View again

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Description
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
Share
Tags

## Equations

Transcript
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.
Related Search
Similar documents

View more...