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 'Third side' rule for triangles

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2. What is the sum of the inside angles of an n-sided polygon?
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.
A²-b²
(n-2)180
x² + 2xy + y²


3. Define the mode of a set of numbers.
1.4
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.
T1 * r^(n-1)
The average - mean - median - or mode.


4. What is the probability?
Middle term
(y2-y1)/(x2-x1)
x²-y²
Number of desired outcomes/number of total outcomes


5. What is the equation of a line?

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6. Does order matter for a permutation? How about for a combination?
1/3pir^2*h
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Order does matter for a permutation - but does not matter for a combination.
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.


7. What is the circumference of a circle?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2(pi)r
1/3Bh
2Length + 2width [or (length + width) x 2]


8. What is the volume of a solid rectangle?
Lwh
Groups - teams - or committees.
Ac+ad+bc+bd
C =?d


9. In a coordinate system - identify the quadrants and describe their location.
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=?r2
2(pi)r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


10. If x² = 144 - does v144 = x?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Not necessarily. This is a trick question - because x could be either positive or negative.
Equal
(n/2) * (t1+tn)


11. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
Total distance/total time
Probability A + Probability B
Percentage Change = Difference/Original * 100


12. What'S the most important thing to remember about charts you'll see on the GRE?
A segment connecting the center of a circle to any point on the circle
1/3pir^2*h
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.
?r²


13. How do you calculate the probability of two events in a row? (Probability of A and B)
?r²
Probability A * Probability B
Number of desired outcomes/number of total outcomes
(0 -0)


14. Arc
x°/360 times (?r²) - where x is the degrees in the angle
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
Part of a circle connecting two points on the circle.
C =?d


15. What is a 'Right isosceles' triangle?
Pi*d
Number of desired outcomes/number of total outcomes
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.
2(pi)r(r+h)


16. What is the area of a circle?
2Length + 2width [or (length + width) x 2]
(pi)r^2
(pi)r^2(h)
2(pi)r(r+h)


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

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18. In a parabola - if the first term is positive - the parabola ________.
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.
Total distance/total time
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.
Opens up


19. What is the surface area of a cylinder?
2(pi)r(r+h)
Sqr( x2 -x1) + (y2- y1)
Arrangements - orders - schedules - or lists.
Pir^2h


20. a²+2ab+b²
(a+b)²
The distance from one point on the circle to another point on the circle.
The distance across the circle through the center of the circle.The diameter is twice the radius.
Groups - teams - or committees.


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

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22. How do you multiply and divide square roots?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The four big angles are equal and the four small angles are equal
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
4s


23. Volume of pyramid
N x M
The total # of possible outcomes.
1/3Bh
T1 + (n-1)d


24. Area of Circle
(a-b)(a+b)
2pir^2 + 2pir*h
Pi*r^2
y = kx


25. Area of Triangle
½(base x height) [or (base x height)÷2]
Arrangements - orders - schedules - or lists.
A=bh
1/2bh


26. Perimeter of rectangle
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.
b±[vb²-4ac]/2a
2(pi)r
2l+2w


27. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Total distance/total time
An ange whose vertex is the center of the circle
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
4pir^2


28. a³+b³
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
(a+b)(a²-ab+b²)
(a-b)(a²+ab+b²)
N x M


29. What is the area of a solid rectangle?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2(lw+wh+lh)
2(pi)r(r+h)
Probability A * Probability B


30. 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.
1/2bh
y = kx
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


31. Surface Area of rectangular prism
2lw+2lh+2wh
N x M
2Length + 2width [or (length + width) x 2]
(x+y)²


32. List two odd behaviors of exponents
Lw
1/2bh
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.
T1 * r^(n-1)


33. In intersecting lines - opposite angles are _____.
Equal
1.7
x°/360 times (?r²) - where x is the degrees in the angle
A=?r2


34. Rough est. of v2 =
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
(y2-y1)/(x2-x1)
1.4
S² - where s = length of a side


35. For a bell curve - what three terms might be used to describe the number in the middle?
(a-b)(a²+ab+b²)
The average - mean - median - or mode.
2l+2w
1/3Bh


36. Area of rectangle - square - parallelogram
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A=bh
Order does matter for a permutation - but does not matter for a combination.
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.


37. Area of a triangle
½(base x height) [or (base x height)÷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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


38. Circumference of a circle
x²-y²
(n degrees/360) * (pi)r^2
?d OR 2?r
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.


39. Slope
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 + (n-1)d
(y2-y1)/(x2-x1)
(a+b)(a-b)


40. What is the factored version of x² + 2xy + y² ?
(x+y)²
A=bh
(n degrees/360) * 2(pi)r
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


41. What is the area of a cylinder?
Groups - teams - or committees.
2(pi)r(r+h)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Less


42. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
(x+y)²
(pi)r^2(h)
A segment connecting the center of a circle to any point on the circle


43. Sector
2x2x2x5x5
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.
Bh
A²-b²


44. Circle
x°/360 times (2 pi r) - where x is the degrees in the angle
The set of points which are all the same distance (the radius) from a certain point (the center).
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.
Sum of terms/number of terms


45. To divide powers with the same base...
(pi)r^2(h)
Groups - teams - or committees.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(x+y)(x-y)


46. a² - b² is equal to
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)(a-b)
2Length + 2width [or (length + width) x 2]
1/2 h (b1 + b2)


47. How do you find the sum of a geometric sequence?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
T1 * r^(n-1)/(r-1)
(n degrees/360) * (pi)r^2
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.


48. What is the area of a triangle?
y2-y1/x2-x1
C =?d
1/2bh
Sqr( x2 -x1) + (y2- y1)


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

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50. Explain the special properties of zero.
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.
2 pi r
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.
y-y1=m(x-x1)