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 is 'absolute value' - and how is it represented?

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2. What is the 'distributive law'?
An ange whose vertex is the center of the circle
Lw
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.


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

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4. If something is possible but not certain - what is the numeric range of probability of it happening?
1/3pir^2*h
Groups - teams - or committees.
Between 0 and 1.
Equal


5. Perimeter of rectangle
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
2l+2w
(pi)r^2(h)
x°/360 times (?r²) - where x is the degrees in the angle


6. What is the equation of a line?

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7. a²-2ab+b²
(a-b)²
1.7
Less
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.


8. 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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9. List two odd behaviors of exponents
1/3pir^2*h
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.
Last term
(pi)r^2


10. Volume of Cone
2l+2w
T1 + (n-1)d
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.
1/3pir^2*h


11. Chord
The distance from one point on the circle to another point on the circle.
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
Pi*r^2
Middle term


12. Area of Square
Opens down
S^2
Arrangements - orders - schedules - or lists.
1/x^a


13. Circle
Sum of the lengths of the sides
Bh
1/2 h (b1 + b2)
The set of points which are all the same distance (the radius) from a certain point (the center).


14. What is the 'Third side' rule for triangles?
(x-y)²
Total distance/total time
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.
Arrangements - orders - schedules - or lists.


15. perimeter of square
1/2bh
2Length + 2width [or (length + width) x 2]
(a-b)(a²+ab+b²)
4s


16. For a bell curve - what three terms might be used to describe the number in the middle?
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'.
N x M
The average - mean - median - or mode.
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


17. Area of rectangle - square - parallelogram
Not necessarily. This is a trick question - because x could be either positive or negative.
A=bh
Opens down
(n/2) * (t1+tn)


18. Volume of sphere
4/3pir^3
(x+y)²
Total distance/total time
1/x^a


19. What is the sum of the inside angles of an n-sided polygon?
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.
Opens down
(n-2)180
Probability A + Probability B


20. Central Angle
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.
y = k/x
(a+b)(a²-ab+b²)
An ange whose vertex is the center of the circle


21. How do you find the sum of an arithmetic sequence?
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(n/2) * (t1+tn)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
x°/360 times (2 pi r) - where x is the degrees in the angle


22. Does order matter for a permutation? How about for a combination?
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.
S*v2
Order does matter for a permutation - but does not matter for a combination.
x°/360 times (?r²) - where x is the degrees in the angle


23. What is the length of an arc?
1
(n/2) * (t1+tn)
x² + 2xy + y²
(n degrees/360) * 2(pi)r


24. a² - b² is equal to
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
S^2
1/3pir^2*h
(a+b)(a-b)


25. (a+b)(c+d)
Ac+ad+bc+bd
1
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.
(pi)r^2(h)


26. What is the side ratio for a 30:60:90 triangle?
The average - mean - median - or mode.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.


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

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28. Define the range of a set of numbers.
(y2-y1)/(x2-x1)
Middle term
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.
Lw


29. What do permutation problems often ask for?
The total # of possible outcomes.
(0 -0)
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.
Arrangements - orders - schedules - or lists.


30. How do you multiply and divide square roots?
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
Bh
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2Length + 2width [or (length + width) x 2]


31. What is the volume of a cylinder?
1/3Bh
(pi)r^2(h)
Total distance/total time
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.


32. In a coordinate system - identify the quadrants and describe their location.
(a-b)(a²+ab+b²)
C =?d
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


33. What is the factored version of (x+y)(x-y) ?
1/2bh
1.7
x²-y²
1


34. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
b±[vb²-4ac]/2a
(x+y)²
2lw+2lh+2wh
Probability A + Probability B


35. Perimeter of a square
4s (where s = length of a side)
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
(x-y)²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


36. a³+b³
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.
(a+b)(a²-ab+b²)
Equal
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


37. length of a sector
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
4/3pir^3
The distance across the circle through the center of the circle.The diameter is twice the radius.


38. Circumference Formula
C =?d
Sum of the lengths of the sides
1.7
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.


39. What is inversely proportional?
y = k/x
4s
x² + 2xy + y²
(a+b)²


40. What is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Probability A * Probability B
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
The distance from one point on the circle to another point on the circle.


41. What is the prime factorization of 200?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2x2x2x5x5
1. Given event A: A + notA = 1.
A=bh


42. What is a 'Right isosceles' triangle?
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 four big angles are equal and the four small angles are equal
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(y-y1)=m(x-x1)


43. How do you calculate the surface area of a rectangular box?
Order does matter for a permutation - but does not matter for a combination.
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.
A segment connecting the center of a circle to any point on the circle
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.


44. Surface Area of rectangular prism
Last term
The distance from one point on the circle to another point on the circle.
2lw+2lh+2wh
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


45. Circumference of a circle using radius
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2pi*r
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


46. In a coordinate system - what is the origin?
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.
(0 -0)
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.
y = k/x


47. Area of a triangle
½(base x height) [or (base x height)÷2]
Number of desired outcomes/number of total outcomes
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2l+2w


48. a²+2ab+b²
1. Given event A: A + notA = 1.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a+b)²
The total # of possible outcomes.


49. Define the 'Third side' rule for triangles

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50. When you reverse FOIL - the term that needs to add out is the _____
2x2x2x5x5
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.
Middle term
An ange whose vertex is the center of the circle