MATHEMATICS

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  Algebra is a branch of mathematics that substitutes letters for numbers. Important Formulas in Algebra Here is a list of Algebraic formulas  – a 2  – b 2  = (a – b)(a + b) (a + b) 2  = a 2  + 2ab + b 2 a 2  + b 2  = (a + b) 2  – 2ab (a – b) 2  = a 2  – 2ab + b 2 (a + b + c) 2  = a 2  + b 2  + c 2  + 2ab + 2bc + 2ca (a – b – c) 2  = a 2  + b 2  + c 2  – 2ab + 2bc – 2ca (a + b) 3  = a 3  + 3a 2 b + 3ab 2  + b 3  ; (a + b) 3  = a 3  + b 3  + 3ab(a + b) (a – b) 3  = a 3  – 3a 2 b + 3ab 2  – b 3  = a 3  – b 3  – 3ab(a – b) a 3  – b 3  = (a – b)(a 2  + ab + b 2 ) a 3  + b 3  = (a + b)(a 2  – ab + b 2 )

 

 

 

  PYTHAGORAS THEOREM P T  

 PARALLELOGRAM PARALLELOGR AM  

  Long division method for square roots short tricks  Long division method for square roots short tricks

 trinometry https://www.slideshare.net/ThangathilakaManju1/trignometrypptx   trigonometry

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  Quadrilateral Formulas There are two basic formulas for quadrilaterals, that are: Area  Perimeter Area of Quadrilateral The area of the quadrilateral is the total space occupied by the figure.  The area formula for the different quadrilaterals are given below: Area of a Parallelogram Base x Height Area of a Rectangle Length x Width Area of a Square Side x Side Area of a Rhombus (1/2) x Diagonal 1 x Diagonal 2  Area of a Kite 1/2 x Diagonal 1 x Diagonal 2 Perimeter of Quadrilateral Perimeter is the total distance covered by the boundary of a 2d shape. Since we know the quadrilateral has four sides, therefore, the perimeter of any quadrilateral will be equal to the sum of the length of all four sides. If ABCD is a quadrilateral then, the perimeter of ABCD is: Perimeter = AB + BC + CD + AD Quadrilateral Name Perimeter Square 4 x Side Rectangle 2(Length + Breadth) Parallelogram 2(Base + Side) Rhombus 4 x Side Kite 2 (a + b), a and b are adjacent pairs  Important F...

  Fibonacci Sequence The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it: the 2 is found by adding the two numbers before it (1+1), the 3 is found by adding the two numbers before it (1+2), the 5 is (2+3), and so on! Example: the next number in the sequence above is 21+34 =   55 It is that simple! Here is a longer list: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ... Makes A Spiral When we make squares with those widths, we get a nice spiral: Do you see how the squares fit neatly together? For example 5 and 8 make 13, 8 and 13 make 21, and so on. This spiral is found in nature! See:  Nature, The Golden Ratio, and Fibonacci The Rule The Fibonacci Sequence can be written as a "Rule" (see  Sequences and Series ). First, the terms are numbered from 0 onwards like this: n ...

  Circle   A circle is easy to make: Draw a curve that is "radius" away from a central point. And so: All points are the same distance from the center. You Can Draw It Yourself Put a pin in a board, put a loop of string around it, and insert a pencil into the loop. Keep the string stretched and draw the circle!   The  Radius  is the distance from the center outwards. The  Diameter  goes straight across the circle, through the center. The  Circumference  is the distance once around the circle. And here is the really cool thing: When we divide the circumference by the diameter we get 3.141592654... which is the number  π  ( Pi ) So when the diameter is 1, the circumference is 3.141592654...   We can say: Circumference =  π  × Diameter Example: You walk around a circle which has a diameter of 100m, how far have you walked? Distance walked = Circumference =  π  × 100m =  314m  (to the nearest m) Also n...