Page 211 - Jurnal Pendidikan Tingkatan Enam 2019 - Jilid 3
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JURNAL PENDIDIKAN TINGKATAN ENAM 2019 JILID 3
5.3.1 Method of Carrying Out the Study
The preliminary exercises done through observation, interview and pre-test were able to
show the need for intervention particularly to help students' mastery in solving first order
linear differential equation. In response, the researcher designed the "KIMCI CERIA"
Objective 1: Improve students’ ability to determine the correct method to solve the
Objective 1: Improve students’ ability to determine the correct method to solve the
technique as a tool to solve the problems identified and achieve the objectives set in the
first-order linear differential equations
first-order linear differential equations
study.
Students are often confused in determining which methods they should use in solving
Students are often confused in determining which methods they should use in solving
Objective 1: Improve students’ ability to determine the correct method to solve the
Objective 1: Improve students’ ability to determine the correct method to solve the
Objective 1: Improve students’ ability to determine the correct method to solve the
Objective 1: Improve students’ ability to determine the correct method to solve the
problems involving differential equations. Figure 5.3 shows an example of a question on
problems involving differential equations. Figure 5.3 shows an example of a question on
Objective 1: Improve students’ ability to determine the correct method to solve the
first-order linear differential equations
first-order linear differential equations
first-order linear differential equations
first-order linear differential equations
equations.
equations.
first-order linear differential equations
Students are often confused in determining which methods they should use in solving
Students are often confused in determining which methods they should use in solving
Students are often confused in determining which methods they should use in solving
Students are often confused in determining which methods they should use in solving
Students are often confused in determining which methods they should use in solving
problems involving differential equations. Figure 5.3 shows an example of a question on
problems involving differential equations. Figure 5.3 shows an example of a question on
problems involving differential equations. Figure 5.3 shows an example of a question on
problems involving differential equations. Figure 5.3 shows an example of a question on
Find the general solution of cos ( ) = csc , expressing y in terms of x.
Find the general solution of cos ( ) = csc , expressing y in terms of x.
problems involving differential equations. Figure 5.3 shows an example of a question on
2 2
2 2
equations.
equations.
equations.
equations.
equations.
Figure 5.3 Sample differential equation question
Figure 5.3 Sample differential equation question
Find the general solution of cos ( ( ) = 2 2 2csc 2 2 2 , expressing y in terms of x.
) = csc , expressing y in terms of x.
Find the general solution of cos
( ) = csc , expressing y in terms of x.
Find the general solution of cos
Find the general solution of cos ( ) = csc , expressing y in terms of x.
2
2
Two steps can be used to guide students to choose between the variable isolation method
Two steps can be used to guide students to choose between the variable isolation method
Figure 5.3 Sample differential equation question
Figure 5.3 Sample differential equation question
Figure 5.3 Sample differential equation question
or factor extraction method.
or factor extraction method.
Figure 5.3 Sample differential equation question
Figure 5.3 Sample differential equation question
Two steps can be used to guide students to choose between the variable isolation method
Two steps can be used to guide students to choose between the variable isolation method
Two steps can be used to guide students to choose between the variable isolation method
Two steps can be used to guide students to choose between the variable isolation method
Two steps can be used to guide students to choose between the variable isolation method
Step 1: Make the subject to the left of the equation
or factor extraction method. t to the left of the equation
Step 1: Make the subjec
or factor extraction method.
or factor extraction method.
or factor extraction method.
or factor extraction method.
The first step they need to do is to make the subject to the left of the equation and move
The first step they need to do is to make the subject to the left of the equation and move
Step 1: Make the subject to the left of the equation
Step 1: Make
the subject to the left of the equation
bles left to right including the variables y and x.
all the other variables left to right including the variables y and x.
all the other varia the subject to the left of the equation
Step 1: Make the subject to the left of the equation
Step 1: Make
Step 1: Make the subject to the left of the equation
The first step they need to do is to make the subject to the left of the equation and move
The first step they need to do is to make the subject to the left of the equation and move
the subject to the left of the equation and move
2 2
csc
The first step they need to do is to make
csc
The first step they need to do is to make the subject to the left of the equation and move
2 2
=
=
The first step they need to do is to make the subject to the left of the equation and move
cos
cos
all the other variables left to right including the variables y and x.
all the other variables left to right including the variables y and x.
all the other variables left to right including the variables y and x.
all the other variables left to right including the variables y and x.
all the other variables left to right including the variables y and x.
