Mathematics 2008 Jamb Examination

Order the values:
0, 0, 1, 1, 2, 4, 4, 4, 4
The middle (5th) term is:\[ 2 \]

Find maximum and minimum expressions.
Minimum term: \(x-3\).
Maximum term: \(3x+2\).
Range:\[ (3x+2) - (x-3) = 3x + 2 - x + 3 = 2x + 5 \]

Mean deviation is the average of the absolute deviations from the mean.
The mean of the numbers is:\[ \dfrac{2 + 4 + 5 + 9}{4} = 5 \]Find the absolute deviations:
\( |2 - 5| = 3 \), \( |4 - 5| = 1 \), \( |5 - 5| = 0 \), \( |9 - 5| = 4 \)
Sum of deviations:\[ 3 + 1 + 0 + 4 = 8 \]Mean deviation:\[ \dfrac{8}{4} = 2 \]The mean deviation shows how far each value is from the mean on average.

The word ACCEPTANCE has 10 letters in total.
Repeated letters:
A appears 2 times, C appears 2 times, and E appears 3 times.
The number of distinct permutations of a word with repeated letters is:\[ \dfrac{10!}{2! \cdot 2! \cdot 3!} \]This accounts for over-counting caused by identical letters appearing in multiple positions.

Since order does not matter, this is a combination problem.
Use the formula:\[ ^{10}C_6 = \dfrac{10!}{6!4!} \]Simplifying:\[ ^{10}C_6 = 210 \]This gives the number of possible groups of 6 subjects from 10 available subjects.

Count total letters in OBSTRUCTION: 11.
The letter T appears 2 times in the word.
Probability is therefore:\[ \dfrac{2}{11} \]This expresses the ratio of favourable outcomes (selecting T) to the total possible selections.

The total number of rolls is 150.
Sum all frequencies:\[ 12 + 18 + x + 30 + 2x + 45 = 150 \]Combine like terms:\[ 105 + 3x = 150 \]Solve for x:\[ 3x = 45 \Rightarrow x = 15 \]Frequency of rolling a 5 is \(2x = 30\).
Probability:\[ \dfrac{30}{150} = \dfrac{1}{5} \]This gives the likelihood of landing on 5 when rolling the die.

Angle at centre = 2 × angle at circumference\[ 2 \times s = 280^{\circ}\] \[ s = \dfrac{280^{\circ}}{2} = 140^{\circ}\] \[ \angle O = 360^{\circ} - 280^{\circ} = 80^{\circ}\] Sum of angles in a quadrilateral\[ 60^{\circ} + 80^{\circ} + 140^{\circ} + a = 360^{\circ}\] \[ 280^{\circ} + a = 360^{\circ}\] \[ a = 360^{\circ} - 280^{\circ} = 80^{\circ}\]