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 the 'Third side' rule for triangles?
1.7
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.


2. For a bell curve - what three terms might be used to describe the number in the middle?
Pi*d
2(lw+wh+lh)
The average - mean - median - or mode.
4s (where s = length of a side)


3. What is the equation of a line?

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4. Lines reflected over the x or y axis have ____ slopes.
Probability A + Probability B
A segment connecting the center of a circle to any point on the circle
2Length + 2width [or (length + width) x 2]
Negative


5. Volume of prism
Bh
4pir^2
2(pi)r
S² - where s = length of a side


6. How do you find the sum of an arithmetic sequence?
(n/2) * (t1+tn)
Equal
2pir^2 + 2pir*h
y = kx


7. Perimeter of rectangle
T1 + (n-1)d
2l+2w
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
1/1


8. Area of Circles
Sum of terms/number of terms
The four big angles are equal and the four small angles are equal
A=?r2
The distance across the circle through the center of the circle.The diameter is twice the radius.


9. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
y = kx
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


10. 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).
y-y1=m(x-x1)
Opens down
Probability A + Probability B


11. a²-2ab+b²
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.
Lw
(a-b)²
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.


12. What is the volume of a solid rectangle?
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.
Lwh
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.
Part of a circle connecting two points on the circle.


13. What is the volume of a cylinder?
(pi)r^2(h)
?d OR 2?r
1.7
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.


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

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

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16. Central Angle
2(pi)r
An ange whose vertex is the center of the circle
(y-y1)=m(x-x1)
(n degrees/360) * 2(pi)r


17. Volume of Cone
(x+y)²
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'.
1/3pir^2*h
x² + 2xy + y²


18. Diameter
Equal
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.
Probability A * Probability B


19. Surface Area of rectangular prism
N x M
2lw+2lh+2wh
(a-b)²
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.


20. What is the 'distributive law'?
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.
Probability A * Probability B
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A=?r2


21. What is directly proportional?
x²-y²
(y-y1)=m(x-x1)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
y = kx


22. What is the circumference of a circle?
Percentage Change = Difference/Original * 100
(a+b)(a-b)
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.
2(pi)r


23. a²-b²
The four big angles are equal and the four small angles are equal
(a-b)(a²+ab+b²)
(a-b)(a+b)
Pi*r^2


24. Rough est. of v2 =
Total distance/total time
1.4
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.


25. Does order matter for a permutation? How about for a combination?
1
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Order does matter for a permutation - but does not matter for a combination.
(a+b)(a²-ab+b²)


26. What are the side ratios for a 30:60:90 triangle?
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.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


27. Area of Parallelogram
4pir^2
Bh
T1 * r^(n-1)/(r-1)
N x M


28. In a coordinate system - identify the quadrants and describe their location.
y = kx
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Order does matter for a permutation - but does not matter for a combination.
(x-y)²


29. How do you calculate the percentage of change?
x°/360 times (?r²) - where x is the degrees in the angle
Lwh
Percentage Change = Difference/Original * 100
S^2


30. How do you solve a permutation?
x°/360 times (2 pi r) - 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
Middle term
A²-b²


31. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
y = k/x
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.
4s
S^2


32. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
x² -2xy + y²
4s (where s = length of a side)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


33. Volume of pyramid
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The distance from one point on the circle to another point on the circle.
1/3Bh


34. What is the formula for the diagonal of any square?
S*v2
N x M
b±[vb²-4ac]/2a
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


35. In a coordinate system - what is the origin?
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.
(a-b)(a²+ab+b²)
(0 -0)
b±[vb²-4ac]/2a


36. What is the unfactored version of (x-y)² ?
x² -2xy + y²
Sum of terms/number of terms
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.
(a+b)(a-b)


37. Area of Rectangle
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.
Sum of terms/number of terms
x²-y²


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

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39. Circumference of cirlce using diameter
4s
Pi*d
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
½(b1 +b2) x h [or (b1 +b2) x h÷2]


40. Define the mode of a set of numbers.
Part of a circle connecting two points on the circle.
2(pi)r(r+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.
(n degrees/360) * 2(pi)r


41. In intersecting lines - opposite angles are _____.
Arrangements - orders - schedules - or lists.
Equal
x°/360 times (?r²) - where x is the degrees in the angle
2pi*r


42. What do combination problems usually ask for?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Groups - teams - or committees.
S² - where s = length of a side
Sqr( x2 -x1) + (y2- y1)


43. Rough est. of v1 =
Pi*d
?d OR 2?r
2(pi)r(r+h)
1


44. Perimeter of polygon
Sum of the lengths of the sides
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1/3pir^2*h
Probability A * Probability B


45. Arc
A segment connecting the center of a circle to any point on the circle
Part of a circle connecting two points on the circle.
2l+2w
(pi)r^2


46. Volume of Cylinder
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.
Pir^2h
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
1/3pir^2*h


47. What is the area of a triangle?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/2bh
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.
T1 * r^(n-1)/(r-1)


48. Define the 'Third side' rule for triangles

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49. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
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.
x²-y²
Between 0 and 1.


50. Define the range of a set of numbers.
x°/360 times (?r²) - where x is the degrees in the angle
(n degrees/360) * (pi)r^2
A²-b²
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.