Study Mathematics notes on Partial Variation for JSS 3. Useful for revision, homework, and exam preparation in Zimbabwe.
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This is the Mathematics notes from First Term 2022. It is a free notes for revision. Time allowed: 30 minutes.
JUNIOR SECONDARY SCHOOL, BAKO
FIRST TERM. 2022-2023 ACADEMIC SESSION
LESSON NOTE
DATE:22nd November, 2022.
SUBJECT: Mathematics.
CLASS: J S 3.
DURATION: 30 Minutes.
TOPIC: Variation continues.
SUB TOPIC: Partial variation.
PARTIAL VARIATION
Note that partial variation involves two(2) equation.
EXAMPLE1.
$x$ is partly constant and partly varies as $y$. When $y=2$ and $x=30$, and when $\mathrm{y}=6, \mathrm{x}=50$.
Find the relationship between $x$ and $y$.
SOLUTION
\[
\begin{array}{l}
x=k+c y(k \text { and } c \text { are constant })
30=k+2 c
K+2 c=30
\end{array}
\]
Also:
\[
\begin{array}{l}
50=k+6 c
k+6 c=50
\end{array}
\]
Then:
\[
\begin{array}{l}
k+2 c=30-\cdots-\cdots-\cdots-\cdots-\cdots-\cdots-\cdots-\cdots-\cdots-\cdots
k+6 c=50---------------------2
\end{array}
\]
Equation( 1) - equation ( 2 )
\[
\begin{aligned}
-4 c | =-20
c | =5
\end{aligned}
\]
Put $\mathrm{c}=5$ in equation 1
\[
\begin{aligned}
k+2 c | =30
k+2(5) | =30
k | =30-10
k | =20
\end{aligned}
\]
Recall:
\[
\begin{array}{l}
x=k+c y
x=20+5 y
\end{array}
\]