Correct Answer: C. \(\frac{5?6}{12}\)

Explanation

(\(\frac{3√6}{√5} + \frac{√54}{3√5}\))\(^{-1}\)

= \(\frac{√5(3√5)}{3√6 + 3√6}\)

= \(\frac{3*5}{6√6} = \frac{5}{2√6}\)

= \(\frac{5*2√6}{2√6+2√6} = \frac{10√6}{4*6}\)

= \(\frac{5√6}{12}\)

Correct Answer: A. \(-\left(\frac{12}{39}-\frac{10\sqrt{3}}{39}\right)\)

Correct Answer: (b) 99

Correct Answer: A. 44

Explanation

Number of students that scored at least 3 marks = 9 + 1 + 12 + 7 + 5 + 10 = 44

Correct Answer: B. 46

Explanation

\(T_{n} = a + (n-1)d\)

\( d = T_{2} - T_{1} = T_{3} - T_{2} = -1.5 - (-4) = 2.5\)

\(T_{21} = -4 + (21 - 1) \times 2.5 = -4 + (20\times 2.5) \)

= \(-4 + 50 = 46\)

Correct Answer: B. -2, 1

Correct Answer: B. 4

Correct Answer: A. 1\(\frac{1}{2}\)

Explanation

If x : y : z = 3 : 3 : 4, evaluate \(\frac{9x + 3y}{6x - 2y}\)

\(\frac{x}{y}\) = \(\frac{2}{3}\) and \(\frac{y}{z}\) = \(\frac{3}{4}\)

Thus; x = \(\frac{2}{3}T_1\) and z = \(\frac{3}{5}T_1\)

y = \(\frac{3}{7}T_2\) and z = \(\frac{4}{7}T_2\)

Using y = y

\(\frac{3}{5}T_1\) = \(\frac{3}{7}T_2\); \(\frac{T_1}{T_2}\) = \(\frac{3}{7}\) x \(\frac{5}{3}\)

\(\frac{T_1}{T_2}\) = \(\frac{15}{21}\)

\(T_1\) = 15 and \(T_2\) = 21

Therefore;

x = \(\frac{2}{5}\) x 15 = 6

y = \(\frac{3}{5}\) x 15 = 9

y = \(\frac{3}{7}\) x 21 = 9 (again)

z = \(\frac{4}{7}\) x 21 = 12

Hence;

\(\frac{9x + 3y}{6z - 2y}\) = \(\frac{9(6) + 3(9)}{6(12) - 2(9)}\)

\(\frac{54 + 27}{72 - 18}\) = \(\frac{81}{54}\) = \(\frac{3}{2}\)

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

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

Explanation

(a) First, change the given linear equation to the gradient- intercept form:

\(2x + y = 6 \implies y = 6 - 2x\)

Thus, \(m_{1} = -2, c = 6\). Thus, for a line to be parallel, the gradient \(m_{2} = -2\) (condition for parallelism).

Using \(y - y_{1} = m(x - x_{1})\), we have

\(y - (-3) = -2(x - 2)\)

\(y + 3 = - 2x + 4\)

\(2x + y = 4 - 3 = 1\)

Thus, the line passing through (2, -3) parallel to 2x + y = 6 is 2x + y = 1.

(b) (i)

(ii) (a) \(2 \Delta (5 \Delta 7) = 2 \Delta 7 = 7\)

(b) \(2 \Delta n = 5 \Delta 7\)

\(2 \Delta n = 7\)

By comparison, n = 7.