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. Define the mode of a set of numbers.
(x+y)²
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.
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.
2Length + 2width [or (length + width) x 2]


2. Arc
2x2x2x5x5
Total distance/total time
(pi)r^2
Part of a circle connecting two points on the circle.


3. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Order does matter for a permutation - but does not matter for a combination.
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.
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.
1.4


4. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
4s
(pi)r^2(h)
A+b


5. What is the formula for the diagonal of any square?
(a+b)(a-b)
½(base x height) [or (base x height)÷2]
S*v2
x°/360 times (2 pi r) - where x is the degrees in the angle


6. Surface Area of Sphere
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.
Less
x² + 2xy + y²
4pir^2


7. How do you find the sum of an arithmetic sequence?
x²-y²
(n/2) * (t1+tn)
x² -2xy + y²
Probability A + Probability B


8. Central Angle
Groups - teams - or committees.
An ange whose vertex is the center of the circle
Opens up
(n degrees/360) * 2(pi)r


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

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10. Rough est. of v1 =
y = kx
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


11. Area of a square
S² - where s = length of a side
?r²
T1 + (n-1)d
Probability A * Probability B


12. a² - b² is equal to
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
4s
(a+b)(a-b)
Bh


13. How do you multiply powers with the same base?
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 ange whose vertex is the center of the circle
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


14. What is the equation of a line?

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15. How do you calculate a diagonal inside a 3-dimensional rectangular box?
1/2bh
Bh
(a+b)²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


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

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17. Perimeter of polygon
Last term
2(lw+wh+lh)
Total distance/total time
Sum of the lengths of the sides


18. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
y = k/x
The four big angles are equal and the four small angles are equal
Groups - teams - or committees.


19. Define the formula for calculating slope.
2pi*r
1/3Bh
1.4
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


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

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21. (a+b)(a-b)=
A²-b²
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 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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]


22. Area of Square
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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
S^2
Lwh


23. How do you calculate the probability of two events in a row? (Probability of A and B)
(pi)r^2(h)
Probability A * Probability B
Pir^2h
T1 * r^(n-1)/(r-1)


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

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25. Point-Slope form
(x-y)²
y-y1=m(x-x1)
Part of a circle connecting two points on the circle.
(pi)r^2


26. Volume of Cylinder
Pir^2h
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
x²-y²


27. Define the range of a set of numbers.
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 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.
2l+2w
x°/360 times (?r²) - where x is the degrees in the angle


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

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29. What are the side ratios for a 30:60:90 triangle?
T1 * r^(n-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.
4s
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


30. If x² = 144 - does v144 = x?
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.
N x M
Not necessarily. This is a trick question - because x could be either positive or negative.
Lw


31. Circumference of a circle using radius
(a-b)²
2(pi)r(r+h)
2pi*r
½(base x height) [or (base x height)÷2]


32. To divide powers with the same base...
(n degrees/360) * (pi)r^2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Pi*r^2
N x M


33. What number goes on the bottom of a probability fraction?
1
The total # of possible outcomes.
?d OR 2?r
Lw


34. a²-2ab+b²
Part of a circle connecting two points on the circle.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(a-b)²
(a+b)(a²-ab+b²)


35. 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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36. perimeter of square
2(pi)r(r+h)
Bh
4s
y = k/x


37. Volume of pyramid
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1/3Bh
x² -2xy + y²


38. What is the 'distributive law'?
Bh
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.
(n degrees/360) * (pi)r^2
S² - where s = length of a side


39. What is the area of a cylinder?
2(pi)r(r+h)
T1 * r^(n-1)
Arrangements - orders - schedules - or lists.
The four big angles are equal and the four small angles are equal


40. What is the prime factorization of 200?
Sum of terms/number of terms
2x2x2x5x5
Lwh
4pir^2


41. What is the area of a solid rectangle?
2(lw+wh+lh)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
4s
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.


42. What is the average speed?
S*v2
Pir^2h
(a-b)(a²+ab+b²)
Total distance/total time


43. Sector
Sqr( x2 -x1) + (y2- y1)
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.
Number of desired outcomes/number of total outcomes
2Length + 2width [or (length + width) x 2]


44. Circumference Formula
Sum of the lengths of the sides
A=bh
Percentage Change = Difference/Original * 100
C =?d


45. Perimeter of rectangle
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.
Lwh
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2l+2w


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


47. What is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2(lw+wh+lh)
4s
2(pi)r(r+h)


48. What is the area of a circle?
(pi)r^2
The four big angles are equal and the four small angles are equal
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Order does matter for a permutation - but does not matter for a combination.


49. 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
Bh
S² - where s = length of a side
Negative


50. Area of Triangle
1/2bh
y = kx
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.