Soalan 3(a):
Hitung nilai yang berikut.
$$ \text { (a) Diberi } w=\frac{x+y}{1+x} \text {, hitung nilai } $$
(i) w, jika x = 2 dan y = − 8
(ii) x, jika w = 20 dan y = 5
(iii) y, jika w = 5 dan x = 6
Penyelesaian:
(a)(i)
$$ \begin{aligned} &\text { Nilai } w \text { jika } x=2 \text { dan } y=-8\\ &\begin{aligned} w & =\frac{x+y}{1+x} \\ w & =\frac{2+(-8)}{1+2} \\ w & =\frac{-6}{3} \\ w & =-2 \end{aligned} \end{aligned} $$
(a)(ii)
$$ \begin{aligned} &\text { Nilai } x \text { jika } w=20 \text { dan } y=5\\ &\begin{aligned} w & =\frac{x+y}{1+x} \\ 20 & =\frac{x+5}{1+x} \\ 20(1+x) & =x+5 \\ 20+20 x & =x+5 \\ 20 x-x & =5-20 \\ 19 x & =-15 \\ x & =-\frac{15}{19} \end{aligned} \end{aligned} $$
(a)(iii)
$$ \begin{aligned} &\text { Nilai } y \text { jika } w=5 \text { dan } x=6\\ &\begin{aligned} w & =\frac{x+y}{1+x} \\ 5 & =\frac{6+y}{1+6} \end{aligned}\\ &\begin{aligned} (5)(7) & =6+y \\ 35 & =6+y \\ 29 & =y \\ y & =29 \end{aligned} \end{aligned} $$
Hitung nilai yang berikut.
$$ \text { (a) Diberi } w=\frac{x+y}{1+x} \text {, hitung nilai } $$
(i) w, jika x = 2 dan y = − 8
(ii) x, jika w = 20 dan y = 5
(iii) y, jika w = 5 dan x = 6
Penyelesaian:
(a)(i)
$$ \begin{aligned} &\text { Nilai } w \text { jika } x=2 \text { dan } y=-8\\ &\begin{aligned} w & =\frac{x+y}{1+x} \\ w & =\frac{2+(-8)}{1+2} \\ w & =\frac{-6}{3} \\ w & =-2 \end{aligned} \end{aligned} $$
(a)(ii)
$$ \begin{aligned} &\text { Nilai } x \text { jika } w=20 \text { dan } y=5\\ &\begin{aligned} w & =\frac{x+y}{1+x} \\ 20 & =\frac{x+5}{1+x} \\ 20(1+x) & =x+5 \\ 20+20 x & =x+5 \\ 20 x-x & =5-20 \\ 19 x & =-15 \\ x & =-\frac{15}{19} \end{aligned} \end{aligned} $$
(a)(iii)
$$ \begin{aligned} &\text { Nilai } y \text { jika } w=5 \text { dan } x=6\\ &\begin{aligned} w & =\frac{x+y}{1+x} \\ 5 & =\frac{6+y}{1+6} \end{aligned}\\ &\begin{aligned} (5)(7) & =6+y \\ 35 & =6+y \\ 29 & =y \\ y & =29 \end{aligned} \end{aligned} $$
Soalan 3(b):
Hitung nilai yang berikut.
$$ \text { Diberi } 6 b=\sqrt{\frac{c-d^2}{9}} \text {, hitung nilai } $$
(i) b, jika c = 20 dan d = 2
(ii) c, jika b = 1/9 dan d = 2
(iii) d, jika b = 1/2 dan c = 90
Penyelesaian:
(b)(i)
$$ \begin{aligned} &\text { Nilai } b \text { jika } c=20 \text { dan } d=2\\ &\begin{aligned} 6 b & =\sqrt{\frac{c-d^2}{9}} \\ 6 b & =\sqrt{\frac{20-2^2}{9}} \\ 6 b & =\sqrt{\frac{16}{9}} \\ 6 b & =\frac{4}{3} \\ b & =\frac{4}{18} \\ b & =\frac{2}{9} \end{aligned} \end{aligned} $$
(b)(ii)
$$ \begin{aligned} &\text { Nilai } c \text { jika } b=\frac{1}{9} \text { dan } d=2\\ &\begin{aligned} 6 b & =\sqrt{\frac{c-d^2}{9}} \\ 6\left(\frac{1}{9}\right) & =\sqrt{\frac{c-2^2}{9}} \\ \frac{2}{3} & =\sqrt{\frac{c-4}{9}} \\ \frac{4}{9} & =\frac{c-4}{9} \longleftarrow \text { Kedua-dua belah persamaan dikuasaduakan } \\ 4(9) & =9(c-4) \\ 36 & =9 c-36 \\ 72 & =9 c \\ 9 c & =72 \\ c & =8 \end{aligned} \end{aligned} $$
(b)(iii)
$$ \begin{aligned} &\text { Nilai } d \text { jika } b=\frac{1}{2} \text { dan } c=90\\ &\begin{aligned} 6 b & =\sqrt{\frac{c-d^2}{9}} \\ 6\left(\frac{1}{2}\right) & =\sqrt{\frac{90-d^2}{9}} \\ 3 & =\sqrt{\frac{90-d^2}{9}} \\ 9 & =\frac{90-d^2}{9} \longleftarrow \text { Kedua-dua belah persamaan dikuasaduakan } \\ 81 & =90-d^2 \\ d^2 & =9 \\ d & =\sqrt{9} \\ d & =3 \end{aligned} \end{aligned} $$
Hitung nilai yang berikut.
