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. Circumference of a circle using radius
A segment connecting the center of a circle to any point on the circle
x² + 2xy + y²
(pi)r^2
2pi*r


2. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Order does matter for a permutation - but does not matter for a combination.
The four big angles are equal and the four small angles are equal
b±[vb²-4ac]/2a


3. Area of Rectangle
Pi*d
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.
½(base x height) [or (base x height)÷2]


4. What is the formula for the diagonal of any square?
S*v2
?r²
Opens down
(a-b)(a²+ab+b²)


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

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6. How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
?r²
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
x² -2xy + y²


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

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8. Define the mode of a set of numbers.
1/3pir^2*h
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
x² + 2xy + y²


9. If something is certain to happen - how is the probability of this event expressed mathematically?
Part of a circle connecting two points on the circle.
1/1
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.
4pir^2


10. What is the factored version of (x+y)(x-y) ?
Sqr( x2 -x1) + (y2- y1)
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
x²-y²
Pir^2h


11. Volume of sphere
?d OR 2?r
1.7
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4/3pir^3


12. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
b±[vb²-4ac]/2a
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°/360 times (2 pi r) - where x is the degrees in the angle
2 pi r


13. What'S the most important thing to remember about charts you'll see on the GRE?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
1.7
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


14. Circumference of cirlce using diameter
(pi)r^2
1
Pi*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.


15. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
2(pi)r(r+h)
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. 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.
1.7


16. Volume of prism
Bh
(a-b)(a+b)
1/3pir^2*h
(x1+x2)/2 - (y1+y2)/2


17. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
2(pi)r(r+h)
1. Given event A: A + notA = 1.
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.


18. Rough est. of v2 =
1.4
Number of desired outcomes/number of total outcomes
1/2bh
1/1


19. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Sum of terms/number of terms
1/2 h (b1 + b2)
2lw+2lh+2wh
1. Given event A: A + notA = 1.


20. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
2(pi)r
Sum of terms/number of terms
The total # of possible outcomes.


21. Perimeter of a square
2 pi r
A²-b²
Opens down
4s (where s = length of a side)


22. What is the distance formula?
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.
y2-y1/x2-x1
Percentage Change = Difference/Original * 100
Sqr( x2 -x1) + (y2- y1)


23. Surface Area of Sphere
Pi*r^2
2(pi)r
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'.
4pir^2


24. How do you find the nth term of an arithmetic sequence?
A segment connecting the center of a circle to any point on the circle
S*v2
T1 + (n-1)d
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


25. What is the area of a circle?
(a-b)²
Sum of the lengths of the 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.
(pi)r^2


26. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
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
2l+2w
N x M
Not necessarily. This is a trick question - because x could be either positive or negative.


27. What is the area of a sector?
(n degrees/360) * (pi)r^2
Groups - teams - or committees.
A²-b²
T1 + (n-1)d


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

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29. perimeter of square
4s
A+b
Middle term
(a-b)(a²+ab+b²)


30. What is the average?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2(pi)r
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.
Sum of terms/number of terms


31. How do you find the sum of a geometric sequence?
(n/2) * (t1+tn)
Pi*d
T1 * r^(n-1)/(r-1)
Sqr( x2 -x1) + (y2- y1)


32. x^-a =
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.
(x+y)(x-y)
1/x^a
A+b


33. How do you calculate a diagonal inside a 3-dimensional rectangular box?
2Length + 2width [or (length + width) x 2]
Lwh
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Pi*d


34. What is the circumference of a circle?
Pi*d
x°/360 times (2 pi r) - where x is the degrees in the angle
(x-y)²
2(pi)r


35. In a parabola - if the first term is positive - the parabola ________.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Opens up
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.
Less


36. What is the point-slope form?
4pir^2
2lw+2lh+2wh
x² -2xy + y²
(y-y1)=m(x-x1)


37. 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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38. What is the unfactored version of (x+y)² ?
1/2bh
T1 * r^(n-1)/(r-1)
Groups - teams - or committees.
x² + 2xy + y²


39. x^a * x^b = x^__
x² -2xy + y²
A+b
2lw+2lh+2wh
The distance across the circle through the center of the circle.The diameter is twice the radius.


40. Area of Parallelogram
Bh
(n/2) * (t1+tn)
Last term
y2-y1/x2-x1


41. Point-Slope form
4s (where s = length of a side)
x² + 2xy + y²
y-y1=m(x-x1)
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.


42. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
(pi)r^2
The four big angles are equal and the four small angles are equal
2(lw+wh+lh)


43. Circumference Formula
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
C =?d
The distance across the circle through the center of the circle.The diameter is twice the radius.
1. Given event A: A + notA = 1.


44. Perimeter of rectangle
Bh
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.
Sum of terms/number of terms
2l+2w


45. a³+b³
N x M
1/3pir^2*h
(a+b)(a²-ab+b²)
Probability A + Probability B


46. Area of Square
y = kx
Total distance/total time
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
S^2


47. 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
A+b
The equation must be set equal to zero. If during the test one appears that'S not - before you can solve it you must first manipulate it so it is equal to zero.
C =?d


48. 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.
1.4
(a+b)(a-b)
The distance from one point on the circle to another point on the circle.


49. What is the equation of a line?

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50. (a+b)(a-b)=
Middle term
S*v2
A²-b²
Total distance/total time