 144 - does v144 = x?
C =?d
Pi*d
Not necessarily. This is a trick question - because x could be either positive or negative.
1/3pir^2*h


38. Area of Parallelogram
Bh
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.
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.
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.


39. Area of Circle
Pi*d
Lw
Pi*r^2
Part of a circle connecting two points on the circle.


40. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
The average - mean - median - or mode.
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.
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. How do you find the midpoint?
2l+2w
Opens up
4s (where s = length of a side)
(x1+x2)/2 - (y1+y2)/2


42. 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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43. Does order matter for a permutation? How about for a combination?
2(lw+wh+lh)
Bh
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.
Order does matter for a permutation - but does not matter for a combination.


44. What is the equation of a line?

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45. Perimeter of a square
2(pi)r
1.7
1/1
4s (where s = length of a side)


46. What is the formula for the diagonal of any square?
Middle term
Groups - teams - or committees.
S*v2
(a-b)(a²+ab+b²)


47. 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.
Sum of terms/number of terms
2l+2w
T1 * r^(n-1)


48. Point-Slope form
Opens down
T1 * r^(n-1)
4s
y-y1=m(x-x1)


49. How do you find the slope?
b±[vb²-4ac]/2a
2pir^2 + 2pir*h
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.
y2-y1/x2-x1


50. The length of one side of any triangle is ____ than the sum of the other two sides.
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.
2Length + 2width [or (length + width) x 2]
Less
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.