$$ \text { Diberi } 6 b=\sqrt{\frac{c-d^2}{9}} \text {, hitung nilai } $$
(i) b, jika c = 20 dan d = 2
(ii) c, jika b = 1/9 dan d = 2
(iii) d, jika b = 1/2 dan c = 90
Penyelesaian:
(b)(i)
$$ \begin{aligned} &\text { Nilai } b \text { jika } c=20 \text { dan } d=2\\ &\begin{aligned} 6 b & =\sqrt{\frac{c-d^2}{9}} \\ 6 b & =\sqrt{\frac{20-2^2}{9}} \\ 6 b & =\sqrt{\frac{16}{9}} \\ 6 b & =\frac{4}{3} \\ b & =\frac{4}{18} \\ b & =\frac{2}{9} \end{aligned} \end{aligned} $$
(b)(ii)
$$ \begin{aligned} &\text { Nilai } c \text { jika } b=\frac{1}{9} \text { dan } d=2\\ &\begin{aligned} 6 b & =\sqrt{\frac{c-d^2}{9}} \\ 6\left(\frac{1}{9}\right) & =\sqrt{\frac{c-2^2}{9}} \\ \frac{2}{3} & =\sqrt{\frac{c-4}{9}} \\ \frac{4}{9} & =\frac{c-4}{9} \longleftarrow \text { Kedua-dua belah persamaan dikuasaduakan } \\ 4(9) & =9(c-4) \\ 36 & =9 c-36 \\ 72 & =9 c \\ 9 c & =72 \\ c & =8 \end{aligned} \end{aligned} $$
(b)(iii)
$$ \begin{aligned} &\text { Nilai } d \text { jika } b=\frac{1}{2} \text { dan } c=90\\ &\begin{aligned} 6 b & =\sqrt{\frac{c-d^2}{9}} \\ 6\left(\frac{1}{2}\right) & =\sqrt{\frac{90-d^2}{9}} \\ 3 & =\sqrt{\frac{90-d^2}{9}} \\ 9 & =\frac{90-d^2}{9} \longleftarrow \text { Kedua-dua belah persamaan dikuasaduakan } \\ 81 & =90-d^2 \\ d^2 & =9 \\ d & =\sqrt{9} \\ d & =3 \end{aligned} \end{aligned} $$
Soalan 3(c):
Hitung nilai yang berikut.
