2011 - JAMB Mathematics Past Questions and Answers - page 5

ELATION
Since there are 7 letters. The first letter can be arranged in 7 ways, , the second letter in 6 ways, the third letter in 5 ways, the 4th letter in four ways, the 3rd letter in three ways, the 2nd letter in 2 ways and the last in one way.

therefore, 7 x 6 x 5 x 4 x 3 x 2 x 1 = 7! ways

The first person will sit down and the remaining will join.

i.e. (n - 1)!

= (5 - 1)! = 4!

= 24 ways

Prime numbers = (43,47,53,59)

N = (43, 44, 45,..., 60)

The universal set contains 18 numbers.

The prime numbers between 43 and 60 are 4

Probability of picking a prime number = \(\frac{4}{18}\)

= \(\frac{2}{9}\)

\(\frac {\sin\theta}{\cos\theta}\)

\(\frac{\cos \theta {\frac{d(\sin \theta)}{d \theta}} - \sin \theta {\frac{d(\cos \theta)}{d \theta}}}{\cos^2 \theta}\)

\(\frac{\cos \theta. \cos \theta - \sin \theta (-\sin \theta)}{cos^2\theta}\)

\(\frac{cos^2\theta + \sin^2 \theta}{cos^2\theta}\)

Recall that sin² \(\theta\) + cos² \(\theta\) = 1

\(\frac{1}{\cos^2\theta}\) = sec² \(\theta\)

\(\frac{70}{360} \times 36 = \frac{70}{10}\)

= 7