2 2
csc
csc 2
csc
2 2
2 2of the equation (between variables x and
Step 2: Factor the expressions to the right of the equation (between variables x and
Step 2: Factor the expressions to the right
=
=
=
csc cos
2
cos
y) y) = cos cos
Step 2: Factor the expressions to the right of the equation (between variables x and y)
Next, students are required to factor the expressions on the right of the equation, namely,
Next, students are required to factor the expressions on the right of the equation, namely,
Step 2: Factor the expressions to the right of the equation (between variables x and
Step 2: Factor the expressions to the right of the equation (between variables x and
Next, students are required to factor the expressions on the right of the equation, namely,
Step 2: Factor the expressions to the right of the equation (between variables x and
two factors that include only the x-variables, and the second factor that only include the y
two factors that include only the x-variables, and the second factor that only include the y--
Step 2: Factor the expressions to the right of the equation (between variables x and
y)
y)
two factors that include only the x-variables, and the second factor that only include the
y)
y) variables. If these differential equations can be factored into two factors involving different
variables. If these differential equations can be factored into two factors involving different
y-variables. If these differential equations can be factored into two factors involving different
Next, students are required to factor the expressions on the right of the equation, namely,
Next, students are required to factor the expressions on the right of the equation, namely,
Next, students are required to factor the expressions on the right of the equation, namely,
variables, then the method of separating the variables should be used.
variables, then the method of separating the variables should be used.
Next, students are required to factor the expressions on the right of the equation, namely,
variables, then the method of separating the variables should be used.
two factors that include only the x-variables, and the second factor that only include the y-
two factors that include only the x-variables, and the second factor that only include the y-
two factors that include only the x-variables, and the second factor that only include the y-
two factors that include only the x-variables, and the second factor that only include the y-
2 2
variables. If these differential equations can be factored into two factors involving different
csc
csc
variables. If these differential equations can be factored into two factors involving different
) )
2 2
variables. If these differential equations can be factored into two factors involving different
= ( ) ( ) (
= (
variables. If these differential equations can be factored into two factors involving different
cos
cos
variables, then the method of separating the variables should be used.
variables, then the method of separating the variables should be used.
variables, then the method of separating the variables should be used.
Since the differential expression above can be factored into two factors involving only x
Since the differential expression above can be factored into two
variables, then the method of separating the variables should be used. factors involving only x
Since the differential expression above can be factored into two factors involving only x
2 2
csc
csc 2
csc )
2 2
= ( ) ) csc
2 2 ) ( (
22
= (
variables in the first factor ( ) and only y variables in the second factor,
then the
), then the
csc
variables in the first factor ( ) and only y variables i ) ), then the
= (
csc ) (cos
2 22
variables in the first factor (x ) and only y variables in the second factor, (
cos n the second factor, (
2
= ( ) ( ) cos cos
cos
method of separating the variables can be used.
cos
Since the differential expression above can be factored into two factors involving only x
Since the differential expression above can be factored into two factors involving only x
method of separating the variables can be used.
method of separating the variables can be used.
Since the differential expression above can be factored into two factors involving only x
Since the differential expression above can be factored into two factors involving only x
2 2
csc
csc ), then the
2 2
2 2
csc
csc
variables in the first factor (
variables in the first factor ( ) and only y variables in the second factor, ( csc 2 ), then the
2 ) and only y variables in the second factor, (
), then the
) )
csc cos
2 2
variables in the first factor ( ) and only y variables in the second factor, (cos
2
= (
= ( ) ( ) (
2
cos
variables in the first factor ( ) and only y variables in the second factor, ( ), then the
cos
cos
method of separating the variables can be used.
method of separating the variables can be used. cos
method of separating the variables can be used.
method of separating the variables can be used.
cos
cos
2
csc ∫
∫ ∫ 2 2 = ∫ 2 22 2
=
csc
csc )
2 2
csc
csc
= ( )
210 Bahagian Pengurusan Sekolah Harian = ( 2 2 ) ( ( cos )
)
= (
csc ) (cos
2
= ( ) ( ) cos
2 2
cos
∫ sin 2 2 cos = ∫
∫ sin cos
cos cos = ∫
2 2
2
∫ ∫ cos = ∫
= ∫
2 2
cos ∫csc = ∫
csc
2
2
csc
∫ = ∫
2
csc
∫ sin cos = ∫
2 cos = ∫
2 2
2 2
∫ sin
∫ sin cos = ∫
2
∫ sin cos = ∫
2
2