$$ \text { Diberi }-2 p=\frac{(q+1)}{(r+q)} \text {, hitung nilai } $$
(i) p, jika q = 3 dan r = 3q
(ii) q, jika p = 3 dan r = 2q
(iii) r, jika p = − 1/3 dan q = 2p
Penyelesaian:
(c)(i)
$$ \begin{aligned} &\text { Nilai } p \text { jika } q=3 \text { dan } r=3 q\\ &\begin{aligned} -2 p & =\frac{(q+1)}{(r+q)} \\ -2 p & =\frac{(3+1)}{(3 q+q)} \\ -2 p & =\frac{4}{4 q} \\ -2 p & =\frac{4}{4(3)} \\ -2 p & =\frac{1}{3} \\ p & =-\frac{1}{6} \end{aligned} \end{aligned} $$
(c)(ii)
$$ \begin{aligned} &\text { Nilai } q \text { jika } p=3 \text { dan } r=2 q\\ &\begin{aligned} -2 p & =\frac{(q+1)}{(r+q)} \\ -2(3) & =\frac{(q+1)}{(2 q+q)} \\ -6 & =\frac{q+1}{3 q} \\ -6(3 q) & =q+1 \\ -18 q & =q+1 \\ -19 q & =1 \\ 19 q & =-1 \\ q & =-\frac{1}{19} \end{aligned} \end{aligned} $$
(c)(iii)
$$ \begin{aligned} &\text { Nilai } r \text { jika } p=-\frac{1}{3} \text { dan } q=2 p\\ &\begin{aligned} -2 p & =\frac{(q+1)}{(r+q)} \\ -2 p & =\frac{(2 p+1)}{(r+2 p)} \\ -2\left(-\frac{1}{3}\right) & =\frac{2\left(-\frac{1}{3}\right)+1}{r+2\left(-\frac{1}{3}\right)} \\ \frac{2}{3} & =\frac{-\frac{2}{3}+1}{r-\frac{2}{3}} \end{aligned} \end{aligned} $$
$$ \begin{aligned} \frac{2}{3}\left(r-\frac{2}{3}\right) & =\frac{1}{3} \\ \frac{2}{3} r-\frac{4}{9} & =\frac{1}{3} \\ \frac{2}{3} r & =\frac{1}{3}+\frac{4}{9} \\ \frac{2}{3} r & =\frac{7}{9} \\ r & =\frac{7}{9} \times \frac{3}{2} \\ r & =\frac{7}{6} \\ & =1 \frac{1}{6} \end{aligned} $$
Hitung nilai yang berikut.
$$ \text { Diberi }-2 p=\frac{(q+1)}{(r+q)} \text {, hitung nilai } $$
(i) p, jika q = 3 dan r = 3q
(ii) q, jika p = 3 dan r = 2q
(iii) r, jika p = − 1/3 dan q = 2p
Penyelesaian:
(c)(i)
$$ \begin{aligned} &\text { Nilai } p \text { jika } q=3 \text { dan } r=3 q\\ &\begin{aligned} -2 p & =\frac{(q+1)}{(r+q)} \\ -2 p & =\frac{(3+1)}{(3 q+q)} \\ -2 p & =\frac{4}{4 q} \\ -2 p & =\frac{4}{4(3)} \\ -2 p & =\frac{1}{3} \\ p & =-\frac{1}{6} \end{aligned} \end{aligned} $$
(c)(ii)
$$ \begin{aligned} &\text { Nilai } q \text { jika } p=3 \text { dan } r=2 q\\ &\begin{aligned} -2 p & =\frac{(q+1)}{(r+q)} \\ -2(3) & =\frac{(q+1)}{(2 q+q)} \\ -6 & =\frac{q+1}{3 q} \\ -6(3 q) & =q+1 \\ -18 q & =q+1 \\ -19 q & =1 \\ 19 q & =-1 \\ q & =-\frac{1}{19} \end{aligned} \end{aligned} $$
(c)(iii)
$$ \begin{aligned} &\text { Nilai } r \text { jika } p=-\frac{1}{3} \text { dan } q=2 p\\ &\begin{aligned} -2 p & =\frac{(q+1)}{(r+q)} \\ -2 p & =\frac{(2 p+1)}{(r+2 p)} \\ -2\left(-\frac{1}{3}\right) & =\frac{2\left(-\frac{1}{3}\right)+1}{r+2\left(-\frac{1}{3}\right)} \\ \frac{2}{3} & =\frac{-\frac{2}{3}+1}{r-\frac{2}{3}} \end{aligned} \end{aligned} $$
$$ \begin{aligned} \frac{2}{3}\left(r-\frac{2}{3}\right) & =\frac{1}{3} \\ \frac{2}{3} r-\frac{4}{9} & =\frac{1}{3} \\ \frac{2}{3} r & =\frac{1}{3}+\frac{4}{9} \\ \frac{2}{3} r & =\frac{7}{9} \\ r & =\frac{7}{9} \times \frac{3}{2} \\ r & =\frac{7}{6} \\ & =1 \frac{1}{6} \end{aligned} $$
Soalan 3(d):
Hitung nilai yang berikut.
