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1 | Formula Name | Formula | English | |||||||||||||||||||||||

2 | Volume of sphere | V(Sphere) = 4/3 pi r^3 | Volume of the sphere is equal to four thirds pi r cubed where r is the radius of the sphere. | |||||||||||||||||||||||

3 | Perimeter of rectangle | P(Rect) = 2h + 2w | Perimeter of a rectangle is equal to the sum of twice the height and twice the width. | |||||||||||||||||||||||

4 | Regular polygon interior angle | alpha= 180 - 360/n | Interior angle of a regular polygon is equal to 180 minus the exterior angle. The exterior angle is equal to 360 divided by the number of polygon sides. | |||||||||||||||||||||||

5 | Volume of cube | V(cube) = s^3 | Volume of a cube is equal to s cubed where s is the edge of the cube. | |||||||||||||||||||||||

6 | Sum of an Arithmetic Series | Sigma = n(F+L)/2 | The sum of an arithmetic series is equal to the number of terms in the series times the average of the series. The average of the series is equal to half the sum of the first and last terms of the series. | |||||||||||||||||||||||

7 | Volume of a cone | V(cone) = 1/3 pi r^2 h | The volume of the cone is equal to 1/3 the area of the base times the height. The area of the base for a cone is equal to pi times the radius squared. | |||||||||||||||||||||||

8 | Circumference of a circle | C = 2 pi r | The circumference of a circle is equal to two pi r where r is the radius. | |||||||||||||||||||||||

9 | Surface area of a cube | SA(Cube) = 6 s^2 | The surface of a cube is equal to six times the area of one side. The area of a single side is s squared. | |||||||||||||||||||||||

10 | Average a set | xbar = sigma/n | The average of a set is equal to the sum of the terms divided by the number of terms. | |||||||||||||||||||||||

11 | Surface area of cylinder | SA(Cyl) = 2pi r^2 + 2pi r h | The surface area of a cylinder is equal to the sum of areas of the top and bottom circular ends plus the rectangular area of the side. The area of each circular end is equal to 2 pi r squared. The area of the rectangular side is equal to the circumference times the height. The circumference is equal to the 2 pi r. | |||||||||||||||||||||||

12 | Average an aritmetic series | Xbar = (F+L)/2 | The average of an arithmetic series is equal to half the sum of the first term and last term | |||||||||||||||||||||||

13 | Range of a series | R= L-F | The range of a series is equal to the Last term minus the First term. | |||||||||||||||||||||||

14 | Sum of numbers given the mean and number of terms. | Sigma = xbar * n | The sum of set of numbers is equal to the average of the set multiplied by the number of terms. | |||||||||||||||||||||||

15 | General volume of a regular pyramid | V(Prya) = B L/3 | The volume of a pyramid is equal to one third the area of the Base times the pyramid's height. | |||||||||||||||||||||||

16 | Volume of Regular Prism (Vprism, B,L) | Vprism = BL | The volume of a prism is equal to the area of the Base times the length of the prism. | |||||||||||||||||||||||

17 | Volume of cylinder (Vcyl,r,h) | Vcyl = pi r^2 h | The volume of a cylinder is equal to the area of the Base times the height of the cylinder. The area of the Base is equal to pi r squared. | |||||||||||||||||||||||

18 | SA of Rect. prism (SArect,h,w,l) | SArect = 2(hw + hl + lw) | The surface area of a rectangular prism is equal to twice the sum of the areas of the front, top and side faces. The area of the front face is equal to height times width. The area of the top face is equal to length times width and the area of the side face is equal to height time length. | |||||||||||||||||||||||

19 | Volume of a cone or pyramid | Vpyra = B L/3 | The volume of a cone or pyramid is equal to one third the area the Base times the height of the cone or pyramid. | |||||||||||||||||||||||

20 | Perimeter of a triangle | Ptri = a + b + c | The perimeter of a triangle is equal to sum of the three side lengths. | |||||||||||||||||||||||

21 | Area of equilateral triangle | Aequtri = e^2 sqrt(3) / 4 | The area of an equilateral triangle is equal to one fourth the edge squared times the square root of 3. | |||||||||||||||||||||||

22 | Surface area of a sphere | SAsphere = 4 pi r ^2 | The surface area of a sphere is equal to four times the area of a circle with the same radius. The area of the circle is pi r squared. | |||||||||||||||||||||||

23 | Volume of rectangular prism | Vrecpri = h w l | The volume of a rectangular prism is equal to the area of the base times the length. The area of the base is equal to the height times width. | |||||||||||||||||||||||

24 | Area of a rhombus | Arhom = d1d2/2 | The area of a rhombus is equal to half the product of the diagonals. | |||||||||||||||||||||||

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26 | 30-60-90 triangle given the long leg length | |||||||||||||||||||||||||

27 | The short leg of a 30-60-90 triangle is the long leg length divided by 3 times the square root of 3. | |||||||||||||||||||||||||

28 | The hypotenuse of a 30-60-90 triangle is twice the short leg length times. The length is two thirds the long leg length times the square root of 3. | |||||||||||||||||||||||||

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30 | 30-60-90 triangle given the short leg length | |||||||||||||||||||||||||

31 | The long leg of a 30-60-90 triangle is the short leg length multiplied by the square root of 3. | |||||||||||||||||||||||||

32 | The hypotenuse of a 30-60-90 triangle is twice the short leg length times. The length is two thirds the long leg length times the square root of 3. | |||||||||||||||||||||||||

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34 | 45-45-90 triangle give the hypotenuse length. | |||||||||||||||||||||||||

35 | Each leg of the 45-45-90 triangle is equal to half the length of the hypotenuse times the square root of two. | |||||||||||||||||||||||||

36 | Permutations | nPr=n!/(n-r)! | The number of permutations of n items when you remove r items is n! divided by the quantity (n-r)! The (n-r)! term trims the tail factorial off of n!. Permutations are order sensitive. | |||||||||||||||||||||||

37 | Combinatorial | nCr=n!/((n-r)!r!) | The number of combinations of n items when you choose r items is n! divided by the product of (n-r)! and r!. It is identical to nPr/r!. You're dividing nPr by r! because order does not matter when you're using nPr. | |||||||||||||||||||||||

38 | Probability of event a AND event b. | Pa&Pb = Pa Pb | The probability of event a and event b happening is the product of the probability of event a times the probability of event b. | |||||||||||||||||||||||

39 | Probability of event a or event b. | Pa | Pb = Pa + Pb -PaPb. | The probability of event a or event b happening is the sum of probability of event a and the probability of event b less the probability of event a and event b. You're subtracting PaPb from the sum to eliminate double counting doubles. | |||||||||||||||||||||||

40 | Probability of event a or event b but not both. | Pa|| Pb = Pa + Pb -2PaPb | The probability of event a or event b happening but not both is the sum of probability of event a and the probability of event b less twice the probability of event a and event b. You're subtracting 2 PaPb from the sum to eliminate the chance of doubles altogether. | |||||||||||||||||||||||

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