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 a triangle
T1 + (n-1)d
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2 pi r
½(base x height) [or (base x height)÷2]


2. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Total distance/total time


3. When you reverse FOIL - the term that needs to add out is the _____
A=?r2
(a+b)²
Pi*d
Middle term


4. Area of Triangle
The four big angles are equal and the four small angles are equal
1/2bh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(n-2)180


5. x^-a =
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/x^a
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.


6. What is the formula for the diagonal of any square?
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.
?r²
S*v2
Pi*d


7. What is the surface area of a cylinder?
1.7
The four big angles are equal and the four small angles are equal
2x2x2x5x5
2(pi)r(r+h)


8. What is the factored version of (x+y)(x-y) ?
N x M
4s (where s = length of a side)
(a-b)(a²+ab+b²)
x²-y²


9. In a parabola - if the first term is negative - the parabola ________.
The set of points which are all the same distance (the radius) from a certain point (the center).
Last term
Opens down
(a-b)²


10. How do you find the sum of an arithmetic sequence?
Between 0 and 1.
(n/2) * (t1+tn)
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


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

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12. a²+2ab+b²
(a+b)²
b±[vb²-4ac]/2a
(a-b)²
Pi*d


13. Area of Circles
T1 * r^(n-1)/(r-1)
Between 0 and 1.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A=?r2


14. How do you calculate the percentage of change?
?r²
Percentage Change = Difference/Original * 100
Groups - teams - or committees.
(n degrees/360) * (pi)r^2


15. What is the area of a solid rectangle?
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.
x²-y²
2(lw+wh+lh)
2(pi)r


16. Perimeter of rectangle
(pi)r^2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2l+2w
Opens up


17. What is a 'Right isosceles' triangle?
Sqr( x2 -x1) + (y2- y1)
Percentage Change = Difference/Original * 100
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.
Total distance/total time


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

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19. In a coordinate system - identify the quadrants and describe their location.
C =?d
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
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/3pir^2*h


20. In a coordinate system - what is the origin?
(0 -0)
Opens up
2(pi)r(r+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


21. a³+b³
y2-y1/x2-x1
4s (where s = length of a side)
The distance from one point on the circle to another point on the circle.
(a+b)(a²-ab+b²)


22. How do you solve a permutation?
S*v2
Lw
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
(a-b)(a²+ab+b²)


23. Area of Trapezoid
C =?d
1/2 h (b1 + b2)
Opens up
The distance across the circle through the center of the circle.The diameter is twice the radius.


24. Does order matter for a permutation? How about for a combination?
T1 * r^(n-1)
Sqr( x2 -x1) + (y2- y1)
Order does matter for a permutation - but does not matter for a combination.
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.


25. What are the side ratios 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.
1/x^a
?d OR 2?r
1. Given event A: A + notA = 1.


26. What is the side ratio for a 30:60:90 triangle?
1/x^a
Order does matter for a permutation - but does not matter for a combination.
The set of points which are all the same distance (the radius) from a certain point (the center).
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


27. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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=bh


28. What is the area of a cylinder?
Bh
2(lw+wh+lh)
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.
2(pi)r(r+h)


29. What is the equation of a line?

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30. How do you find the slope?
2pir^2 + 2pir*h
y2-y1/x2-x1
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(pi)r^2(h)


31. If something is possible but not certain - what is the numeric range of probability of it happening?
Opens down
C =?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.
Between 0 and 1.


32. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
Lw
(a+b)(a-b)
Total distance/total time


33. Define the 'Third side' rule for triangles

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

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35. Circumference of a circle
?d OR 2?r
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.
y = kx
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.


36. In a parabola - if the first term is positive - the parabola ________.
1/3pir^2*h
Number of desired outcomes/number of total outcomes
T1 + (n-1)d
Opens up


37. Define a factorial of a number - and how it is written.
1/2bh
Pi*r^2
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.
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.


38. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
The distance across the circle through the center of the circle.The diameter is twice the radius.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1/x^a


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

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40. What is the sum of the inside angles of an n-sided polygon?
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.
(n-2)180
(y-y1)=m(x-x1)
2pir^2 + 2pir*h


41. How do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(a-b)(a+b)
1/3pir^2*h
2Length + 2width [or (length + width) x 2]


42. a²-2ab+b²
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.
(a-b)²
Opens down
(x+y)(x-y)


43. Perimeter of polygon
Sum of the lengths of the sides
Sqr( x2 -x1) + (y2- y1)
2pir^2 + 2pir*h
Middle term


44. What is the volume of a cylinder?
S² - where s = length of a side
(n-2)180
A=bh
(pi)r^2(h)


45. When you reverse FOIL - the term that needs to multiply out is the _____
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
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.
x°/360 times (?r²) - where x is the degrees in the angle
Last term


46. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
T1 * r^(n-1)/(r-1)
N x M
1/3pir^2*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.


47. In intersecting lines - opposite angles are _____.
Equal
(n-2)180
(a-b)(a²+ab+b²)
(n/2) * (t1+tn)


48. What is the area of a sector?
(a+b)(a²-ab+b²)
(y2-y1)/(x2-x1)
4s
(n degrees/360) * (pi)r^2


49. Perimeter (circumference) of a circle
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.
2 pi r
S^2
x² + 2xy + y²


50. Circle
The set of points which are all the same distance (the radius) from a certain point (the center).
A=?r2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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'.