Add Math 13.Linear Law

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LINEAR LAW SPM questions involved this chapter are tested in : 1. Paper 1 (3 or 4 marks) 2. Paper 2 (Part B, 10 marks) A. General Form of Linear Relations ã Any non-linear relations can be reduced to linear relations in the form of: Y = mX + c. Horizontal axis Only represented by variable/s and multiply with the constant that is represented by gradient. Vertical axis Only represented by variable/s Vertical axis intercept Only formed by constant . Y = mX+c Gradient constant Only formed by consta
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  LINEAR LAW SPM questions involved this chapter are tested in :1.Paper 1 (3 or 4 marks)2.Paper 2 (Part B, 10 marks) A. General Form of Linear Relations ã Any non-linear relations can be reduced to linear relations in the form of: Y  = mX  + c. ã The method of reducing to linear relation depends on the srcinal relation (non-linear) given. ã It is vital to determine what form of variables and constants in a relation. ã When the variables and constant are determined, the process of reducing non-linear to linear will form a general linear equation, Y  = mX  + c. ã The value of the  x -variable and the  y -variable must follow the corresponding horizontal axisand the vertical axis of the linear form of the equation. B. Method of conversion The method used depend on the non-linear relation that is given. In general, three (3) methods apply:i.use of log;ii.operation of algebra i.e. multiplication or division; andiii. squaring of equation i. Application of Log  The use of log is needed in reducing relation if there is form of algebraic or instance of indices . For example; SPM2000.P1.Q16  y = ab  x − 1 where  x and  y are variables and a and b are constants.    Horizontal axis Only represented by variable/sand multiply with the constantthat is represented by gradient. Vertical axis Only represented byvariable/s Gradient constant  Only formed by constantand rely on or multiply tothe variable of horizontalaxis. Vertical axis intercept  Only formed by constant .   Y  = m X  + c  log y = log    ab  x − 1 log y = log a + log b  x − 1 log y = log a + (x-1) log blog y =   log b(x-1) + log ay = m x + c Therefore  y is the vertical axis,  x-1 is the horizontal axis, log b is the gradient and log a is theintercept. ii. Operation of Algebra The use of algebraic operation usually involves non-linear relation in a quadratic function form. For example; SPM2001.Q1.Q16 S = ut  + at  2 S  and t  are variables and u and a are constants.Divide t  on both sides of the equation: S t  = ut t   at  2 t  S t  = u  at S t  = at   u    y = mx + c Hence,  S t  is the vertical axis  , a is the gradient  , t  is the horizontal axis and u is the intercept. iii. Squaring of Equation The use of square is used when a relation has a (square) root form i.e.   . . For example;SPM1995.P1.Q15 T  = 2 π      M k  where T  and  M  are variables and k  is a constant.Squaring both sides of the equation result in: T  2 =  2    M k   2 T  2 = 4  2  M k   T  2 = 4  2 k  M     y = mx + cT  2 is the vertical axis,4  2 k  is the gradient,  M  is the horizontal axis and the gradient is zero.
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