2013 - JAMB Mathematics Past Questions and Answers - page 4

\((1 \leq x \leq 25)\) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}

Number N of x divisible by both 2 and 3 is 4.

n(\(\varepsilon\)) = 25

= \(\frac{N}{n(\varepsilon)}\)

= \(\frac{4}{25}\)

n(apples) = 9
n(bananas) = 9
n(oranges) = 9

n(\(\varepsilon\)) = 24

Hence Prob(not apple, nor orange) = Prob(banana) = \(\frac{8}{24}\) = \(\frac{1}{3}\)

The graph crosses the x-axis at x = -1 and x = 2

Thus, x + 1 = 0 and x - 2 = 0

x² - 2x + x - 2 = 0

x² - x - 2 = 0

giving y = x² - x - 2

In the diagram above, < CDE = < CED = 15^o

(base < s of isos. \(\bigtriangleup\))

< ECD = 180^o - (15 + 15)^o

= 180^o - 30^o = 150^o

But x + 110^o = 150^o

(Sum of opp. interior < s of a\(\bigtriangleup\) = opp. exterior < )

x = 150^o - 110^o = 40^o

80 + 160 + 200 + 80 = 128 + 72 = 720minutes

5x^o + (16x - 24)^o + 5x^o + (4x + 12)^o + (6x + 12)^o = 360^o

360x^o - 24 + 12 + 12 = 360^o

36x^o = 360^o

x^o = \(\frac{360^0}{36}\)

= 10^o

Thus, the angle of sector representing Mathematics is 5 x 10^o = 50^o. Hence the number of students who offer mathematics is

\(\frac{55^o}{36} \times 80 \approx 11\)