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. a²-2ab+b²
x°/360 times (2 pi r) - where x is the degrees in the angle
1
(a-b)²
Pi*r^2


2. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
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.
S^2
b±[vb²-4ac]/2a


3. Point-Slope form
Total distance/total time
(pi)r^2
y-y1=m(x-x1)
Sqr( x2 -x1) + (y2- y1)


4. Circumference of a circle
(0 -0)
?r²
?d OR 2?r
1/2bh


5. Perimeter of a square
Between 0 and 1.
Pi*r^2
4s (where s = length of a side)
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.


6. a²-b²
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)(a+b)
S² - where s = length of a side
2(pi)r(r+h)


7. The probability of an event happening and the probability of an event NOT happening must add up to what number?
A+b
x°/360 times (2 pi r) - where x is the degrees in the angle
Arrangements - orders - schedules - or lists.
1. Given event A: A + notA = 1.


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

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9. How do you solve a permutation?
Bh
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Opens down
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


10. What is the average speed?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Probability A + Probability B
Total distance/total time
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


11. Lines reflected over the x or y axis have ____ slopes.
Negative
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
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


12. What is the sum of the inside angles of an n-sided polygon?
Between 0 and 1.
The four big angles are equal and the four small angles are equal
(n-2)180
2pir^2 + 2pir*h


13. What is the surface area of a cylinder?
Less
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The four big angles are equal and the four small angles are equal
2(pi)r(r+h)


14. How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
½(b1 +b2) x h [or (b1 +b2) x h÷2]
A=?r2
C =?d


15. 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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16. What is the 'Third side' rule for triangles?
1/x^a
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.
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.
T1 * r^(n-1)/(r-1)


17. How do you calculate a diagonal inside a 3-dimensional rectangular box?
N x M
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Number of desired outcomes/number of total outcomes
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.


18. What is directly proportional?
T1 + (n-1)d
y-y1=m(x-x1)
y = kx
?r²


19. (a+b)(a-b)=
(x+y)(x-y)
A²-b²
(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.


20. Area of a circle
The distance from one point on the circle to another point on the circle.
?r²
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.
(pi)r^2(h)


21. a² - b² is equal to
(n-2)180
The total # of possible outcomes.
2x2x2x5x5
(a+b)(a-b)


22. What is the factored version of (x+y)(x-y) ?
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.
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'.
x²-y²
2(pi)r


23. What is the 'distributive law'?
2Length + 2width [or (length + width) x 2]
(n degrees/360) * 2(pi)r
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.
4pir^2


24. Surface Area of rectangular prism
2lw+2lh+2wh
Pir^2h
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.
Probability A * Probability B


25. How do you find the sum of an arithmetic sequence?
(n/2) * (t1+tn)
(x+y)(x-y)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.


26. Circle
Sum of terms/number of terms
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.
Order does matter for a permutation - but does not matter for a combination.
The set of points which are all the same distance (the radius) from a certain point (the center).


27. If something is certain to happen - how is the probability of this event expressed mathematically?
1
1.7
1/1
C =?d


28. 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.
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
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'.
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.


29. Does order matter for a permutation? How about for a combination?
A+b
Total distance/total time
Order does matter for a permutation - but does not matter for a combination.
1/2 h (b1 + b2)


30. Surface Area of Sphere
x°/360 times (?r²) - where x is the degrees in the angle
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.
Opens up
4pir^2


31. What is the factored version of x² + 2xy + y² ?
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.
(x+y)²
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.
(x-y)²


32. What is the area of a sector?
T1 * r^(n-1)
2lw+2lh+2wh
½(base x height) [or (base x height)÷2]
(n degrees/360) * (pi)r^2


33. Rough est. of v1 =
2(pi)r(r+h)
2l+2w
1
1/2bh


34. Chord
The distance from one point on the circle to another point on the circle.
Percentage Change = Difference/Original * 100
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Order does matter for a permutation - but does not matter for a combination.


35. What is the side ratio for a 30:60:90 triangle?
Bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Pir^2h
Percentage Change = Difference/Original * 100


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

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

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38. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
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.
(n-2)180


39. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
Total distance/total time
The total # of possible outcomes.
Opens down


40. Rough est. of v3 =
Pi*d
1.7
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.
Total distance/total time


41. Volume of prism
Bh
1/1
Number of desired outcomes/number of total outcomes
b±[vb²-4ac]/2a


42. Area of a sector
Less
Opens down
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
x°/360 times (?r²) - where x is the degrees in the angle


43. What is inversely proportional?
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'.
y = k/x
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.
1/1


44. What is a '30:60:90' triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4pir^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
Pir^2h


45. What is the equation of a line?

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46. Area of Triangle
?d OR 2?r
An ange whose vertex is the center of the circle
(pi)r^2
1/2bh


47. (a+b)(c+d)
S*v2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2l+2w
Ac+ad+bc+bd


48. What is the length of an arc?
A=bh
(n degrees/360) * 2(pi)r
A=?r2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


49. Surface Area of Cylinder
The distance across the circle through the center of the circle.The diameter is twice the radius.
1/3pir^2*h
2pir^2 + 2pir*h
2l+2w


50. Perimeter (circumference) of a circle
2 pi r
Part of a circle connecting two points on the circle.
Number of desired outcomes/number of total outcomes
Arrangements - orders - schedules - or lists.