Answers

Question 1

(a) \( R = \frac{V}{I} \) (b) \( r = \frac{C}{2\pi} \) (c) \( x = \frac{y - 2}{3} \)
(d) \( u = v - at \) (e) \( b = \frac{x + 7}{2a} \) (f) \( T = \frac{PV}{nR} \)
(g) \( t = \frac{v - u}{a} \) (h) \( x = \frac{5 - y}{3} \) (i) \( p = \frac{9 - t}{2q} \)
(j) \( n = \frac{2S}{a + d} \) (k) \( sin\theta = \frac{n\lambda}{2d} \) (l) \( s = \frac{v^2 - u^2}{2a} \)

Question 2

(a) \( b = \frac{2A}{h} \) (b) \( L = \frac{p}{2}-B \) (c) \( h = \frac{3V}{\pi r^2} \)
(d) \( t = \frac{d}{s} \) (e) \( u = \frac{2S - at^2}{2t} \) (f) \( h = \frac{A}{2\pi r} - r \)
(g) \( a = \frac{3d}{2k}-\frac{c}{2} \) (h) \( d = \frac{2A}{a + b} \) (i) \( a = \frac{2A}{d} - b \)
(j) \( x = \frac{a - b}{y} \) (k) \( a = \frac{2S}{n}- d \) (l) \( cosA = \frac{b^2 + c^2 - a^2}{2bc} \)

Question 3

(a) \( r = \sqrt{\frac{A}{\pi}} \) (b) \( c = \sqrt{\frac{E}{m}} \) (c) \( r = \sqrt{\frac{3V}{\pi h}} \)
(d) \( u = \sqrt{v^2 - 2as} \) (e) \( b = \sqrt{h^2 - a^2} \) (f) \( L = g\left( \frac{T}{2\pi}\right) ^2 \)
(g) \( v = \sqrt{\frac{2E}{m}} \) (h) \( a = \frac{2(s - ut)}{t^2} \) (i) \( g = L\left(\frac{2\pi}{T}\right)^2 \)
(j) \( r = \sqrt[3]{\frac{3V}{4\pi}} \) (k) \( x = \sqrt{r^2 - y^2} \) (l) \( x = \sqrt{2 - \left(\frac{y}{5}\right)^2} \)

Question 4

(a) \( x = \frac{c}{b - a} \) (b) \( x = \frac{y}{p - q} \) (c) \( x = \frac{a + c}{3 - b} \)
(d) \( x = \frac{2a}{a - b} \) (e) \( x = \frac{2p + 5q}{q - p} \) (f) \( x = \frac{2b -a}{3} \)
(g) \( x = \frac{b +cy}{d + y - 3} \) (h) \( x =\frac{2}{1-bc} \) (i) \( x = \frac{15 - 2a}{a - b - 5} \)
(j) \( x = \frac{bd - 4a}{5 - a - b} \) (k) \( x = \frac {2 + cd - ab}{a - c} \) (l) \( x = \frac{4 - 2a}{a - 2 - bc} \)

Question 5

(a) \( h = \frac{V}{\pi r^2} \) (b) \( y = \frac{2x - a}{x + 1} \) (c) \( m = \frac{E}{c^2} \)
(d) \( a = \frac{v - u}{t} \) (e) \( I = \frac{V}{R} \) (f) \( d = \frac{n\lambda}{2sin\theta} \)
(g) \( t = \frac{v - u}{a} \) (h) \( x = \frac{10d - ad^2}{ad + 1 - 2d} \) (i) \( v = \frac{fu}{u - f} \)
(j) \( x = \frac{a - y^2}{2} \) (k) \( h = \sqrt{\frac{W}{I}} \) (l) \( x = \frac{bc - 5a - 2}{a - b -1} \)