$$ \text { Diberi } 4 s^2=\left(\frac{3 t-4 u}{5}\right)^2 \text {, hitung nilai } $$
(i) s, jika t = s − 1 dan u = 2s
(ii) t , jika s = −5u dan u = 3
(iii) u, jika s = 1/3 t dan t = 2 − u
Penyelesaian:
(d)(i)
$$ \begin{aligned} &\text { Nilai } s \text { jika } t=s-1 \text { dan } u=2 s\\ &\begin{aligned} 4 s^2 & =\left(\frac{3 t-4 u}{5}\right)^2 \\ 2 s & =\frac{3 t-4 u}{5} \\ 2 s & =\frac{3(s-1)-4(2 s)}{5} \\ 10 s & =3 s-3-8 s \\ 10 s-3 s+8 s & =-3 \\ 15 s & =-3 \\ s & =-\frac{1}{5} \end{aligned} \end{aligned} $$
(d)(ii)
$$ \begin{aligned} &\text { Nilai } t \text { jika } s=-5 u \text { dan } u=3\\ &\begin{aligned} 4 s^2 & =\left(\frac{3 t-4 u}{5}\right)^2 \\ 2 s & =\frac{3 t-4 u}{5} \\ 2(-5 u) & =\frac{3 t-4(3)}{5} \\ -10(3) & =\frac{3 t-12}{5} \\ -30(5) & =3 t-12 \\ 3 t & =-150+12 \\ t & =-\frac{138}{3} \\ t & =-46 \end{aligned} \end{aligned} $$
(d)(iii)
$$ \begin{aligned} \text { Nilai } u, \text { jika } s & =\frac{1}{3} t \text { dan } t=2-u \\ 4 s^2 & =\left(\frac{3 t-4 u}{5}\right)^2 \\ 2 s & =\frac{3 t-4 u}{5} \\ 2\left(\frac{t}{3}\right) & =\frac{3(2-u)-4 u}{5} \\ \frac{2(2-u)}{3} & =\frac{6-3 u-4 u}{5} \end{aligned} $$
$$ \begin{aligned} \frac{4-2 u}{3} & =\frac{6-7 u}{5} \\ 5(4-2 u) & =3(6-7 u) \\ 20-10 u & =18-21 u \\ 11 u & =-2 \\ u & =-\frac{2}{11} \end{aligned} $$
Hitung nilai yang berikut.
$$ \text { Diberi } 4 s^2=\left(\frac{3 t-4 u}{5}\right)^2 \text {, hitung nilai } $$
(i) s, jika t = s − 1 dan u = 2s
(ii) t , jika s = −5u dan u = 3
(iii) u, jika s = 1/3 t dan t = 2 − u
Penyelesaian:
(d)(i)
$$ \begin{aligned} &\text { Nilai } s \text { jika } t=s-1 \text { dan } u=2 s\\ &\begin{aligned} 4 s^2 & =\left(\frac{3 t-4 u}{5}\right)^2 \\ 2 s & =\frac{3 t-4 u}{5} \\ 2 s & =\frac{3(s-1)-4(2 s)}{5} \\ 10 s & =3 s-3-8 s \\ 10 s-3 s+8 s & =-3 \\ 15 s & =-3 \\ s & =-\frac{1}{5} \end{aligned} \end{aligned} $$
(d)(ii)
$$ \begin{aligned} &\text { Nilai } t \text { jika } s=-5 u \text { dan } u=3\\ &\begin{aligned} 4 s^2 & =\left(\frac{3 t-4 u}{5}\right)^2 \\ 2 s & =\frac{3 t-4 u}{5} \\ 2(-5 u) & =\frac{3 t-4(3)}{5} \\ -10(3) & =\frac{3 t-12}{5} \\ -30(5) & =3 t-12 \\ 3 t & =-150+12 \\ t & =-\frac{138}{3} \\ t & =-46 \end{aligned} \end{aligned} $$
(d)(iii)
$$ \begin{aligned} \text { Nilai } u, \text { jika } s & =\frac{1}{3} t \text { dan } t=2-u \\ 4 s^2 & =\left(\frac{3 t-4 u}{5}\right)^2 \\ 2 s & =\frac{3 t-4 u}{5} \\ 2\left(\frac{t}{3}\right) & =\frac{3(2-u)-4 u}{5} \\ \frac{2(2-u)}{3} & =\frac{6-3 u-4 u}{5} \end{aligned} $$
$$ \begin{aligned} \frac{4-2 u}{3} & =\frac{6-7 u}{5} \\ 5(4-2 u) & =3(6-7 u) \\ 20-10 u & =18-21 u \\ 11 u & =-2 \\ u & =-\frac{2}{11} \end{aligned} $$