Quick Maths

If \(M = \frac{2ab}{a + b}\), make \(b\) the subject.

Solve for \(x\) so \(\frac{1}{x^{2}-4x+3}\) is undefined.

A box contains 4 red, 3 blue and 5 green balls. A ball is drawn, replaced, and a second drawn. What is the probability that the two balls are of different colours?

A mother is six years older than twice her daughter’s age. In six years she will be three times her daughter’s age. How old is the daughter now?

If \(\dfrac{2x+y}{3}=x-y\), find \(x:y\).

Find the range of 120, 135, 128, 140, 132, 126.

The bearing of \(P\) from \(Q\) is \(045^{\circ}\). What is the bearing of \(Q\) from \(P\)?

Preamble: \(M\!:\) “Ali practises.” \(N\!:\) “Ali wins the match.” Given \(M\Rightarrow N\), select the valid deduction.