Live practice

If (a+ib)(c+id)(e+if)(g+ih)=A+iB, prove that the product of the four squared moduli equals A²+B².

Prove the four sum-to-product identities: \(\cos x+\cos y=2\cos\frac{x+y}{2}\cos\frac{x-y}{2}\), \(\cos x-\cos y=-2\sin\frac{x+y}{2}\sin\frac{x-y}{2}\), \(\sin x+\sin y=2\sin\frac{x+y}{2}\cos\frac{x-y}{2}\), and \(\sin x-\sin y=2\cos\frac{x+y}{2}\sin\frac{x-y}{2}\).

Find the domain of \(f(x)=\dfrac{x^2+2x+1}{x^2-8x+12}\).

Choose a suitable method to separate a mixture of calcium sulfate and camphor.

Predict the products of electrolysis in each of the following: (i) An aqueous solution of AgNO3 with silver electrodes (ii) An aqueous solution AgNO3 with platinum electrodes (iii) A dilute solution of H2SO4 with platinum electrodes (iv) An aqueous solution of CuCl2 with platinum electrodes.

The equilibrium constant for the following reaction is 1.6 ×105 at 1024K H2(g) + Br2(g) 2HBr(g) Find the equilibrium pressure of all gases if 10.0 bar of HBr is introduced into a sealed container at 1024K.

Explain orbital formation of the C=C bond in ethene and C≡C bond in ethyne.

Use the periodic table to give: (a) an element with five electrons in its outer subshell(b) one tending to lose two electrons(c) one tending to gain two electrons(d) a group containing metals, a non-metal, a liquid and a gas at room temperature.

State the number of electrons in

Convert to SI base units: (i) 28.7 pm(ii) 15.15 pm(iii) 25365 mg.