1.4.1 Ubahan, SPM Praktis (Kertas 1)

1.4.1 Ubahan, SPM Praktis (Soalan Pendek)

Soalan 1:

Diberi bahawa y berubah secara langsung dengan kuasa tiga x dan y = 192 apabila x = 4.
Hitungkan nilai x apabila y = –24.

Penyelesaian:

y α x³

y = kx³

192 = k (4)³

k = 3

y = 3x³

Apabila y = – 24

–24 = 3x³

x = –2

Soalan 2:

Diberi bahawa y berubah secara langsung dengan kuasa dua xdan y = 9 apabila x = 2.
Hitungkan nilai x apabila y = 16.

Penyelesaian:

y α x²

y = kx²

9 = k (2)

\begin{array}{l} k = \frac{9}{4} \\ y = \frac{9}{4} x^{2} \\ Apabila y = 16 \\ 16 = \frac{9}{4} x^{2} \\ x^{2} = \frac{64}{9} \\ x = \frac{8}{3} \end{array}

Soalan 3:

Diberi bahawa y berubah secara songsang w dan x dan y = 45 apabila w = 2 dan x = 1/6.
Hitungkan nilai x apabila y = 15 dan w = ⅓

Penyelesaian:

\begin{array}{l} y α \frac{1}{w x} \\ y = \frac{k}{w x} \\ 45 = \frac{k}{(2) (\frac{1}{6})} \\ k = 45 \times \frac{1}{3} = 15 \\ y = \frac{15}{w x} \end{array}

\begin{array}{l} apabila y = 15, w = \frac{1}{3} \\ 15 = \frac{15}{(\frac{1}{3}) x} \\ \frac{x}{3} = 1 \\ x = 3 \end{array}

Soalan 4:

Diberi bahawa

p α \frac{1}{q \sqrt{r}}

dan p = 3 apabila q = 2 dan r = 16, cari nilai bagi p apabila q = 3
dan r = 4.

Penyelesaian:

\begin{array}{l} p α \frac{1}{q \sqrt{r}} \\ p = \frac{k}{q \sqrt{r}} \\ 3 = \frac{k}{(2) \sqrt{16}} \\ k = 24 \\ p = \frac{24}{q \sqrt{r}} \end{array}

\begin{array}{l} apabila q = 3, r = 4 \\ p = \frac{24}{3 \sqrt{4}} \\ p = \frac{24}{6} = 4 \end{array}

Soalan 5:

Diberi bahawa

P α \frac{1}{\sqrt{Q}} dan Q = 4 M + 1.

Jika P = 5 apabila M = 2, ungkapkan P dalam sebutan Q.

Penyelesaian:

\begin{array}{l} Diberi P α \frac{1}{\sqrt{Q}} \\ Maka, P = \frac{k}{\sqrt{Q}} \\ P = \frac{k}{\sqrt{4 M + 1}} \\ 5 = \frac{k}{\sqrt{4 (2) + 1}} \\ 5 = \frac{k}{\sqrt{9}} \\ k = 15 \\ P = \frac{15}{\sqrt{Q}} \end{array}