Correct Answer: B. 6\(\frac{11}{15}\)

Explanation

10\(\frac{2}{5} - 6 \frac{2}{3} + 3\)

\(\frac{52}{5} - \frac{20}{3} + \frac{3}{1}\)

= \(\frac{156 - 100 + 45}{15}\)

\(\frac{156 + 45 - 100}{15}\)

= \(\frac{201 - 100}{15}\)

= \(\frac{101}{15}\)

= 6\(\frac{11}{15}\)

Correct Answer: A. 2y - x -5 = 0

Explanation

We are given the equation \(x^{2} + y^{2} - 4x - 2y = 0\)

\(y = x^{2} + y^{2} - 4x - 2y \)

Using the method of implicit differentiation,

\(\frac{\mathrm d y}{\mathrm d x} = 2x + 2y\frac{\mathrm d y}{\mathrm d x} - 4 - 2\frac{\mathrm d y}{\mathrm d x}\)

For the tangent, \(\frac{\mathrm d y}{\mathrm d x} = 0\),

\(\therefore 2x + 2y\frac{\mathrm d y}{\mathrm d x} - 4 - 2\frac{\mathrm d y}{\mathrm d x} = 0\)

\((2y - 2)\frac{\mathrm d y}{\mathrm d x} = 4 - 2x \implies \frac{\mathrm d y}{\mathrm d x} = \frac{4 - 2x}{2y - 2}\)

At (1, 3), \(\frac{\mathrm d y}{\mathrm d x} = \frac{4 - 2(1)}{2(3) - 2} = \frac{2}{4} = \frac{1}{2}\)

Equation: \(\frac{y - 3}{x - 1} = \frac{1}{2} \implies 2y - 6 = x - 1\)

= \(2y - x - 6 + 1 = 2y - x - 5 = 0\)

Correct Answer: B. 30√3m

Correct Answer: D. zero

Explanation

\(\begin{array}{c|c} x & 2 & 3 & 5 & 9 \\ \hline 2 & 4 & 6 & 10 & 18 \\ \hline 4 & 8 & 12 & 20 & 36 \\ \hline 6 & 12 & 18 & 30 & 54 \\ \hline 8 & 16 & 24 & 40 & 72 \end{array}\)

Note: A {horizontal}

B {vertical}

Pr (Odd Product) = \(\frac{0}{16}\)

= 0

Correct Answer: A. \(\frac{3}{2}\)

Explanation

2 log x (3\(\frac{3}{8}\)) = 6(divide both sides by 2)

\(\frac{2 log_x(3 \frac{3}{8})}{2} = \frac{6}{2}\)

\(\log_x \frac{27}{8} = 3\)

\(\frac{27}{8} = x^3\)

\(x^3 = \frac{27}{8}\)

x = \(\sqrt{\frac{27}{8}}\)

= (\(\frac{27}{8}\))^{\(\frac{1}{3}\)}

= \(\frac{(3^3)^{\frac{1}{3}}}{(2^3)^{\frac{1}{3}}}\)

= \(\frac{3}{2}\)

Correct Answer: A. 4

Explanation

\(\sqrt{2}(\sqrt{6} + 2\sqrt{2}) - 2\sqrt{3}\)

\(\sqrt{12}\) + 2 x 2 - 2\(\sqrt{3}\)

2 \(\sqrt{3}\) - 2 \(\sqrt{3}\) + 4

= 4

Correct Answer: B. y - 4 = 0

Correct Answer: A. 41.2%

Explanation

Error =12.75 - 7.50 = 5.25

Error % = \(\frac{5.25}{12.75}\) x 100% = 41.2%

Explanation

(a)

(b)(i) PS = 6.0cm

(ii) Perpendicular disstance between RS and PQ i.e. RK = 5.9cm

(iii) QRSP is a trapezium.

Explanation

(a) \(y = ax^{2} - bx - 12\)

When a = 1, b = 2 and y = 3.

\(3 = x^{2} - 2x - 12\)

\(x^{2} - 2x - 12 - 3 = 0 \implies x^{2} - 2x - 15 = 0\)

\(x^{2} - 5x + 3x - 15 = 0\)

\((x - 5)(x + 3) = 0\)

\(\text{x = 5 or -3}\)

(b) \(\sqrt{x^{2} + 1} = \frac{5}{4}\)

Squaring both sides,

\(x^{2} + 1 = \frac{25}{16}\)

\(x^{2} = \frac{25}{16} - 1 = \frac{9}{16}\)

\(x = \sqrt{\frac{9}{16}} = \pm \frac{3}{4}\)

The positive value of x = \(\frac{3}{4}\).