JAMB Mathematics Past Questions & Answers - Page 334

\(y = (2x + 2)^{3}\)

\(\frac{\mathrm d y}{\mathrm d x} = 3(2x + 2)^{3 - 1} . 2\)

= \(6(2x + 2)^{2}\)

y = x sin x

Where u = x and v = sin x

Then \(\frac{\delta u}{\delta x}\) = 1 and \(\frac{\delta v}{\delta x}\) = cos x

By the chain rule, \(\frac{\delta y}{\delta x} = v\frac{\delta u}{\delta x} + u\frac{\delta v}{\delta x}\)

= (sin x)1 + x cos x

= sin x + x cos x

Let A = \(\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}\)

Then |A| = \(\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}\) = 20 - 18 = 2

Hence A-1 = \(\frac{1}{|A|}\begin{pmatrix} 4 & -3 \\ -6 & 5 \end{pmatrix}\)

= \(\frac{1}{2}\begin{pmatrix} 4 & -3 \\ -6 & 5 \end{pmatrix}\)

= \(\begin{pmatrix} 4 \times 1/2 & -3 \times 1/2 \\ -6 \times 1/2 & 5 \times 1/2 \end{pmatrix}\)

= \(\begin{pmatrix} 2 & -\frac{3}{2} \\ -3 & \frac{5}{2} \end{pmatrix}\)

2P + Q = 2\(\begin{pmatrix} 5 & 3 \\ 2 & 1 \end{pmatrix}\) + \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\)

= \(\begin{pmatrix} 10 & 6 \\ 4 & 2 \end{pmatrix}\) + \(\begin{pmatrix} 4 & 2 \\ 3 & 5 \end{pmatrix}\)

= \(\begin{pmatrix} 14 & 8 \\ 7 & 7 \end{pmatrix}\)

x * y = x + 2y (given)

3 * 4 = 3 + 2(4) = 11

Hence, 2 * (3 * 4) = 2 * 11

= 2 + 2(11)

= 2 + 22

= 24