Mathematics 2016 Jamb Examination

First, list the elements of set Q (factors of 18): \( Q = \{1, 2, 3, 6, 9, 18\} \). Next, list set T (prime numbers between 2 and 18, inclusive of 2): \( T = \{2, 3, 5, 7, 11, 13, 17\} \). The intersection \( Q \cap T \) consists of elements common to both sets: \[ Q \cap T = \{2, 3\} \]

< TVS = 180^o - (80 + 20) = 180 - 100 = 80^o

The mean is calculated by finding the sum of all values and dividing by the count (n = 10): \[ \text{Sum} = 10 + 8 + 5 + 11 + 12 + 9 + 6 + 3 + 15 + 23 = 102 \] \[ \text{Mean} = \dfrac{\sum x}{n} = \dfrac{102}{10} = 10.2 \]

PRO = 180° - (110 + 50)°
= 180 - 160 = 20°

An Ogive, also known as a cumulative frequency polygon, is a graph that represents the cumulative frequencies of a dataset. It is constructed by plotting cumulative frequencies against the upper class boundaries of the data intervals.

To rationalize the expression, multiply the numerator and denominator by the conjugate of the denominator, which is \( \sqrt{6} - \sqrt{4} \). Since \( \sqrt{4} = 2 \), we simplify it to: \[ \dfrac{\sqrt{6} - 2}{\sqrt{6} + 2} \times \dfrac{\sqrt{6} - 2}{\sqrt{6} - 2} = \dfrac{(\sqrt{6})^2 - 2(2)\sqrt{6} + 2^2}{(\sqrt{6})^2 - 2^2} \] \[ = \dfrac{6 - 4\sqrt{6} + 4}{6 - 4} = \dfrac{10 - 4\sqrt{6}}{2} = 5 - 2\sqrt{6} \]

3 + 2 + 5 + 5 + + 5 + 10 + 4 + 3 + 1 + 2 = 40

To calculate the mean:
\[ \begin{aligned}
\text{Mean} &= \frac{(3 \times 0) + (1 \times 2) + (5 \times 2) + (5 \times 3) + (5 \times 4)}{40} \\
&\quad + \frac{(10 \times 5) + (4 \times 6) + (3 \times 7) + (1 \times 8) + (2 \times 9)}{40} \\
&= \frac{168}{40} \\
&= 4.2
\end{aligned}\]

\(\theta\) = 180^o -(90 + 60) \(\theta\)
= 180^o - 150^o = 30^o
Fraction of shaded position
= \(\dfrac{30}{360}\) + \(\dfrac{30}{360}\)
= \(\dfrac{1}{12}\) + \(\dfrac{1}{12}\) = \(\dfrac{1}{6}\)

The graph represents a quadratic function (parabola) that opens upwards and intersects the x-axis at \( x = -1 \) and \( x = 4 \). The shaded region is the part of the curve below the x-axis, which corresponds to the inequality where the function is less than or equal to zero. \[ \text{The region is } -1 \le x \le 4 \]