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. Area of rectangle - square - parallelogram
1/3Bh
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Arrangements - orders - schedules - or lists.
A=bh


2. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
?d OR 2?r
S² - where s = length of a side
x² + 2xy + y²


3. Circumference Formula
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
C =?d
(0 -0)
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


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

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5. Volume of Cone
1/3pir^2*h
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
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


6. Circumference of cirlce using diameter
Pi*d
(y2-y1)/(x2-x1)
Probability A * Probability B
Sqr( x2 -x1) + (y2- y1)


7. What is the volume of a solid rectangle?
The average - mean - median - or mode.
Pi*r^2
(a+b)²
Lwh


8. Sector
x²-y²
2x2x2x5x5
Lw
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.


9. perimeter of square
2Length + 2width [or (length + width) x 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.
4s
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.


10. Define the 'Third side' rule for triangles

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11. Chord
The distance from one point on the circle to another point on the circle.
(a+b)²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Opens up


12. Area of Rectangle
The four big angles are equal and the four small angles are equal
Lw
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Less


13. Perimeter of rectangle
2l+2w
2pir^2 + 2pir*h
1/2bh
The distance across the circle through the center of the circle.The diameter is twice the radius.


14. Lines reflected over the x or y axis have ____ slopes.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Negative
(y2-y1)/(x2-x1)
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.


15. Perimeter of a square
1/1
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.
1/2 h (b1 + b2)
4s (where s = length of a side)


16. a³-b³
(a-b)(a²+ab+b²)
4s (where s = length of a side)
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.


17. 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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18. Diameter
Total distance/total time
The distance across the circle through the center of the circle.The diameter is twice the radius.
x² -2xy + y²
(a-b)(a²+ab+b²)


19. If something is certain to happen - how is the probability of this event expressed mathematically?
1.4
x²-y²
1/1
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'.


20. Circumference of a circle
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
x² + 2xy + y²
?d OR 2?r
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.


21. Volume of Cylinder
The average - mean - median - or mode.
(a-b)²
(y2-y1)/(x2-x1)
Pir^2h


22. If x² = 144 - does v144 = x?
x°/360 times (?r²) - where x is the degrees in the angle
Probability A + Probability B
(a-b)(a+b)
Not necessarily. This is a trick question - because x could be either positive or negative.


23. In a parabola - if the first term is positive - the parabola ________.
Part of a circle connecting two points on the circle.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Opens up
Last term


24. Area of a trapezoid
Between 0 and 1.
A+b
½(b1 +b2) x h [or (b1 +b2) x h÷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


25. What is the area of a cylinder?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
y = kx
2(pi)r(r+h)
A=bh


26. a³+b³
T1 * r^(n-1)
4s (where s = length of a side)
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+b)(a²-ab+b²)


27. x^-a =
The average - mean - median - or mode.
(y2-y1)/(x2-x1)
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.
1/x^a


28. length of a sector
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°/360 times (2 pi r) - where x is the degrees in the angle
Arrangements - orders - schedules - or lists.
4/3pir^3


29. How do you multiply powers with the same base?
(a+b)(a²-ab+b²)
?r²
The total # of possible outcomes.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


30. What is the side ratio for 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.
?r²
(pi)r^2(h)
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.


31. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
1/3pir^2*h
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


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

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33. What is the point-slope form?
(y-y1)=m(x-x1)
A=?r2
(x+y)(x-y)
Pir^2h


34. In a coordinate system - what is the origin?
Equal
(0 -0)
1/2bh
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.


35. (a+b)(a-b)=
Opens up
(x-y)²
1/2 h (b1 + b2)
A²-b²


36. How do you calculate the surface area of a rectangular box?
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.
C =?d
Sqr( x2 -x1) + (y2- y1)
2(lw+wh+lh)


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

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38. What is directly proportional?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
y = kx
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.
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.


39. Rough est. of v2 =
x°/360 times (?r²) - where x is the degrees in the angle
1.4
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(x1+x2)/2 - (y1+y2)/2


40. What is the equation of a line?

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41. What is the unfactored version of (x+y)² ?
2(pi)r
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.
Arrangements - orders - schedules - or lists.


42. Surface Area of rectangular prism
2lw+2lh+2wh
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.
1/2 h (b1 + b2)
(a-b)²


43. What is the average?
2(pi)r
(x1+x2)/2 - (y1+y2)/2
(n-2)180
Sum of terms/number of terms


44. Surface Area of Sphere
Order does matter for a permutation - but does not matter for a combination.
(a-b)(a+b)
4pir^2
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.


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

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46. What is the factored version of x² + 2xy + y² ?
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.
Ac+ad+bc+bd
(x+y)²
Total distance/total time


47. Volume of sphere
4/3pir^3
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1/1
Sum of terms/number of terms


48. What is the unfactored version of (x-y)² ?
N x M
Groups - teams - or committees.
½(base x height) [or (base x height)÷2]
x² -2xy + y²


49. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
1.7
2Length + 2width [or (length + width) x 2]
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


50. Volume of pyramid
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
?d OR 2?r
½(base x height) [or (base x height)÷2]
1/3Bh