Math Formulas

Area of a: 
        square Area = side ²             (side x side)

        rectangle Area = l*b         (length * breadth)
        parallelogram Area = b*h        (breadth * height)
        triangle Area= 1/2 * bh           (breadth * height (perpendicular))
        trapezoid Area=1/2 * h(b1 + b2)          (b = length of base and top line of trapezoid )
        circle Area= πr ²

 Perimeter of a: (P=perimeter)
        square P = 4*side                 (4*side)
        rectangle P = 2(l + w)          (l=length, w= width)
        triangle P = side1 + side2 + side3    
        circumference of a circle C = 2πr OR C = πd;               π ≈ 3.14

Surface area and volume of a: (SA= surface area, V= volume)
        rectangular box         = l*b*h
        square box                =side*side*height
        rectangular prism SA = 2(lw + lh + wh)       (l= length, w= width, h= height)    
        rectangular prism   V = lwh
        right prism SA = ph + 2B                       (p = perimeter of base with area B)
        right prism V = Bh
        cylinder SA = 2πrh + 2πr ²                
        cylinder V =πr ² h 
        pyramid SA = 1/2 *  ps + B
        pyramid V = 1/2  *  Bh
        cone SA = πrs + πr 2
        cone V = 1/3 * πr ² h 
        sphere SA = 4πr ² 
        sphere V = 4/3 * πr ³
         Note:  (p = perimeter of base with area B; π ≈ 3.14)

         10cm * 10 cm * 10 cm = 1 liter or 1000cm ³  =  1 leter


Data
       Mean    =  mean is equal to the total of the values of a data set, divided by the number of                             elements in the data set
       Median   = median is the middle value in an odd number of ordered values of a data set,or
                   the mean of the two middle values in an even number of ordered values in a data set
       Mode =   the number which appears the most often in a number set

Algebra
     slope of a line m = (y2 − y1) /(x2 − x1)
     slope-intercept form of the equation of a line y = mx + b     (m= slope, b= y intercept)
     point-slope form of the equation of a line y – y1 = m(x – x1)
     standard form of a quadratic equation y = ax² + bx + c
     quadratic formula
            OR

           

   
OR


          2x²-3x-5 = 0

               a*c = 2*-5 = -10,

               Select two numbers whose product is -10 and sum is -3

               i.e, 2 & -5,      (2+(-5) = -3) therefore

               ( x+2) (x-5) = 0, x = -2 or 5 

     Pythagorean theorem:-      a² + b² = c ² 

     simple interest:-     I = Prt /100               (I = interest, P = principal, r = rate in %, t = time)
     Compound Interest:-


     distance between two points formula                                  

     total cost = (number of units) × (price per unit)


Distance, Speed, Time     

Percentage Change      

Conversion between km/hr & m/sec

      

Quadratic Equation Expansion

Sign Change when we take to other side of the equation
i) x+2 = 0
   x = -2      (+ becomes - when we take to other side)

ii) x-2 = 0
    x = 2     (- becomes + when we take to other side)

iii) x/2 = 6
     x= 6*2       (/ becomes * when we take to other side) (/ is divide & * is multiply)

iv) 2x = 6
     x = 6/2      (* becomes / when we take to other side)


Logarithm

b^y=x, changing this to logarithm log_b(x) = y

log₂(16) = 4  is 2⁴ = 16

log (1 + 2 + 3) = log 1 + log 2 + log 3

Powers

Geometry

Trigonometry Addition and Subtraction 

 




















Permutation and Combination
If the order doesn't matter then we have a combination, if the order do matter then we have a permutation
 permutation:

Combination

If the order doesn't matter then we have a combination, if the order do matter then we have a permutation
n = 10     (0,1,2,3,4,5,6,7,8,9)
r= 4
10! = 10x9x8x7x6x5x4x3x2x1
4! =4x3x2x1